Dr Jean-Marc Roelandt

Frédéric Lamarque

Dr Laurent Petite

Dr Emmanuel Doré

Dr Mr Phillipe Pouille

Dr Monika Leester-Schädel

Tobias Beutel

Ahmad Jawad

Sajid Zaidi

Shahid Umer Khan

Shazia Tanveer

Nabil Jouni

Neha Arora

Zeina El Rawashdeh

Pengfei Huyan

Balaji Ragavan

Jan Dittmer

Keywords: Permanent magnet array, Electromagnetic actuator, Positioning system, Electric coil design, Optical sensor, Microfabrication, Thin layer coating, Anisotropic etching Millimeter reduziert. Diese Miniatur Positioniersysteme sind kostengünstige Lösungen in vielen Mikro Anwendungen Verschiebung des beweglichen Teils zu messen, ein kontaktloser Langstrecken-Wegsensor entworfen. Die Gesamtabmessungen des Sensors wurden mit einem geometrischen Modell optimiert. Die Herstellung des Sensors wurde mittels beweglichen Teil des Positionierungssystems integriert werden konnte. Der Sensor erreicht eine Auflösung von 30, 8 nm in einem linearen Messbereich von 12.5 mm. Am Ende der Arbeit wurde eine neue Kreuz-Struktur konzipiert und hergestellt, gleichfalls mit Hilfe der Mikrostrukturierungstechnik. Hieraus ergibt sich die Perspektive den Langstrecken Wegsensor problemlos zu integrieren Permanentmagnet Array, Elektromagnetischer Antrieb, Positioniersystem, Elektrospulen, Direkter Antrieb, Optischer Sensor, Mikrotechnik, Anisotropes Ätzen von Silizium, Dünnschichtabscheidung, Trockenätzen von Silizium

The work presented deals with the realization of an integrated miniature positioning system. It combines the design and development of a positioning platform and a long range optical displacement sensor. From the perspective to be used either as a stand alone system or a subsystem to pre-existing macro scale positioning machines in macro/micro realm, the design of the positioning platform has been optimized to reach overall small foot print size for whole positioning system.

Résumé

Les systèmes modernes de positionnement sont grandement utilisés dans de nombreux domaines de l'ingénierie portant sur des produits issus de différentes technologies aux échelles macro, micro et nano. Ces systèmes sont les pierres angulaire de toutes tâches de manipulation à ces échelles. Actuellement, la tendance à la miniaturisation a entraîné de nombreuses communautés scientifiques à réaliser des versions miniaturisées des ces systèmes d'une taille allant jusqu'à quelques centaines de millimètres. Ces systèmes de positionnement miniature deviennent alors des solutions adaptéess à de nombreuses applications à l'échelle microscopique.

Cette thèse présente la conception et le développement d'un système de positionnement qui intègre un capteur de déplacement sans contact. L'originalité du système de positionnement présenté réside dans sa conception épurée avec la possibilité d'effectuer des déplacements micrométriques sur une étendue millimétrique avec une fonction de guidage intégrée. Le dispositif est constitué d'une partie mobile entraînée par quatre moteurs linéaires électromagnétiques. Chaque moteur est constitué d'un bobine fixe à deux phases et d'une barre d'aimants réalisée avec 14 aimants permanents disposés dans une configuration nord-sud. Afin que le mouvement s'effectue sans heurt la structure repose sur quatre points grâce à des billes de verre hémisphériques dans le but de minimiser l'effet d'adhérence. La conception globale du système de positionnement planaire a été optimisée pour tenir sur une surface 80 mm×80 mm. Le dispositif peut se déplacer sur une course de 10×10 mm 2 dans le plan xy avec une résolution submicrométrique et à une vitesse de 12 mm/s. De plus, le dispositif peut se déplacer en rotation (±11 • ) autour de l'axe z dans le plan xy.

En second lieu, afin de mesurer le déplacement effectué par la partie mobile et dans le but d'asservir le système de positionnement, un capteur optique, sans contact, de longue étendue de déplacement linéaire, a été conçu. Les dimensions globales et les performances du capteur ont été optimisées en utilisant un modèle géométrique. Le réseau a été microfabriqué en silicium dans un but de compacité, afin qu'il puisse être intégré dans la partie mobile du système de positionnement. Le capteur est capable de fournir une résolution de 30,8 nm sur une plage de mesure linéaire de 12.5 mm. Enfin, une structure mobile a été conçue et microfabriquée en silicium avec l'objectif d'arriver à une meilleure intégration du capteur longue étendue.

Mots-clés:

Introduction

The accelerated research and developments in the field of system miniaturization technology has played an important role over past sixty years after the invention of integrated circuits in 1950s. These developments have introduced innovative products in our society.

Personal computers, digital camera, and smart phones are few of the triumphs of these developments. The ever greater diversity, economy and power of integrated electronic components have provided an inspiration to develop miniaturized mechatronic systems in various engineering domains. The evolution of automobile industry is one of the prominent examples in this era. Currently, automobiles are equipped with numerous systems composed of sensors (pressure sensor, temperature sensor, light sensor, fuel sensor, etc.) and actuators (micro valves, control switches, micro motors, etc.) to control the status of an automobile via on-board computer to ensure the safety and comfort of the user.

Apart from this industrial sector, the success behind the increasing demand in mechatronic systems is related to facilitate positioning/manipulation tasks in micro applications such as cell manipulation in biomedicine, surface analysis in meteorology, etc. These applications, demand modern positioning systems that should be able to deliver displacement strokes with sub micrometer level accuracy, high precision and repeatability. Currently, the scale down versions of these modern positioning systems are often developed with embedded functionalities such as multiple-DOF, integrated sensors, etc., by taking into account the current miniaturization trend. Numerous solutions have been introduced over time to economize these systems with compact dimensions. The work presented in this thesis is also based on the development of a compact miniature positioning system for micro applications.

The main objectives of the work presented in this manuscript include:

• Design and development of a miniaturized planar actuation platform that is able to deliver millimeter level strokes with sub micrometer level resolution

• Design and development of a high resolution non contact long range displacement measurement sensor

• Realization of an integrated compact miniature positioning system.

In order to reach these objective, the work presented in this manuscript is divided into six chapters.

Chapter 1 provides the state of the art regarding the different existing miniature multi-DOF positioning systems. The classification of these systems have been carried out on the basis of the actuation technologies. It also provides the state of the art related to the different displacement measurement sensor technologies and their integration approach.

Chapter 2 is dedicated to the working principle and modelling of a planar actuation system. At first, the concept of the actuation system is described along with the general layout of the system. Due to the symmetrical design of the system, the construction and functioning of a single linear electromagnetic actuator is discussed for the purpose of simplification. In addition, analytical models have been realized and verified using Finite Element Analysis (FEA). These models have been implemented to perform static and dynamic simulations in order to evaluate the performance of the whole system in open and closed loop control.

In chapter 3, the development of the Miniature Positioning System (MPS) prototype has been carried out. In the first part, the detail design layout of the MPS and the construction of its components have been discussed. Different design and fabrication solutions have been presented to realize a two part based compact system with optimal foot print dimensions on the basis of the concept introduced in chapter 2. Afterward, experiments have been performed in order to examine the different motion characteristics of the MPS in open and closed loop control.

Chapter 4 presents the design and development of a miniature long range optical displacement sensor. The long range sensor concept and working principle have been discussed and its geometrical optimisation has been carried out. In order to realize the long range sensor, a microfabrication approach was used to fabricate the silicon grating.

Chapter 5 details the sensor integration approach into the MPS. A novel silicon material based cross structure has been developed in order to facilitate the sensor integration and reduce the fabrication/assembly errors. In this chapter, some initial experiments have been conducted with whole system to provide an overview of the functioning of the integrated positioning system.

Chapter 6 provides a general conclusion and perspectives regarding the work presented in this manuscript.

The details regarding the published and presented papers can be found in Appendix-A.

Chapter 1

State of the art

This chapter provides the literature review in the field of the miniature multi-DOF positioning systems. Current design trends and different actuation technologies have been presented to realize these systems. Further, displacement sensors from their interaction and integration aspect have been discussed. At the end, a conclusion has been carried out based on the regarding actuation technique and displacement measurement sensors from their compactness and integration point of view.

Mechanical positioning system

Mechanical positioning systems are back-bone systems behind every object manipulation task. The functioning of these systems is based on the conversion of some form of input energy (mostly electrical) into the mechanical motion. One whole positioning system consists of single or multiple actuators, feedback sensors, mechanical platform, a central control unit and a power source (see figure 1.1). These components perform their respective functions to achieve positioning tasks in a workspace. Actuators are the components that convert input energy into specific tasks such as motion, force or a combination of both. Sensors are the components that measure a physical quantity (for example position, speed, force, etc.) and convert it into electrical signals that are interpreted by the central control unit. The central control unit analyzes the signal according to the desired inputs and generates respective electric signals to control the actuators. In addition, a power source delivers the input power to these components. The task of a mechanical structure is to provide a movable output platform and integrate the mobile parts of the sensors and actuators to guide their operation during motion.

In general, positioning systems are employed in different applications in order to gain high precision and automation in object handling/positioning tasks. For example, in the semiconductor industries, the production of Integrated Circuits (ICs) such as Microprocessors, etc., is carried out on a semiconducting material such as silicon, using a multiple-step sequence of photolithographic and chemical processes. In photolithographic steps, micro or nano level geometric patterns are transferred from photo mask to silicon substrate (coated with light sensitive chemical "called photo resist"). High precision positioning systems are used to align silicon wafers with photo masks during a photolithographic process to ensure accurate transfer of geometric patterns.

In micromechanics field, micro mechanical parts (e.g. micro gears) are fabricated and assembled. Different fabrication approaches have been realized such as microfabrication (similar to the technology used in semiconductor industry), laser cutting, etc. Due to the small size, human precision is not sufficient to handle these delicate mechanical parts during manufacturing, assembly and inspection stages. In this scenario, positioning systems along with various tools are used to carefully manipulate these parts during manufacturing, assembly and inspection.

In biomedicine, often single or multiple biological cells are cultured and studied in response to certain medicine. These biological cell studies demand high resolution optical and positioning systems for culturing and inspection.

In contact surface metrology, surface parameters (e.g. roughness, flatness, etc.) measurement of micro components is often needed for their qualification. High resolution positioning stages are applied as scanning platform to handle the part under the scanning probe.

In early 90s, the researchers at the Mechanical Laboratory (MEL) in Japan have in- Apart from the application area, the main task of a positioning system can be recognized as object (e.g. part, raw material, etc.) conveyance, its manipulation or combination of both. In order to realize the above mentioned positioning tasks, conventional macro application based positioning systems are not cost effective solutions. For example, in automated auto mobile industries, mechanical parts are fabricated on Computer Numerically Controlled (CNC) machines (e.g. milling, turning, drilling, machines, etc.).

troduced
These machines are equipped with positioning stages to position the raw material in front of the cutting tool during the machining process. The integration of such sized positioning stages are inappropriate in micro applications and can lead to expensive, bulky overall systems. However, the miniaturization trend has introduced numerous technological solutions to realize down scale versions of these machines to make it compatible with the micro world. This chapter discusses these kinds of solutions into positioning systems used in the micro applications.

Innovation into the positioning systems

In

Mechanical design approach

The mechanical design of the positioning system is realized in either with serial or parallel In micro applications, positioning systems realized with serial configuration provide large stroke (up to centimeters) as compared to parallel configuration, but they suffer from low stiffness, poor dynamics and large weight [ Wim 06]. Moreover the first positioning device takes all the load of the rest of the devices and so on, which makes it more sensible to uncertainties (e.g. vibrations, assembly errors, etc.) that lead to accumulation of precision errors. Despite having small stroke, parallel configuration based positioning systems does not suffer from the above mentioned problems [Ratc 06]. This makes parallel configuration a suitable candidate for the positioning systems used for micro application as the required maximum stroke size in these applications are up to few millimeters.

Motion drive technology

According to the literature, the motion drives can be classified into

Sensor interaction and integration approach

A sensor is a device that when exposed to a physical phenomenon (temperature, displacement, force, etc.) produces an output signal (electrical, mechanical, magnetic, Modern positioning system designs are either integrated or non-integrated with the non-contact displacement measurement sensors. In non-integrated approach the displacement sensors are outside of the physical boundary of the positioning system (figure 1.3(a)). The main reason is that the dimensions of the sensor are too big to be accommodated into the positioning system. For example, a high resolution camera can be used as a sensor to measure the displacement via image processing technique, but its volumetric size is too big to be integrated in the MPS. On the other hand, in integrated approach the sensors are installed inside the physical boundary of the positioning system (figure 1.3(b)). This approach involves fusion of complete sensor or sensor part directly into the positioning systems. The integrated approach demands miniaturization of sensor dimensions so that it could be easily accommodated within the geometrical dimensions of the MPS. Microfabricated MPS are often integrated with sensors to achieve monolithic and compact designs.

Miniature positioning system actuation technologies

The most common MPS actuation technologies are based on the use of active material or the field interaction technique. The first trend is to utilize the physical deformation characteristics of an active material (mostly a smart material) for the actuation purpose.

The second approach involves the interaction of the electric and/or magnetic field to realize actuation forces. In micro applications, these trends can be classified with respect to different actuation principles. According to the literature review, the most common actuation principles adapted to realize multi-DOF MPSs are:

Stepping mode actuators

Another method to increase the work stroke in MPS is to use the actuators based on step mode operation. The actuation principle of the stepping mode actuators is an inspiration taken from the movement of some earthworms.

Inchworm actuator:

The simplest linear inchworm actuator design comprises of three independently driven actuators. Piezoelectric ceramics and magnetostrictive materials are the most common active material used in these actuators. These materials can be configured in different ways, but the most typical one is depicted in figure 1.6(a) using PiezoWalk drives: These drives consist of piezo legs, that are actuated in multi-steps.

The piezo legs are piezoceramic shear modules that contract to release the rotor, and then deforms to achieve next step. The continuous operation of each piezo leg displace the rotor. The operation of these actuators are presented in figure 1.6 (c).

Physik Instrumente has developed a NEXLINE R actuator. The actuator consists of a runner and two piezoWalk drive modules (see figure 1.6 (d)). The continuous operation of these drive modules displaces the rotor along motion direction. This technology has been used to realize a nano positioning system PI N-512 as shown in figure 1.6(d).

The positioning system provides 6×6 mm travel in a plane with 10 nm resolution. The dimensions of the system is not provided.

Stick-slip actuator:

The functioning of stick-slip actuator mainly consists of two steps. In first step, a slow expansion of the Piezo Actuator (PA) moves the load along the actuation direction using the driving object that is fixed to the PA (figure 1.7(a)). Due to the static friction between the slider and the driving object a stick effect appears that holds the driving object and load together. In second step, a rapid contraction of the PA slides the driving object towards its initial position. Due to the rapid contraction, the inertial force due to the mass of slider dominates the static friction forces between slider and driving object (slip effect). With the assumption of no friction loss, this effect results in the final displacement "∆x ". with a resolution of 1 nm (1 µrad), respectively. Moreover the MPS has been integrated

with micro encoders for displacement measurement.

Friction-inertia drives:

The operating principle of these drives are based on the reaction caused when a mass is accelerated. The functioning of these actuators is similar in concept as of stick-slip actuators. However, these actuators use the inertial force for the actuation purpose. A slow expansion of active material, such as piezoceramic, drags the inertial mass to be moved relative to the ground, while ensures the adhesion of the load with the ground. The rapid contractions accelerate the inertial load towards each other.

In this scenario, the inertial force dominates the adhesion forces thus allowing the load to move "∆x" as shown in figure 1 inertial drive actuator will travel along one direction. When the other two are activated in an opposite manner, the inertial drive actuator will travel towards another direction.

If either pair of PAs in a parallel position is activated in the same manner, the inertial drive actuator will rotate. The robot is compact in design and provides a displacement resolution of 17 nm with a maximum travel speed of 1 mm/s.

Ultrasonic linear motors

Ultrasonic motors utilize the vibration of the elastic body (stator) in the ultrasonic frequency band and the reverse piezoelectric effect of the piezoceramic materials [Zhao 11].

These motors have two energy conversion processes. The first process converts electrical energy into mechanical energy using reverse piezoelectric effect. The second process changes vibration of the stator into macro one direction movement of the slider due to the friction between the elastic body and slider (figure 1.9(a)). For optimal operation, the slider and elastic body must be maintained in contact at all times. The most common technique is to use the weight of the slider to ensure permanent contact. The second approach is to assemble multiple ultrasonic linear motors to realize a multi-DOF positioning system. Devos et al., have developed a xy-planar drive based on this approach that combines the fast positioning capability of the resonant motors for fine positioning in the nanometer range [Devo 04]. A pair of piezoelectric actuators is assembled to a pair of tuning blocks along each axis (figure 1.9(d)). These tuning blocks are in contact with the cube and acts as deformable legs. Upon excitation, each pair of legs describe an elliptical trajectory in the plane corresponding to the excited pair, thus realizing a planar motion of the cube in xy-plane. A maximum speed of 60 mm/s speed under no load conditions was reported by the authors.

Thermal actuation principle

Thermal actuators are based on the thermal expansion of materials (mostly solids) when subjected to a heating source. In MPS designs, thermal expansion/contraction of the material are carried out based on resistive heating technique. It involves the utilization of the current carrying coil wrapped around or embedded in the material to generate heat based on joule heating effect. Bimetal and bimorph type configurations are more commonly adapted to realize linear actuation. In bimetal, two same sized metals but having different coefficient of thermal expansion are assembled together (figure 1.10(a)).

Upon resistive heating, the material with higher value of coefficient of thermal expansion will expand more with respect to other which results in motion.

Similarly, a bimorph consists of two metallic arms (referred as hot and cold arms) fabricated in the same material (figure 1.10 (b)). In this configuration the cross section of the hot arm is smaller than the cold arm. when current is injected in the bimorph, the hot arm will expand more due to smaller cross section relative to the cold arm. Due to the difference in volumetric expansion an actuation can be realized. Figure 1.10(c) represents another approach to realize linear motion by means of applying fixed constraints. In this approach the expansion legs have same cross section and material. When heated, the expansion legs will experience change in dimensions. In order to compensate the change in length due to temperature rise, an in-plane deformation will be realized by the expansion legs which will move the translating shuttle. Ebefors et al., have constructed a micro conveyance system based on arrays of movable robust silicon legs. Figure 1.12(a) represents the step by step actuation technique proposed by authors for moving a flat abject in the horizontal plane. The conveyance system is realized with curved polyimide joint (figure 1.12(b)). These joints deform when electrically heated, which create "∆z" and "∆x" displacement. When the heating is turned off the polyamide joint returns to its original position. Based on this actuation concept, the authors developed a platform composed of several polyamide actuators using heating resistors [Ebef 00]. The fabricated conveyor (see figure 1.12(c)) consists of a 15×15 mm 2 chip having 12 silicon legs to move a flat object at millimeter range. It can perform translational and rotational motion in horizontal plane. The maximum conveyance velocity of 12 mm/sec has been reported by the authors.

Direction of motion

Contact pad

Metal with higher coefficient of thermal expansion

Pneumatic actuation principle

Positioning systems based on pneumatic actuation method utilize the pressure of the compressed gas (i.e. air, nitrogen, etc.) injected via small inlets (called nozzles, see figure 1.13(a)) to move and levitate the object at the same time. One of the methods to generate an air-flow is by using several nozzles fabricated into a flat mechanical structure.

The inlets of the nozzles are controlled using pneumatic valves. The direction of motion can be achieved by systematic operation of these pneumatic valves. Pneumatic actuation technique is commonly adapted for small size and lightweight object conveyance. This technology results in cleaner, non flammable and low cost object conveyance systems. The basic cell size in the micro fabricated conveyance system is 1×1 mm 2 and the size of the nozzle is 165×590 µm 2 . The system utilizes nitrogen gas at 17 kPa and can carry up to 4 mg weight. surface is of 120 mm×120 mm in dimensions. The system consists of an upper block having an array of 15×15, 0.4 mm drilled holes (nozzles) and a lower block with 112 drilled holes in staggered rows. These holes are connected to two independent air inlets.

The network of holes creates the air cushion under the object to levitate and move in a plane.

Electrostatic actuation principle

Electrostatic actuators are based on the well known Coulomb law, which was reported in 1780. In these actuators, electrostatic charge arises from a build up or deficit of free electrons in a material, which can exert an attractive or repulsive force on oppositely or The purpose of this manipulator is to provide accurate and stable positioning of a small sample (10×20×0.2 µm 3 ) in nano applications. Three comb actuators (arranged at 120 • ) are used to actuate a triangular platform over ±10 µm stroke in the xand y-directions with a maximum rotation of ±2 µm. The displacement measurement was carried out using image-processing technique by taking a set of pictures and counting the pixel resolutions.

Electromagnetic actuation principle

Electromagnetic actuation principle is based on the appearance of the electromagnetic force exerted on an electrically charged particle moving in the presence of a magnetic field. The main advantages of actuators based on this principle include, hight speed, fast response, simple design and low cost. In multi-DOF MPS designs, one of the major problems is the appearance of frictional forces due to the mechanical contact between mobile and fixed part of the MPS. One of the ways to reduce/eliminate this problem is by levitating the mobile part using pneumatic drives (see section 1.3.3). However, electromagnetic actuators can offer both translation and levitation in a single module, thus making them a fruitful choice. The actuators realized with electromagnetic principle can be classified into three types based on the generation of the electromagnetic forces.

The description regarding these forces is mostly taken from [Mole 00, Furl 01, Benc 06].

Linear Induction Actuator (LIA)

The working principle of the LIA is based on the generation of the induction force. When a conductive plane is exposed to a magnetic field, currents are induced in it according to the Faraday's law. The interaction between the induced currents (which lead to secondary magnetic field according to Lenz's law) and the magnetic field leads to induction forces.

A typical configuration of a LIA consists of a movable slider with conductor windings, a fixed stator and a conducting material as shown in figure 1.19(a).

LIAs possess high temperature bearing capability and deliver extremely high speeds.

However, they are mostly applied in application-specific drives such as compressors, pumps, etc., due some drawbacks. These include force-ripple effect, acoustic noise, high power consumption due to absence of permanent magnets [Mole 00].

In mechatronics field, LIAs are often used to construct multi-DOF planar motors for small object conveyance.

Linear Reluctance Actuator (LRA)

The principle of LRA is analogous to the flow of the electric energy in an electrical circuit.

In electric circuit, the electric field causes an electric current to follow the path of least resistance. Similarly, in a magnetic circuit the magnetic field causes magnetic flux to follow the path of least magnetic reluctance/resistance. In a magnetic circuit the magnetic energy is stored rather than dissipating it like in electrical circuit. So, when the coil in the magnetic circuit is energized, the reluctance force appears in order to minimize the overall reluctance of the magnetic circuit.

LRAs are strong, compact and power economic actuators. The maximum force density of the reluctance force depends on the saturation level of the yoke material, geometrical parameters, material's relative permeability and air gap. The construction of an LRA is similar to LIA, but it requires one less element, since a coil and an iron target is enough to generate reluctance forces (figure 1.21(a)). However, in micro applications, LRAs

a) MPS realized with moving coil and fixed PMs technique

This construction technique is the inspiration taken from conventional rotary motors.

In these motors the permanent magnets are located at the stator part of the motor and the rotor include the conductor windings. DC motors is one of the example of such motors that are mostly found in the appliances. The same construction approach is being The application of the aerostatic bearings in the MPSs based on the moving coil and fixed permanent magnet technique is often needed to first, levitate the heavy mobile part and second, to remove the joule heat generated during their functioning. However, this solution often reduces the availability of the potential space on the mobile part due to the extensive wires or air manifold tubes that are connected to it (see figure 1.24). This problem often leads to positioning limitation in a plane as the length of the mentioned elements restricts the movement of mobile part to a certain range.

b) MPS realized with fixed coil and moving PMs technique

In this technique, the permanent magnets are directly assembled to the slider (or mobile part) and coils are fixed at the stator (figure 1 sensor measurement system (optical+capacitive) installed beneath the mobile platform.

The sensing system utilizes a structured grid plate to measure the displacement. The maximum speed of 100 mm/s (limited due to the controller) with a maximum carrying load of 500 grams was reported by the authors. Based on moving PMs and fixed current coils technique, N.Bencheikh at Roberval laboratory of the Université de Technologié de Compiègne (UTC), developed a long range linear EMA to realize compact miniature conveyance device for desktop factories. In order to achieve planar motion, the miniature conveyor was realized with four orthogonally arranged EMAs assembled to a Zerodur cross structure (figure 1.30). The prototype is able to perform xymotion in a plane and a rotation about z-axis. Each EMA is driven using a two phase planar electric drive coils that are injected with 1.6 A (peak to peak) currents. In order to measure the displacement, two non contact external fibre optic sensors (resolution ≈ 2 nm). The conveyor prototype was designed for 5 mm×5 mm travel in xy-plane but was tested for only 2 mm due to the limited range of the fiber optic sensors. In addition, the resolution of the device was reported around 20 µm due to the friction between the mobile and fixed part of the system. Further, a maximum rotation of sensors is made of a bundle that consists of at least one emission and one receiving fiber.

±8 • about z-axis was reported [Benc 06].
In reflective principle based fiber optic displacement senors, the light injected by the LED into the emission fiber exits from the probe and is reflected by a flat mirror. The reflected light feeds through the reception fiber bundle that is connected to a photodiode on the other end as shown in figure 1.31(a). When the facing mirror moves perpendicular to the probe axis, the angle of incident light changes. This results in variation in the intensity of the reflected light collected by the reception fiber which is interpreted by the photo diode.

The typical output response curve of this type of sensor is presented in figure 1.31(b).

Due to the small dimensions of the probe, their integration in compact MPS designs is easy as compared to other optical sensors, as they can reach in congest places without consuming too much space. Further, in order to measure the motion characteristics along multiple axes the integration of multiple fiber optic probes does not affect the cost and volume of the overall system. In addition, the arrangement of the fibers in the probe can be used to measure two dimensional and angular displacement with nano meter level resolution. However, their application in MPSs is not common as they exhibit small working range (up to few hundred microns) in their high sensitivity region. resolution of 27.4 nm over a linear working range of 9 mm in a plane. Further details regarding this sensor will be discussed later in this thesis.

Overview of the presented positioning systems

The presented actuation technologies have been analyzed on the basis of the physical characteristics (e.g. maximum work stroke, overall size, etc.) of the developed positioning systems for micro applications. Table 1.1 represents some of these characteristics for the MPSs discussed in the previous section. For precise positioning, feedback sensors play a vital role in controlling the motion behaviour of these systems. Their selection is mostly carried out on the basis of their compatibility with the MPS environment that include, actuation technology, overall volume, work stroke, etc. For example, in electromagnetically actuated MPSs, the application of sensors based on capacitive, magnetic or inductive measurement principle are in common as the electromagnetic field from the PMs can disturb their functionality. On the other hand, optical sensors are the ones which can work in almost every environment.

The only constraint that limit their functionality is the quality of the reflecting surface. In most of the MPSs presented in table 1.1, the displacement measurement has been carried out using optical sensors, e.g. camera, interferometers, etc. However, due to their large volume their integration is difficult. Fiber optic displacement sensors are easy to integrate due to their small dimensions and offer nano meter level resolution. The only limitation concerning these sensors is their ability to measure at long range. The research carried out at our Roberval Laboratory, has led our team to realize a compact version of these sensors to enhance their ability to measure at long range in two dimensions.

Taking into the account the presented actuation technologies, an analysis have been carried out in the following section to select a drive technology in order to realize a multi-DOF MPS in this work.

Conclusion

In this section, based on the start of the art regarding the miniature positioning system technologies presented in this chapter and summarized in table 1.1, different actuation technologies have been evaluated in table 1.2 for different design parameters such as working stroke, resolution, compactness, sensor integration, etc. From table 1.2, it can be seen that smart material, thermal and electrostatic actuation based MPSs mostly suffer from their small work stroke size. Different engineering solutions may be employed in order to maximize their work stroke but it results in complex design of the whole MPS.

Pneumatic, induction and reluctance actuators based MPSs offer larger work strokes but their poor resolution often limit their applications to conveyance systems. On the other hand, Lorentz force actuator based MPS provide millimeter level strokes with possibility to achieve nanometer level resolution. The only drawback in these MPSs is their smaller output force. However, different solution can be employed to solve this problem. In this work, Lorentz force actuator has been selected as a drive choice to realize the MPS.

Thesis objectives

After selecting the actuation technology to realize a compact integrated MPS, the research realized in this manuscript has been divided into three main tasks as shown in the figure 1.33. The description of these tasks are provided in the following text:

Task 1: The initial task is based on the improvement of the previous prototype developed by the Dr. Nabil Bencheikh [Benc 06]. In this task, redesigning of the prototype will be carried out in order to increase its planar working stroke while selecting a minimum foot print size for the new miniature positioning system prototype. In addition, the new design should be adaptable to integrate top and bottom side planar electric drive coils to optimize its output characteristics such as load carrying capacity, current input, etc.

Task 2:

The second task deals with the improvement of the long range optical sensor. For this task, the fabrication of the silicon gratings using microfabrication technology will be carried out using the fabrication process proposed by Dr. Ali Khiat [Khia 07].

However, the main objectives behind this fabrication are to obtain improved surface parameters for the silicon gratings and to achieve a micro machining process that must deliver homogenous silicon gratings with better roughness and flatness parameters. In addition, taking into the design parameters of the new MPS design in task 1, the geometrical parameters of the long range sensor will be optimized for integration purpose.

Task 3: Finally, an integrated MPS capable to deliver 3DOF motion will be realized. For this task, the silicon gratings will be integrated in the mobile part of the miniature positioning system.

During each task, analytical models will be developed and experimentations will be performed in order to validate the MPS design.

Realization of an

Principle and modeling of a miniature planar actuation system

In this chapter the working principle and modeling of the planar actuator system has been carried out. At first, the concept of the actuation system is described along with the general layout of the system. Due to the symmetrical design of the system, the construction and functioning of a single linear electromagnetic actuator is discussed for the purpose of simplification. Then, analytical models have been realized and dynamic simulation results are shown to evaluate the performance of the whole system in open and closed loop control.

Miniature positioning system concept

The Miniature Positioning System (MPS) presented in this work is based on in-plane symmetrical assembly of four direct drive Linear1 Motors (LMs) as shown in the figure 2 The functioning of the positioning system is tied up to the electromagnetic force generated by each LM. In order to perform displacement in xy-plane between any two positions P 1 and P 2 , all four LMs can be used simultaneously to generate motion forces (see figure 2.1(b)). If we assume no assembly errors between LMs situated along an axis, the generated electromagnetic force is the sum of the forces generated by each LM along an axis. Moreover, in order to realize linear displacement along a single axis the device only requires two active LMs. For example, to achieve linear displacement "∆x" along

x-axis, LM A and LM B can be used, similarly for "∆y" displacement along y-axis, LM C and LM D can be used. The direction of the generated motion force depends on the direction of injected current into each LM. So, by inverting the current in the PEDCs, the motion direction can be reversed. In addition, if the direction of the current in the LMs situated along an axis is reversed with respect to each other, a torque can be produced about the center of the mobile part of the MPS. Hence, by this means a rotation of the mobile part can be realized.

Actuation principle

The actuation principle of a single linear motor is based on generation of the Lorentz forces. When a PM is placed near a current carrying conductor, an electromagnetic force appears due to the magnetic field from the PM and magnetic field generated from the electric current in the conductor. The relative interaction between two fields results in a force F which appears over the PM (figure 2.2(a)). Taking into account the case that the current carrying conductor is fixed and PM is free, the generated electromagnetic force will move the PM in xz-plane in order to align the magnetic field relative to the magnetic field of the conductor. The amount of this generated electromagnetic force (or Lorentz force) can be computed using equation (2.1) [Furl 01].

F = I wire dl × B ext (2.1)
Where, F is the generated electromagnetic force, l is the length of the current carrying conductor facing PM, I is the current in the conductor and B ext is the external magnetic The components of the electromagnetic force can be written as,

F =      F x F y F z      =      +I y • B z • l 0 -I y • B x • l      (2.2)
The components F x and F z represents the translational and levitation forces in xzplane. The magnitude of these forces depends on the intensity of the magnetic flux density, magnitude of the current and length of the current carrying conductor facing the PM.

In order to increase the magnitude of the electromagnetic force, these parameters can be altered toward maximum. However, their maximum value is often limited due to the design constraints. For example, the magnitude of the current depends on the cross sectional area of the conductor. So, for a fixed cross sectional area of the conductor the increase in the current could lead to Joule heating effect, which may either destroy or degrade the remanent magnetization of the PM or the conductor itself. Similarly, the intensity of the magnetic flux density from the PM depends on the volumetric shape, its material and its relative distance from the current carrying conductor. For the same material, the intensity of the magnetization is proportional to the increase in the geometrical dimensions, however, increasing the geometrical dimensions means more weight, which may lead to reduction of usable net motion forces. Another way to increase the electromagnetic force is to reduce the relative distance (known as air gap, "d" in the figure 2.2(a)) between the conductor and PM. In MPSs, the above mentioned parameters are carefully dealt with as they can change the overall performance the system.

Linear motor layout and its working principle

The actuation principle presented in the previous section is extended to realize long range linear motion by adding a larger number of PMs and conductors in the mobile part and the fixed part, respectively, as shown in figure 2.3. The combination of these parts results in an LM that is able to perform continuous motion along ±x-axis . In order to illustrate the functioning of the LM, the solutions regarding the construction of the mobile and fixed part is first presented. in electromagnetic actuators designed for the MPS used in micro applications. However, where this configuration results in the increase in the magnetic field is increased along the one side of the PMA, the other side cannot be exposed to current carrying conductors due to the unsymmetrical magnetic field (see [ Benc 06]). Due to this reason the application of this configuration is mostly limited in the designs where the availability of the potential space for placing current carrying conductors on the both sides of the PMA is difficult [ Hu 06]. For example, in MPS based on the moving PMs and fixed current coils technique, the current carrying conductors cannot be placed on the both sides due to the design constraints. So, in such case the Halbach array configuration is suitable to increase the magnetic field to the side which is exposed to conductor to gain more power.

The second approach is to assemble the PMs in "North-South (NS) array configuration". It consists of the assembly of the PMs with opposite magnetic orientation as shown in figure 2.4(b). The NS array configuration is simple and offers several advantages in MPS designs over Halbach array configuration. For example, the NS configuration offers symmetrical magnetic field on top and bottom sides of the PMA as shown in figure 2.5.

So, in order to increase the magnitude of the electromagnetic forces, another set of conductors can easily be applied with same characteristics. Furthermore, NS array requires a smaller number of phase current coils as compared to Halbach array to generate continuous motion [Lu 12]. This feature of the NS array configuration is very beneficial from miniaturization and control point of view. In addition, from the PMs assembly perspective, Halbach arrays are difficult to realize and demand positioning and bonding equipments to apply pressure to align and bond PMs in this configuration with specific magnetic orientation [Kim 97]. On the other hand, the assembly of the PMs in NS array configuration is very easy and does not need any equipment for bonding and alignment due to the opposite orientation of the PMs magnetization. On the basis of these conclusions, we have adapted NS configuration for the PMA in this thesis.

Drive coil construction

In order to be in accordance with the magnetic pole orientation in PMA, the electrical conductors can be arranged in various configurations to form multi-phase coils. These coil formations that are mainly classified as "core based coil formation" and "planar coil formation", reduce the input current source lines.

The core based coil formation is realized by winding the electric conductor around a ferromagnetic material such as soft iron (see figure 2.6(a)). The presence of the core in this formation enhances the magnetic field strength which can be used to increase the electromagnetic forces as in [Trum 98, Kim 07]. However, this coil formation demands excessive length of the conductor and despite having more number of turns in the coil, the interaction between the PMA and the coil itself remains in the area where the coil is exposed to the magnetic field. This reduces the full usage (> 50%) of the coils with respect to its volume. Furthermore, this coil formation is mostly realized with automated machines to attain compactness and avoid improper shape due to manual winding. One of the common issues related to the coils is the Joule heating due to the current flow. The amount of this heat is a function of the geometrical and physical properties of the coils such as cross section, material, length, etc. So, to gain more power in LMs these parameters are optimized based on application area. In addition, forced or natural cooling (e.g. via gas or liquid) can be used to remove Joule heat. In core based coils this is done by cooling the core and in planar coils an air cooling technique is commonly adapted [Holm 00].

In this work, an overlapped planar coils formation approach has been adapted to reach compact volume (32×20×0.035 mm 3 ) of the Planar Electric Drive Coils (PEDC) of the LM. In order to be in accordance with the magnetic pole orientation of the PMs in the PMA and minimize the number of input currents source lines, the PEDC consists of two phase coils as shown in figure 2.7(a). In addition, the coils have been been fabricated onto a double sided 1.4 mm thick PCB to attain optimal geometric parameters such as conductor length "l=20 mm", height "h c =35 µm" and width "w c =250 µm", etc. The value of these parameters and the number of conductors in the PEDC depends on the design (e.g. motion range, maximum input current, etc.) and PCB fabrication constraints.

The overlapped connections between the conductors in a single phase coil (on the top side) have been carried out from the bottom side of the PCB using through holes called

Working principle of the linear motor

The working principle of the LM to perform long range continuous motion is presented in figure 2.8. To provide a better view of the concept, the PMA (i.e. mobile part) of the LM is constructed with four PMs arranged in NS array configuration and the PEDC (i.e. fixed part) is constructed with eight conductors representing two coils with currents "I 1 " and "I 2 " with a relative phase shift of "π/2" and are expressed as in equation (2.3).

I 1 = I max sin(ωt + ϕ i ) I 2 = I max sin(ωt + (ϕ i + π/2)) (2.3)
Where, I max is the maximum amplitude, ω is the frequency and ϕ i is the initial phase of the current injected into the conductors of the PEDC.

In order to realize, long range continuous motion in xz-plane, the coil pitch "P c " of a single coil should be equal to the period of the PMA "P m " (see figure 2.8(a)). This condition ensures the alignment of the peak current amplitude with respect to the peak magnetic flux density generated by the periodic magnetic poles of the PMA. As a result, the current to magnetic field interaction leads to generation of Lorentz forces along same direction.

To illustrate the working principle of the LM, the generation of the Lorentz forces are presented in four steps at 8 discrete locations which indicates the position of the conductors having currents "I 1 " and "I 2 ". During these steps, it can be seen that when

(a) (c) (b) Position of the conductors Y X Z Reference position
Step 4

Step 3

Step 2

Step 1 2 3 4 5 6 7 8

P P m = c π 2 -I 1 -I 2 +I 1 +I 2 -I 1 -I 2 +I 1 +I 2 FIGURE 2
.8: Working principle of the LM in four steps (a) PMA with respect to the conductors with currents "I 1 " and "I 2 " (b) Magnetic flux density "B z " relative to the position of the conductors (c) Magnetic flux density "B x " relative to the position of the conductors PMA offers peak value of "B z " the value of "B x " is near zero and vice versa (figure 2.8 (b) and (c)). This is due to the orientation of the PMs in the PMA.

When the currents are injected in the conductors, electromagnetic forces will appear over each PM due to the interaction of the current I 1 and magnetic flux density component ±B z at the positions 1, 3, 5 and 7. These forces will move the PMA to distance "x" along x-axis. At the same instant, the interaction of the current I 2 in the conductors and ±B x at position 2, 4, 6 and 8 will generate levitation forces along z-axis.

In step 2, the translation forces will appear at positions 2, 4, 6 and 8 due to the interaction of the currents I 2 and the peak magnetic flux density component "±B z ". Similarly, the levitation forces will appear at positions 1, 3, 5 and 7 due to the interaction of currents I 1 and peak magnetic flux density component "±B x ". The current shifting (i.e. from I 1 to I 2 and vice versa) is because of the relative phase difference (π/2) to compensate the periodic poles of the PMA (see figure 2.8 (a)). Further, in step 3 and 4, the translation and levitation forces are generated in similar fashion which moves the PMA at "2x" and "3x" distances from reference position. For the conductors length "l" along y-axis, the total translation and levitation force is the sum of the individual forces appeared at each conductor locations which are presented in the table 2.1. From the above table it can be seen that during all steps the generated translation force at each conductor location is in the same direction due to which the PMA will translate along +x-axis with respect to the PEDC. So, in similar way if the number of conductors is increased in the PEDC, the travel range of the PMA can be increased. Moreover, in order to increase the magnitude of the translation and levitation forces, the number of PMs can be increased. In this scenario, the equation (2.4) represents the generalized form of the total electromagnetic force due to currents I 1 and I 2 in the conductors.

F total =      F x F y F z      =                l • n i=1 (I 1 B z (x, y, z)) 2i-1 + l • m j=1 (I 2 B z (x, y, z)) 2j 0 l • n i=1 (I 1 B x (x, y, z)) 2i-1 + l • m j=1 (I 2 B x (x, y, z)) 2j                (2.4)
Where, i and j are the position index of the conductors, n and m are number of the conductor with currents I 1 and I 2 , respectively, B x and B z are the horizontal and vertical magnetic flux density components, F x and F z are the total translation and levitation forces.

In practice the distance between the adjacent conductors (in our case d a =0.5mm, see figure 2.7(a)) in the PEDC may be limited due to the fabrication constraints. In this case, the force contribution due to current carrying conductors may lead to small fluctuations during translation of the PMA. This is due to the insufficient overlap of the generated translation force between two adjacent conductors during motion as shown in figure 2.9(a)). In order to reduce this effect, W. J Kim In order to change the direction of the motion, the current phase lead-lag technique is used. The relative phase difference of the injected currents is changed from +π/2 to -π/2 as shown in figure 2.10. Further, if a constant current is injected into the coils. The mobile part (i.e. PMA) will lock its position with respect to the conductors. This effect is due to the appearance of electromagnetic forces in opposite direction because of the NS arrangement of the PMs in the PMA.

(a)

+I 1 -I 2 -I 2 -I 1 +I 1 +I 2 +I 2 -I 1

Translation force

Levitation force Translation force Levitation force

-I 2 -I 2 -I 2 -I 2 +I 1 +I 1 +I 1 +I 1 (b) Y X Z FIGURE 2
.10: (a) Direction of motion by changing the phase of the current I 1 to -π/2 (b) Influence of the steady state currents

In the following section, the single DOF based LMs solution has been used to realize a planar motion system.

Long range planar motion

In order to realize long range planar motion system, multiple LMs based on the working principle described in the previous section can be assembled to a mechanical structure.

The PMAs of the LMs are fixed to a mechanical structure which results in the mobile part of the MPS. Similarly, the PEDCs of the LMs can be assembled accordingly to realize the fixed part of the MPS. In order to assemble multiple LMs, two assembly approaches can be proposed based on the orientation of the translation axes of the LMs as shown in figure 2.11. In the first assembly approach, the translation axes of the LMs merge at a single point and in the second approach the translation axes of the LMs results in multiple merging points. Both methods are equally employed in miniature MPS designs, however the second assembly approach offers an additional rotation motion about the origin of the mobile part of the MPS as compared to the assembly approach presented in figure 2.11(a).

In practice, LMs can be arranged in either "triangle" or "square" formation, e.g. In the case of linear motion, two LMs are sufficient to drive the mobile part of the MPS as shown in figure 2.12 (a). In this case the characteristics of the injected currents are kept identical in the LMs located along motion axis. Further, the total generated translation force will be the sum of the forces generated by individual LMs that are active. However, in real case scenario, these forces are not always identical. For example, the variation in the magnetic field due to the dimension tolerances of the PMs or due to the PMA assembly errors can lead to generation of different magnitude of the forces along an axis.

This variation may introduce a drift effect of the mobile part during linear motion. To solve this problem, constant currents can be injected into the LMs situated perpendicular to the motion axis (see figure 2.12 (b)). These constant currents will guide the mobile part during linear motion and minimize the motion error due to the locking principle presented in figure 2.10 (b).

To realize planar motion, all four LMs are injected with sinusoidal currents. In this case the guidance along a single axis could not be achieved as shown in figure 2.12 (c).

As a result, due to the generation of non-identical forces along single axis a small rotation may occur. However, because of this rotation a restoring torque (t z ) appears over each PMA during motion, which tends to align the mobile part with respect to PEDCs (see figure 2.13(a)). This phenomenon occurs due to the variation in the magnetic flux distribution over the length of the conductors in the PEDC during small rotation [Benc 06].

The magnitude of the restoring torque depends on several parameters such the magnitude of the injected current, the rotation angle, the air gap between the PMA and PEDC, etc.

In order to identify the amount of the restoring torque, an analysis has been performed

Modeling

In this section analytical modeling of the MPS has been carried out. For the purpose of simplification, the modeling has been performed for a single LM due to the symmetrical design of the MPS. At first, the magnetic flux density distribution model have been realized. Then, the electromagnetic force computation model is presented. At the end, the mechanical model has been realized in this section. These models have been implemented

with MATLAB to study the dynamic behaviour of the system.

Magnetic flux density distribution model

The PMs used in our application are parallelepiped in shape with each having cross section 1×1 mm 2 and length 6 mm. Due to the finite length of the PMs, a three dimensional analytical model based on surface charge model was realized to compute the external magnetic flux density components B ext at any point P(x, y, z) located outside the PMA.

However, some assumptions have been carried out. These assumptions include, identical physical characteristics of all PMs in the PMA, perfect alignment of magnetic polarization of each PM along z-axis in free space and no variation in magnetization along the length of the PMs. Based on these assumptions, a single PM with is reduced to a distribution of equivalent magnetic charge as shown in figure 2.14 [Furl 01]. For a PM with the center located at "m" and dimensions (x 2 -x 1 ), (y 2 -y 1 ), (z 2 -z 1 ) along three axes the analytical expression for magnetic flux density components B x , B z at any point located outside a single PM is provided in equation (2.6) [Furl 01].

B x (x, y, z) = µ 0 Ms 4π 2 k=1 2 m=1 (-1) k+m ln (y-y 1 )+((x-xm) 2 +(y-y 1 ) 2 +(z-z k ) 2 ) 1/2 (y-y 2 )+((x-xm) 2 +(y-y 2 ) 2 +(z-z k ) 2 ) 1/2 B y (x, y, z) = µ 0 Ms 4π 2 k=1 2 m=1 (-1) k+m ln (x-x 1 )+((x-x 1 ) 2 +(y-ym) 2 +(z-z k ) 2 ) 1/2 (x-x 2 )+((x-x 2 ) 2 +(y-ym) 2 +(z-z k ) 2 ) 1/2 B z (x, y, z) = µ 0 Ms 4π 2 k=1 2 n=1 2 m=1 (-1) k+n+m × tan -1 (x-xn)(y-ym)(z-z k ) -1 ((x-xn) 2 +(y-ym) 2 +(z-z k ) 2 ) 1/2 (2.6)
where, B x , B y and B z are the magnetic flux density components (T) along x-, yand zaxis, respectively. µ 0 is the magnetic permeability of air (4π × 10 -7 N•A -2 ) and M s is the magnetization of the permanent magnet (A/m).

In similar fashion, the solution presented in (2.6) is used to construct the magnetic flux density distribution model for "R" PMs assembled with NS configuration in a PMA.

All PMs are reduced to the distribution of equivalent magnetic charge as shown in the figure 2.15. The total magnetic field solution at any point in three dimensional space outside the PMA is the sum of the contribution of each PM assembled in the PMA at that point and is calculated using equation (2.7) [Furl 01].

1 2 th R 1 2 th R x z y x z y ---- + + + + +B r -B r + + + + ---- +B r -B r ---- + + + + +B r -B r + + + + ---- +B r -B r
B ext (x, y, z) = R i=1 (-1) i × B (i) ext (x, y, z) (2.7)
Where B ext represents the external magnetic flux density component B x , B y and B z that is computed using (2.6) and "i" is the index of the PM in the PMA.

The analytical model presented in (2.7) was implemented with MATLAB for a PMA with four PMs to illustrate the magnetic flux distribution in xy-plane. Moreover for simulation the vertical distance "z", which represents the air gap between PMA and conductors, was kept constant at 100 µm. It can be concluded that over the PMA length (along y-axis), the B y component of the magnetic field remains constant except at the edges of the PMA where its value is around 0.3 T. This effect is due to the concentrated magnetic field near the ends of PMs.

However, in our studies we have neglected this component in order to reduce the magnetic flux density computation time during our simulations. The main reason behind this assumption is that the contribution of this magnetic flux density component in the generation of the electromagnetic force is very small (see table 2.2). In addition, during motion the B x and B z magnetics field components are the ones responsible to generate translation and levitation forces. So, in this scenario the assumption for neglecting the B y component can be justified.

Validation of the analytical model

In order to validate the magnetic flux density computation model for a PMA that consists of 14 PMs each having a cross section 1×1 mm 2 , length 6 mm and remanent magnetization B r =1.43 T was carried out using MATLAB c . The B x and B z magnetic field components generated by the PMA at an air gap of 100 µm were compared to Finite Element Analysis (FEA) result that was realized in COMSOL R with 8×10 5 mesh elements.

The comparison of both components is shown in figure 2.17. The result reveals a good agreement with relative error in the order of 10 -5 T.

Conclusion:

The described analytical model is able to compute magnetic field components during translation and rotation motion. However, in rotation case the magnetic field computation time was found to be around 9.7 seconds as compared to translation case which is around 0.83 s. The reason of large computation time in rotation case is total number of mesh elements required to precisely compute the B x and B z over the conductors. Whereas, in translation case the number of these mesh elements can be significantly reduced with the assumption that the coils remain parallel to the PMAs. In addition, It can also be noted that the simulation is performed for a PMA realized with four PMs and in our case the PMA of single LM is realized with 14 PMs which further increases the magnetic flux density computation time. Numerous solutions can be adapted to minimize the computation time such as with the help of Look Up Tables (LUT) the magnetic calculations can be done off line during dynamic simulations. However, due to the motion characteristics of the MPS proposed in this thesis, the translation and rotation cases are dealt separately because the rotation of the mobile can only be achieved by changing the direction of the injected currents in the PEDC.

Electromagnetic force and torque computation

The total force generated by a single LM is the sum of the individual forces that appear over each PM in the PMA and are computed using equation (2.8). Where, the B ext is the external magnetic flux density component in xz-plane. Its computation has been carried out using (2.7). The superscript (k) denotes the relative position index for the magnetic flux density computation with respect to I 1 and I 2 current carrying coils in a PEDC. The N denotes the total number of the current carrying conductors in a single coil. In addition, the total force about the center of the MPS is the vector sum of the electromagnetic forces generated by each LM of the MPS. Further, due to the generated electromagnetic force along an axis, a torque will appear about the center of the stage. The amount of this torque for single LM was computed using equation (2.9). Where, r is the distance from the center of the PMA to the center of the mobile part (see figure 2.18).

F electromagnetic = N 2 k=1 I k wire dl × B (k) ext (2.8) τ z = r × F electromagnetic (2.9)
In order to identify the magnitude of the generated electromagnetic force and torque, a static analysis has been performed for a single LM that consists of a PMA having 14

PMs and a PEDC having 60 conductors representing two phase coil currents. For a 0.8 A amplitude of injected currents in the PEDC at air gap of 100 µm the results are presented in table 2.2. It can be seen that the analytic computation provides a very good agreement with the relatively very small error in comparison with the results obtained with RADIA R .

In addition, it can be seen that the magnitude of the F y is very small as compared to F x and F z . This is due to reason that the currents in PEDC are parallel to the length of PMA, so the effect of this force is neglected in our dynamic simulations.

Units

Mechanical model

The fixed part of the MPS is insulated using a thin glass layer (thickness 130 µm) to provide a smooth motion surface for the mobile part due to the copper height (35 µm).

Further, due to the assembly constraints the mobile part of the MPS is supported with the help of four hemispherical glass beads (see figure 2.20(a)). The detailed discussion regarding these assembly constraints has been carried out in the next chapter. The integration of the glass beads and thickness of the glass layer impose an air gap constraint as shown in the figure 2.20 (b). This air gap reduces the magnetic field intensity near to the coils which as a result reduces the magnitude of the generated electromagnetic force.

Numerous solutions can be applied in order to increase the amount of generated electromagnetic forces. For example, increasing the number of PMs in the PMA can further increase the magnitude of the electromagnetic forces to compensate the reduction force loss due to the air gap. In addition, the smaller value of insulation layer can also improve the motion performance of the LM.

F static = W net × µ static F dynamic = W net × µ dynamic × sign(ν) (2.10)
where, µ static and µ dynamic are the static and dynamic friction coefficients. ν is the velocity of the mobile part. In our study the static friction coefficient was experimentally measured (µ static = 0.47) using an inclined plane technique, however, the dynamic friction coefficient (µ dynamic = 0.43) was approximated due to the difficulty to distinguish between the two coefficients during experimentation. In addition, no data regarding dynamic friction was found for the material that is used as an insulation layer. In order to implement the friction force during dynamic simulations, the condition presented in equation 2.11 was adapted. According to this condition, if the generated electromagnetic forces enters in the range of [-F static , +F static ] its value is set to zero. Otherwise, translation force (F net ) is computed using dynamic friction.

if F net < F static ⇒ F net = 0 if F net > F static ⇒ F net = F total -F dynamic (2.11)
While neglecting the thermal and hysteresis effect as disturbances, Newton's second law is used to develop the general solution for translation as given in equation (2.12).

The total displacement is computed with double integration of the acceleration ẍ (m•s -2 ) of the mobile part.

F net -F f = M ẍ ⇒ x = 1 M t 0 -t 1 (F total -F f ) dt 2 (2.12)
where M represents the total mass of the mobile part in kg, t represent the time in seconds and x is the total displacement realized by the mobile part in meters.

Similarly due to small rotation about the center of the mobile part, the friction force will exert a resistive torque about the center of the stage. The amount of this torque is computed using τ f =R× F f , where R is the radial distance of the glass bead from the center of the mobile part (see figure 2.20 (b)). In addition, the torque generated by a single LM is computed via equation (2.9). The rotation angle realized by a single LM about the z-axis is computed using equation (2.13) by double integration of the angular

acceleration θz (rad•s -2 ). τ net -τ f = J θz ⇒ θ z = 1 J t 0 -t 1 (τ net -τ f ) dt 2 (2.13)
where τ net = R× F net is the net torque in N.m, J is moment of inertia of the mobile part in kg.m 2 , t represent the time in seconds and θ z is the rotation angle about z-axis in radians.

Dynamic simulation of the MPS

In this section, the dynamic simulations have been carried out in order to study the motion behaviour of the MPS. Due to the symmetrical MPS design the control model will be discussed for a single LM. The analytical models developed in the previous section concerning a single LM has been implemented with MATLAB Simulink c . Further, the total weight (5.8×10 -3 kg) of the mobile part (i.e. weight of the four PMA and the cross structure) was used during dynamic simulations.

For simplification purpose, the air gap (d) between the mobile part and the fixed part of the MPS was set to a constant value of 130 µm. This air gap represents the distance between the four PMA and their respective PEDCs. This constant value was adapted due to the reason that the residual levitation force (F z -W ) during motion is small (≈ 10 mN per LM) for a maximum current value of 0.8 A. So, it was assumed that the levitation forces generated by each LM only helps to overcome the adhesion forces between the mobile part and fixed part due to the mechanical contact by compensating the weight of the mobile part during motion. In addition, due to the identical characteristics of each LM it was assumed that the small rotations do not occur to reduce simulation time. This is because, the similar characteristics of each LM lead to the generation of the same amount of translation forces, so the torque generated by each LM located along a single axis about the center of the mobile part will theoretically cancel each other.

Description of the simulation parameters for a single LM

On the basis of the assumptions presented above, a single LM was modeled with 14 PMs

Open loop control

The open loop control of a single LM is presented in figure 2.22. The currents I 1 and I 2 are generated and injected to the force computation model to compute the Lorentz forces.

This model takes into account the magnetic model (see equation (2.7) ) to compute the magnetic flux density distribution of the PMA at the relative position (x, z) of the mobile part. The initial position of the PMA in order to compute the magnetic flux density was selected as (x 0 =0, z 0 =air gap). Further, the generated Lorentz force was inserted in to the mechanical model which calculates the displacement realized by the mobile part via equation (2.12). To realize these calculations, a 10 -3 s simulation step size was selected in MATLAB Simulink c which corresponds to 1 kHz frequency of sinusoidal currents injected into the PEDC.

Sinus generator

Compute force Mechanical model Magnetic flux density model In addition, during planar motion all four motors lead to the generation of much larger levitation forces which results in a total displacement of 961.73 µm along single axis. In our studies, this open loop control have been used to evaluate the experimental results.

I 1 I 2 X (x,z) (x ,z ) 0 0 Initial condition B ext F L

Closed loop control

For precise positioning, a Proportional-Integral (PI) controller was adapted to the open loop control of a single LM as shown in figure 2.25. This control was selected due to its simple application and its ability to exhibit no steady state error due to the integrator [Benc 06]. In our application, this controller was used to control the sinusoidal currents (see equation (2.14)) that have been injected to the PEDC in order to generate electromagnetic forces for translation.

I 1 = I max sin(ωt + ϕ i ) I 2 = I max sin(ωt + (ϕ i + π/2)) (2.14)
Where I max (A) is maximum current amplitude, ω (rad/s) is the frequency of the current, ϕ i (radians) is the initial current phase and t is the time in seconds. The open and closed loop model developed in this section have been used to compare the experimental results in this thesis. In addition, due to the difficulty to adapt the real case scenario regarding the small variations in the forces generated by all four LMs, the small rotation effects are not simulated here in this work. However, the error generated by these small rotations during motion is very small due to the auto alignment feature of the mobile part with respect to the fixed part. In future studies, these errors may be included in order to investigate their influence during motion.

Sinus

Conclusion

In this chapter, a Lorentz force based compact positioning system with a stack of four LMs in parallel configuration is presented. The overall design of the system consists of a mobile and a fixed part. The uniqueness of the proposed MPS lies in its simple design and ability to perform millimeter level strokes with pre-embedded auto guidance feature.

At first, the long range motion concept of the MPS has been explained with a functioning of a single LM due to the symmetrical design of the MPS proposed in this work.

Further, taking into account the earlier research that has been carried out at our Roberval laboratory [Benc 06], the solutions adapted in order to realize the miniature drive components such as planar coils and permanent magnet array have been presented. In addition, a cross structure based orthogonal assembly of the four LMs has been selected to attain a symmetrical design. This assembly approach enhances the magnitude of the electromagnetic forces along single motion axis and reduces the number of input source lines.

After description regarding the planar assembly and planar motion concept, modeling

Design layout of the prototype and component description

The detail layout of the electromagnetically actuated MPS prototype is presented in fig- In addition, the cross structure design was realized in a 1 mm thick Zerodur glass material via conventional machining (see figure 3.2(b)). This material was selected because of its low density (2530 kg•m -3 ), high strength (90.3 GPa) and low thermal deformation coefficient (0.02×10 -10 K -1 ) [Scho 10]. In our MPS prototype, we have used the same mechanical cross structure to build the mobile part due to the above mentioned characteristics. The weight of the fabricated cross structure presented in figure 3.2(b), is 2.3×10 -3 Kg. This small weight is due to the selected design dimensions and low density of the Zerodur material, which is an additional advantage as it results in the construction of a light weight mobile part after assembling the four PMAs and sensory components.

Permanent Magnet Array (PMA)

The translation forces can be generated with even a single period of PMs arranged with NS arrangement in a PMA as described in previous chapter. However, in order to compensate the total weight (8.41 g) of the mobile part with generated levitation force during motion, the PMA of a single LM has been realized with 14 PMs. The total weight of the mobile mainly includes the weight of the mechanical structure (2.3 g), weight of all four PMAs (2.4 g) and the weight of the mirror cube used for displacement measurement (≈ 3.7 g).

In the mobile part, the number of PMs assembled in a set of PMA are limited due to the edge dimension of the Zerodur cross structure. Moreover, each PM is parallelepiped in shape with the cross section 1×1 mm2 and length 6 mm. These dimensions for a single PM were selected in manner to align the magnetization poles with respect to the pitch of the coil in the PEDC (see section 2.2.1.3) and reduce the Joule heating effect by minimizing the overall resistance of the PEDC designed for 10 mm displacement stroke. To realize the PMA with these specifications, the PMs were purchased from supermagnete 1 GmbH in Neodymium Iron Boron (NdFeB) material with gold coating to protect it from corrosion. This material was selected because of its high remanent magnetization (1.41-1.47 T) and high coercive force (1138-1043 kA/m) [Benc 06]. These characteristics of this material lead to the generation of high electromagnetic forces in miniature design.

Mobile part assembly

In practice, the PMA was realized by first finding the orientation of a single PM with the help of a reference PM 2 with marked South pole. Then, by fixing the first PM on a flat surface to avoid its orientation due to earth magnetic field, the rest of the PMs are placed near to it one by one to form a set of 14 PMs. Due to the opposite magnetic pole orientation, the PMs orient and attach automatically to the set of the PMA. This self assembly is fairly easy as it does not require any precise alignment tools or bonding agent. After realizing the four sets of PMAs, each one is fixed to the side edges of the Zerodur cross structure as shown in figure 3.3 (b). A thin layer of cyanoacrylate glue was applied to the assembly area (1×14 mm 2 ) and the PMA with pre-assembled PMs in NS configuration was manually pressed against the assembly area for a short period of time. This assembly approach was selected from the perspective to use both sides of the PMA with the help of two PCBs placing on top side and bottom side of the PMA due to the magnetic field symmetry. In addition, the separation distances (d 1 and d 2 ) between the top and bottom PEDCs with respect to PMA surfaces can manually be adjusted to achieve desired electromagnetic forces (see figure 3.3 (c)). Further, to support the mobile part, the glass layer has been fixed at z 1 distance in a through cavity realized in the fixed part (see figure 3.1(b)). These glass beads have been glued to the bottom side of the cross structure as shown in figure 3.5(c).

Scale in millimeters

Fixed part

In order to construct the fixed part of the MPS, first, the designing of a single PEDC that consists of two phase coils with currents I 1 and I 2 has been carried out. For a PMA with a foot print area (w c ×l c ) of 6×14 mm 2 , the PEDC was designed with an array of 52 conductors, each having length l=20 mm and separated by a distance 500 µm. This separation distance (a) was selected to attain a coil pitch (P c ) of 2 mm in order to align the magnetic poles of the PMs in the PMA with respect to conductors. Further, due to After defining the design parameters of a single PEDC, the fixed part of the MPS was constructed with a circular array of the orthogonally separated four PEDCs in xy-plane.

The center to center distance (D= 56 mm) between the PEDCs situated along single axis was selected due to the dimensions of the mobile part as shown in figure 3.6(a). While taking in to account the PCB fabrication edge tolerances (f 1 , f 2 ) of 2 mm, the minimum foot print size (L×W) of the fixed part was set to 80×80 mm 2 . In addition, at the center of the fixed part, a through cavity of 30×30 mm 2 dimensions was defined in order to fix the glass layers to support the mobile part. These dimensions were selected in order to avoid complexity during assembly of the mirrors into the PCB.

Motion range

The planar motion range of the mobile part with above mentioned fixed part dimensions are found to be 10×10 mm 2 about the center of the fixed part in xy-plane. This range is limited due to the length (w p ) of the PEDC which can be increased by adding more number of conductors in the PEDC. However, the addition of conductors may lead to problems like conductor overlap (see figure 3.6(a)) and increase in the overall resistance of the coil. In our MPS design, we have avoided these constraints in order to reduce the fabrication complexity of the PCB.

For the selected design parameters of the fixed part, the rotation range of the mobile part about z-axis can be geometrically defined. A geometrical limit for which all the PMAs remain in the boundary of their respective PEDC (see figure 3.6(b)) has been selected in our case. This choice has been made in order to continuously expose the current carrying conductors to the full width (w c ) of the PMA which is necessary to realize a symmetrical torque along both axes of the mobile part. On the contrary, if the PMA exits the PEDC area, a sudden reduction in translation force over the PMA may appear which can lead to unsymmetrical torques along both axes, thus making it more difficult to control. In addition, this geometrical limit also eliminates the possibility of any contact between the PMAs and the power connectors that are located at the corners as shown in figure 3.6(b). Based on this geometrical limit, the maximum rotation of the mobile part can be geometrically calculated using equation (3.1).

tan θ w p -2w c (D -l c ) -2l (3.1)
This equation takes into account the geometrical parameters of the fixed part and the mobile part (see figure 3.6) to determine the maximum rotation limit of the mobile part.

However, apart from the geometrical calculation, the magnetic field distribution of the PMAs over PEDC is one of the main criteria that limits the rotation capacity. As presented in the previous chapter, the increase in the relative angle between PMA and PEDC in xyplane, results in the reduction of the torque about the center of the mobile part due to the magnetic field variation over PEDC. In this scenario, the injected currents will not be able to rotate the mobile part for large (i.e., >10 • ) rotation angles.

Printed Circuit Board (PCB) fabrication

In order to realize the fixed part, the PCB layouts was designed in CadSoft EAGLE PCB Design Software3 to meet commercial PCB fabrication standards. The approach for fabricating the PEDCs on a single PCB was selected to eliminate assembly errors and achieve uniform dimensions i.e. copper width, height, air gap, etc.

After developing the PCB design, it was fabricated from Multi Circuit Boards Ltd Furthermore, to support the mobile part (via glass beads) over the fixed part, a set of glass layer were installed at the center cavity of the PCB. This set of glass layers consists of a 130 µm thick fine glass layer and a 0.7 mm thick supportive glass layer. The highly polished surface of the fine glass layer was used to achieve the smaller value of friction coefficient between the glass beads and glass layer it self. However, the direct installation of this layer in the PCB cavity was avoided in order to eliminate the possibility of any deflection due to the weight of the mobile part. In addition, the handling of this glass layer was difficult due to its less thickness. So, to solve these problems, an additional chrome coated glass layer with dimensions 30×30×0.7 mm 3 was used. Another purpose, for using this coated thick glass layer was to achieve a reflective surface so that the fixed part can be leveled using a laser during experimentations.

In order to assemble the set of glass layers in the PCB through cavity, the process presented in figure 3.8 has been adapted to realize a 100 µm air gap between the mobile and the fixed part of the MPS. The assembly has been carried out from the bottom side of the PCB. A combination of different set of glass layers (e.g. glass layer A, B and glass wafer, see figure 3.8) having different thickness was used to achieve the desired height in the through cavity of the PCB to assemble the chrome coated supportive glass layer.

In addition, the copper track height (35 µm) along with the height of the glass beads that are assembled to the mobile part (see figure 3

Analysis of the MPS prototype components

The proposed MPS is designed for conveyance purpose and precise positioning in micro applications. This implies that in practice, the center of the mobile part will be installed with a small load. However, due to the electromagnetic actuation principle and design parameters adapted for the MPS, the influence of the LMs on that load need to be assessed in order to qualify the design for experimentation. So, in this section, some analyses have been performed in order to examine different influential parameters at the center of the mobile part.

Influence of magnetic field generated by PMAs

In the mobile part, the PMs assembled to the cross structure will generate some parasitic magnetic field. This can disturb the characteristics of any object susceptible to magnetic field placed at the center area of the cross structure (14×14 mm 2 ) as shown in figure 3.9(a). For example, in biomedicine applications, this parasitic magnetic field can alter the characteristics of micro cells in the specimen. So, a study has been conducted in order to identify the magnitude of this parasitic magnetic field. This study indicates that the magnetic induction due to the PMAs is 1.28×10 -5 T. From the results presented in figure 3.9(b) it was concluded that the magnetic induction generated by the PMAs is very small. So, its influence on any object placed at the center area can be neglected. In addition, a single PMA (e.g. PMA at position 1) will also be subjected to a static magnetic force due to the rest of the PMAs (i.e. PMAs located at position 2,3,4) in the assembly. An analysis has been performed in RADIA R which revealed that for the selected design dimensions of the mobile part, the magnitude of the static magnetic forces is 3.83 µN. This force is very small and its influence is negligible as compared to the electromagnetic forces generated by a single LM (i.e. 35 mN).

Influence of the vibrations

During functioning of the MPS, the horizontal component of the electromagnetic force (F x ) is responsible to drive the mobile part, whereas, the vertical component (F z ) tends to levitate the mobile part. However, the magnitude of this force does not remain constant and as result a small variation in the form of vibrations occurs. The influence of these vibrations generated by each LM can lead to a resonance condition in which the Zerodur R cross structure can fail. In order to examine the influence of these vibrations, first, an analysis has been carried out in order to determine the natural frequency of the structure.

Modes 1 2 3 4 5 6

Structure without load (Hz) 3320 7340 7340 12400 12700 15700 Structure with load (100 g) (Hz) 665 4152 4507 6711 7027 7304 Table 3.1 represents the corresponding natural frequencies for the first six modes of the cross structure. These frequencies limit the MPS to be used at certain speeds.

For example, the displacement at speed 33 mm/s corresponds to the injected current frequency of 3300 Hz, which represents the first mode of the cross structure. During our experiments, the maximum frequency that has been employed is 1 kHz which corresponds to a speed of 10 mm/s. Due to this constraint, the MPS cannot be used at the frequencies presented in table 3.1. However, the interval between the two natural frequencies can be used.

In order to examine the structure under vibrations, an analysis has been carried out (in the Abaqus software) by employing a sinusoidal displacement of 10 µm at the extremities (the faces where PMAs have been attached). The displacement of the center of the cross structure is plotted as a function of excitation frequencies at the extremities of the cross structure. The analysis reveals two resonance frequencies for which the amplitude (195 and 174 µm) is 10 times more then the source amplitude (10 µm). These resonance frequencies correspond to the 1 st and 6 th modes. From the results it can be concluded that the cross structure cannot be used at higher frequencies. However, in our experimentation, the zerodur R cross structure has been used at lower frequencies (< 1kHz) which is three times less excitation frequency then to reach the first mode of vibration.

Assembly errors and their correction

In practice, the manual assembly of the mobile part can results in some relative assembly errors between the PMAs located along a single axis of the mobile part as shown in figure 3.11. These errors can lead to misalignment of the generated electromagnetic force along an axis during motion. For example, in the case presented in figure 3.11(a), the forces generated about the center of the each PMA located along an axis (e.g. x-axis) are offset by a relative distance of ∆x (mm). Due to this offset a small rotation about the center of the mobile part may appear. In order to solve this problem, the relative phase of the injected currents (I 1 , I 2 and I 3 , I 4 ) between the LMs situated along single axis has been modified by adding a corrective term (∆ψ x ) as presented in equation 3.2. In addition, this solution is valid for any misalignment between the LMs along y-axis or the PEDCs along both axes.

I 1 = I max sin(ωt + ∆ψ x ) I 2 = I max sin(ωt + ( π 2 + ∆ψ x ))
Currents in the P EDC 1 of the LM 1 I 3 = I max sin(ωt)

I 4 = I max sin(ωt + π 2 )
Currents in the P EDC 2 of the LM 2

(3.2) with,

∆ψ x = 2π ∆x P m (3.3)
where, P m is the period of the PMA (in our case, P m = 2 mm), ω and I max is the frequency and amplitude of the injected currents, respectively. align the PMA with respect to conductors in the PEDC by generating a small torque. However, due to the parallel architecture of the MPS, the auto alignment feature will leads to misalignment of other PMAs with respect to their facing PEDCs. As a result, a repetitive torque will appear during motion along a single axis thus resulting in displacement loss.

Unfortunately this kind of error cannot be resolved by adjusting the parameters of the injected current such as amplitude, current phase, etc. In our case, to eliminate this error, the defective PMAs were disassembled and then again re-assembled to the cross structure using some alignment tools.

The assembly errors presented in this section are mainly tied up to the assembly procedure and small assembly area on the cross structure. So, in order to solve this assembly problem a new cross structure has been proposed and developed. The detail description of this cross structure is presented in chapter 5. In our initial prototype, the motion loss due to a small rotation error (∆α ≈ 0.75 • ) was carefully reduced by injecting constant currents in the PEDCs parallel to the motion axis.

Experimentation

In this section, the motion characteristics of the initial MPS prototype have been evaluated. However, before realizing the experimental setup of the whole MPS, first an experiment was performed in order to measure the real magnetic field generated by the PMAs. This is necessary firstly, to verify the orientation of the PMs in each set of the PMA and secondly to examine the real value of the magnetic field generated by the PMAs. In the following section, the detail description of this experiment is presented.

Measurement of the real magnetic induction

The real magnetic induction was measured using a Hall sensor (A1301) fabricated by Allegro Microsystems Inc5 and its characteristics are mentioned in table 3.2. This sensor was selected due to its small size and simple application. Further, it provides a corresponding output voltage when exposed to an external magnetic field, which can be acquired though data acquisition modules in real time. The magnitude of the sensor output voltage depends on the intensity and direction of the applied magnetic field. So, in our case, the only limitation of this sensor is that it only interprets the vertical component (i.e. B z component) of the magnetic field. However, this is sufficient in order to verify the magnetic induction strength, the orientation of PMAs and the magnetic model developed in the previous chapter.

To realize the magnetic induction measurement task, the schematic layout presented in figure 3.12 has been adapted. A motorized linear stage (Newport, M-MFC25CC) was mm beneath the Hall sensor with a speed of 20 µm step/s using the motorized linear stage. At each step, the output voltage of the Hall sensor is stored using Labview R software. After doing so, the comparison between the result obtained for a single PMA and FEA results have been performed. A good agreement was found between both results as presented in figure 3.15(a). In addition, the small variation in the experimental results is due to the non uniform dimensions of the PMs assembled in a PMA. This problem is mainly linked to fabrication tolerances (±100 µm) which can not be controlled in commercially purchased PMs.

Furthermore, an analysis has been performed to measure the magnetic flux density variation between the PMAs along both axis (see figure 3.15(b)). This analysis is necessary to avoid large variation in the magnetic field which can deteriorate the performance of the MPS. From the analysis the mean value of these variations was found to be 0.006 T with a standard deviation of ±0.015 T. So, the influence of these small variations on the generation of the electromagnetic forces has been neglected as compared to the electromagnetic forces generated by the real magnetic flux density generated by each PMA.

After analyzing the PMAs, the experiments have been carried out in order to evaluate different motion characteristics of the MPS. The description of these experiments is presented in the following section.

Performance assessment of initial MPS prototype

To demonstrate the motion characteristics of the initial MPS prototype, first the description of the experimental setup and the details regarding the experimental components that had been employed in order to control the prototype will be presented in this section. Afterward, the different motion performances such as speed, displacement range, etc., in open and closed loop control will be presented.

Realization of the experimental setup

To demonstrate the actual motion characteristics of the MPS prototype, first the experimental setup has been realized. This mechanical setup consists of two types of mechanical mountings as shown in the pictorial view along a single axis as shown in the figure 3.16.

Initially, the MPS prototype mounting has been carried out by installing the fixed part (see figure 3.8) onto the tilt stage (A). In addition, due to small height of the tilt stage, a mechanical support (1) was used to acquire the proper height of the fixed part relative to the feedback sensor. The whole mechanical setup of the MPS was fixed on the experimental platform. Afterward, the fixed part of the MPS was leveled with the help of a flat mirror and a laser as depicted in the figure 3.16. Furthermore, a gold coated mirror cube was fixed on the mobile part to facilitates the measurement via non contact technique along both axes in xy-plane. At the end, the complete mobile part was placed on top of the fixed part.

After realizing the MPS prototype mounting, the feedback sensor mounting has been realized. To examine the planar motion characteristics during experimentation, two Fiber Optic Displacement Sensor (FODS) probes have been installed to measure the displacement realized by the mobile part along both axes in xy-plane (see figure 3.17(a)). In order to position/calibrate these sensors in front of the mirror cube, different components (e.g.

Lab jack, tilt stage, manual and motorized linear stages, mechanical supports, etc. and (c). For example, in linear motion case presented in figure 3.17(b), the FODS y that is installed along the motion axis (i.e. y-axis) has been used to measure the change in the displacement ∆y between two positions (1) and (2) of the mirror cube. At the same time, the FODS x which is installed perpendicular to the motion axis (i.e. x-axis) is used to measure the motion straightness and drift effect of the mobile part during experimentation.

Similarly, in the case of planar motion, both FODSs have been used to measure the change in the displacements (∆x and ∆y) in the xy-plane as shown in the figure 3.17(c).

Realization of the motion control unit

After realizing the complete experimental setup, the schematic layout presented in fig-

Data Acquisition Boards (DAQ)

In our experiment setup, two types of the DAQs (purchased from National instrument) have been used. The typical characteristics of these cards are presented in table 3.4.

The input and output of these cards have been managed via an interface developed in LabView R software. Both cards have 16 bits resolution and can be calibrated to a maximum voltage range of ±10 V. The voltage resolution of these cards have been computed via equation 3.4

NI

Voltage resolution = ∆V 2 n = V max -V min 2 n (3.4)
Where, ∆V is the voltage range and n is the number of bits of the NI R DAQ. According to the equation 3.4, for a voltage range of 10 V, the smallest voltage increment that have been realized with PCI-6733 card is 0.15 mV at its 8 analog output channels. Similarly, for the same voltage range, the input PCI-6030E device is able to measure the smallest voltage value of 0.15 mV.

Voltage-to-Current converter (V-C)

In order to drive the LMs of in the MPS prototype, the driving currents have been generated using V-C converters. According to the literature presented previously in this chapter it has been concluded that 0.8 A current per coils of the PEDC is sufficient to drive the

Fiber Optic Displacement Sensor (FODS)

During the experimentation, the displacement measurement of the mobile part has been carried out via non contact technique in order to avoid any disturbances due to the functioning of the feedback sensor or vice versa. In addition, due to the compact size of the MPS prototype the application of conventional sensors in this configuration was difficult.

In our experiments, two FODS have been employed to measure the position of the mobile part (see figure 3.17 because the sensor exhibits very low (<1 V) output voltage as no light is collected by the reception fibers in this zone. In addition, the range of this zone is few microns and the sensor exhibits non linear characteristics. In the zone (2), the FODS response is linear and exhibits maximum sensitivity with respect to other zones. The span of this zone is around 200 µm which depends on the linearity criterion (usually <1%) and reflectivity of the mirror [Benc 06]. Upon further increasing the distance between the FODS probe and the flat mirror, the output response of the FODS enters in the zone (3) which is termed as "transition zone" in figure 3.21(b). In this zone, the output of the FODS reaches to its peak voltage value (≈ 13 V) and start to decrease with respect to increase in the distance. Moreover, in zone (4) the sensor response is non linear. As compared to other zones, the span of this zone for displacement measurement is large (≈4 mm). However, the sensitivity of the FODS decreases with respect to increase in the displacement and the usable range for displacement measurement is around 2.75 mm. In our experiment, the FODSs have been used in zone (2) for high resolution measurement and in zone (4) for long range measurement.

b) Calibration of the FODS in the experiment

The FODSs installed in our experiment have been calibrated using the mechanical setup presented in figure 3.16. At first, a constant current is injected along a single axis to align the mobile part with respect to the PEDCs. Then, the FODS x and FODS y situated along xand y-axis, respectively, were sequentially calibrated by moving it away from the mirror cube with the help of motorized linear stage (see figure 3.16). In addition, a Labview R software has been used for data acquisition and drive the motorized linear stage at 20 µm/s speed. The data acquisition frequency was 100 Hz which represents the band width of the FODS sensor. Furthermore, due to the maximum input voltage limit of the NI R DAQ 6036E, the calibration of the FODS was carried out in the range of 0-10 V.

Due to this limitation, the complete range of the linear zone was reduced to 140 µm as the NI R DAQ saturates at 10V. Figure 3.22 represents the sensitivity curves for the linear and and non linear zones of the FODS x and FODS y . For a linearity criterion <1%, the functional range for displacement measurement with high resolution was found to be 80 µm for both sensors in linear zone and 2.5 mm in the non linear zone. The variation in the sensitivity curves of the FODS x and the FODS y is mostly due to the electronics of the sensors. In linear zone, the displacement measurement resolution of the FODS x and FODS y was found to be 8 nm and 11 nm, respectively. Theoretically, for a half period of the sinusoidal signal the mobile part should perform a displacement of 1000 µm. However, the net displacement realized by the mobile part was found to be 863.58 µm via experiment and 889.18 µm via simulation. The loss between theoretical displacement and the real/simulation results is mainly due to the friction effect. However, despite this friction loss, the experimental results provide a good correlation with the simulated results thus validates the analytical model.

b) Position repeatability:

In order to measure the position repeatability of the MPS prototype, a 10 cycles test was performed in similar fashion as discussed in the linear displacement section. For a mean displacement of 854.54 µm between position A and position B along x-axis, the position repeatability error was calculated to be 4.41 µm. The relative error was computed to be 3.03%. This result shows that the MPS exhibits a small repeatability error which can be further reduced with a closed loop control. During motion, the straightness error is not only because of the lateral displacement, but also due to the assembly error of the mirror cube. Due to the manual assembly of the mirror cube, the mirror cube surface is not parallel to the FODS x . The angle between the displacement axis and the mirror cube surface facing FODS x was measured to be 0.92 • . However, since the FODS x was used in its linear zone so the real straightness was computed by subtracting this error due to the mirror cube. From figure 3.24(b), the straightness for 1000 µm displacement was calculated to be 2.353 µm with a standard deviation of 0.568 µm. Similarly, for the 500 µm displacement, the straightness error was found to be 1.991 µm with a standard deviation of 0.460 µm. These results reveal the auto alignment characteristics of the LMs as discussed in chapter 2.

d) XY Linear profile:

In order to study the xy displacement, all four LMs were used simultaneously. Both FODS x and FODS y were used in their nonlinear zone to measure the long stroke xy linear displacement as shown in figure 3.17(c). A 30 cycle test of linear trajectory in the xy-plane was performed by injecting one period of 1 Hz sinusoidal currents with 0.8 A per coil (peak-to-peak) amplitude.

From the result shown in figure 3.25(a), it can be seen that the trajectory is repeatable from position A to B and vice versa. However, the mobile part deviates in backward trajectory (from position B to position A). This hysteresis is due to the appearance of different torques along an axis which is caused by the assembly error. Taking into account the drift effect during motion and variable sensitivity of the FODSs in non linear zone the amount of linear profile hysteresis in xy-plane was found to be 57 µm. In order to minimize this error, one solution is to reduce the assembly errors at design level by realizing a cross structure with geometrically pre-defined through cavities. In addition, this error can be reduced by adapting a feedback control to minimize the trajectory deviation in real time.

e) Velocity response:

The velocity response was measured along x-axis using FODS x and presented in figure 3.25(b). This test has been realized by injecting the sinusoidal currents I 1 and I 2 in the LM A and LM B at different control signal frequencies.

The experimentally measured velocities along with theoretical values for 10 cycles of linear travel along single axis, are provided in table 3.5. The variation in the experimental results are due to several phenomenons that occur during translation (e.g. micro rotations, drift effect, etc.). In addition, it can be seen in figure 3.25(b) that as the velocity increases the displacement loss also increases. However, from table 3.5, it can be seen that the real velocities are in good agreement with the theoretical values. Furthermore, the maximum speed is around 12 mm/s which is limited due to the inertia of the mobile part of the MPS.

Performance of the MPS in closed loop control

In this section, the motion of the MPS prototype has been controlled via a PI controller.

The desired displacement was achieved by changing the frequency (ω) of the controlling currents with respect to the error computed between desired and real displacement. The selection of PI controller gains depends on several parameters such as dynamics of the prototype, sensitivity of the FODS, etc. To identify the controller gains (K P and K I ) the linear zone of the FODS has been used as the sensitivity remains constant in this zone.

In practice, there are several uncertainties that change the output of the MPS. For example, micro rotations during linear travel and real system motion error can change the sensitivity of the FODSs, impurities (such as dust) can change the sticking and friction force, etc. These uncertainties require complex multi-physics analyses and significant The variation between the simulated results and experimental results in long stroke is mainly due to the application of the FODS x in its non linear zone where the sensitivity varies with respect to the displacement. Furthermore, to measure the position repeatability and precision of the MPS, 10 cycles of square steps have been conducted along x-axis in similar fashion as described previously. The experimental and simulated results are provided in table 3.6. From the experimental results it can be seen that, in short stroke, precision of the MPS reaches 31 nm with a repeatability error of 25 nm. Where as in long strokes this error is less then 1 µm. In addition, the variation in the simulated and experimental results is mainly due to the adhesion effect and FODS characteristics.

c)

Step train response: A step train motion is one of the most common operations for the MPSs applied in micro applications. For example, in the semiconductor industry this type of motion is used to achieve high quality processing in products such as ICs.

Therefore in order to validate this characteristic an experiment along x-axis, with each step equal to 100 µm and moving toward ± 0.5 mm has been conducted. The gain parameters have been kept same as in the case of step response. A very good agreement was observed among the experimental and desired results as shown in figure 3.27. The average settling time (5%) for 100 µm in continuous step was measured to be 306.2 ms.

From this result it can be evaluated that the MPS prototype is able to perform repeatable desired displacement tasks. Chapter 4

Development of a long range linear displacement sensor

This chapter provides the developments regarding the realization of a long range displacement measurement optical sensor. At first, the architecture and working principle of the fiber optic sensor in its common configuration along with its different performance parameters such as resolution, measurement range, etc., will be discussed. Afterward, the long range sensor principle and its fabrication approach will be presented. At the end, experimentation have been carried out in order to validate the functioning of the long range displacement measurement sensor.

Description of the fiber optic displacement sensor

The architecture of the Fiber Optic Displacement Sensor (FODS) used in our study consists of three main components such as a Signal Processing Unit (SPU), a fibre optic cable (consists of a bundle of one emission fiber and four reception fibers combined into an In addition, a reflective target surface (e.g., flat mirror) is needed in order to realize the complete displacement sensor.

Characteristics of the sensor in its common configuration

In this section, the typical characteristics of the FODS, when used in its common configuration2 will be discussed. From figure 4.2 it can be seen that the output voltage of the sensor delivers a linear and non linear relation with respect to the distance between FODS probe and flat mirror. Despite the ability of the sensor to measure the displacement up to few millimeters when used in its non linear zone, the resolution of the sensor remains very poor [Benc 06]. On the other hand, in linear zone the FODS can reach to a very high displacement measurement resolution (up to few nano meters). In this work, our main objective is to realize a long range displacement sensor while utilizing the linear zone of the FODS due to its high sensitivity in this zone. For this task, first, the different characteristics of the sensor such as sensitivity, resolution, range, etc., of the FODS in the linear zone will be presented.

Sensitivity, measurement range and resolution of the sensor

In the linear zone, the sensitivity of the FODS can be determined by applying a linear fit. In order to achieve a best linear fit, the range of the linear zone (i.e., 200 µm, see Where, S axial (V•mm -1 ) represents the axial sensitivity of the FODS.

The axial resolution (R axial ) of the sensor can be determined using the sensitivity (S axial ) and Root Mean Square (RMS) noise (N rms ) of the output voltage of the sensor. It can be mathematically written as in equation (4.2).

R axial = N rms S axial (4.2)
Obviously, the greater is the value of the sensitivity the better is the resolution. In addition, if the RMS noise of the output voltage is low, the sensor can reach nanometer level resolution. In practice, there are several factors that influence the output characteristics of the FODS which limits its functionality during experimentation. For example, in order to obtain higher sensitivity the quality of the target surface plays an important role. Its characteristics can be defined using parameters such as its roughness, flatness and the reflectivity factor. Higher values of the roughness and the flatness of the surface can lead to high value of the RMS noise and linearity error of the FODS during its application [Khia 07]. According to the earlier studies conducted in [Wang 99], it has been concluded that in order to obtain nanometer level resolution of the FODS, the roughness and flatness values of the reflective surface be less then 10 nm and λ/10 (where, λ ∈ [400 nm : 700 nm]), respectively. In addition to these surface parameters, gold coated surfaces lead better sensitivity for a light with a wavelength higher 650 nm due to its higher coefficient of the reflectivity (≈ 0.98), [Khia 07].

The main limitation of the FODS while using it in linear zone is its displacement measurement range. This means that its application in its common configuration into the MPS developed in the previous chapter will eventually limit the motion range of the MPS to a maximum value of 200 µm. For this reason, in the following section a solution has been proposed in order to realize a compact miniature long range displacement sensor.

Long range displacement sensor principle

In order to extend the displacement measurement range of the FODS while using it in its A consequence of the proposed solution is that the sensitivity and resolution of the FODS becomes the function of the displacement angle (α). The new sensitivity (S α ) and resolution (R α ) of the sensor with respect to the axial sensitivity and resolution (i.e., when α=90 • ) can be mathematically written as in equation (4.3).

S α = S axial sin α R α = R axial sin α (4.3)
From the above equation it can be seen that the sensitivity of the sensor will decrease with decrease in mirror displacement angle (α). This effect can be seen in the figure 4.4(c) as the slope of the linearized zone in the case of α=45 • is reduced as compared to the case, α=90 • . This indicates that the resolution of the sensor will deteriorate.

However, it will remain in the range of few nanometers. For example, if the axial resolution of the sensor is 2 nm, the lateral resolution (R α ) will be around 2.828 nm for α=45 • .

Indeed, the value of the lateral resolution is the function of R axial and α, but the sensor operates in the linear zone.

Extending the solution to realize long range measurement

Even with the 40% increase in the measurement range by moving a single mirror at angle (α=45 • ) with respect to FODS probe surface, it still cannot be employed to measure the long range (millimeter level) displacement. So, to solve this problem, the proposed method has been further extended to implement the FODS with a set of tilted mirrors configuration here called "grating" as shown in figure 4.5. A grating consists of a series of repeated tilted mirror (termed as "grating step"), each inclined at angle α as shown in figure 4.5. The main advantage of this approach is that the measurement range of the sensor becomes a function of the number of the grating steps. So, in order to measure the displacement over millimeter level range, more grating steps can be added. In addition, since the sensor is used in its linear zone it will exhibit high sensitivity over each grating step. However, this solution leads to displacement measurement continuity issue during the transition between two adjacent grating steps because a single FODS probe will provide invalid measurement when it illuminates two adjacent grating steps, simultaneously (see figure 4.5). In order to solve this problem, two FODSs are needed to avoid the crossing edge difficulty by means of switching the measurement in between the FODS probes [Prel 06]. For example, in figure 4.5, it can be seen that when grating is at position x 1 , FODS probe (1) is in front of the grating step and provides a valid measurement while FODS (2) illuminates two grating steps at the same time, thus providing an invalid measurement. Similarly, if the grating are moved laterally to a distance "dx", the FODS probes (1) and (2) will provide invalid and valid measurement respectively, at position x 2 .

The proposed design of the long range sensor depends on different geometric parameters such as height and length of the grating steps, FODS probe dimensions, etc. In order to determine these parameters a geometric modelling has been carried out in the following section.

Geometrical optimisation of the long range sensor

In this section, the geometrical modeling has been realized in order to compute the optimal design parameters of the gratings to achieve smallest possible limit of the resolution (few nanometers). From equation (4.3), it can be seen that the lateral resolution (R α ) is inversely proportional to the sin (α). So, in order to decrease the lateral resolution (R α ), the angle (α) should be as large as possible. However, the value of this angle depends on several geometric parameters as shown in the figure 4 The diameter of the illuminated zone (Φ z ) as a function of the emission fiber diameter (Φ e ) can be mathematically defined as in equation (4.4).

Φ z = Φ e + 2d tan β (4.4)
The relation represents that (Φ z ) is a function of the numerical aperture of the emission fiber and the distance between the FODS probe and grating surface (d=d s +d x ).

Since the numerical aperture is constant once the fibers have been selected, the illuminated surface becomes a function of the distance between the probe and gratings (d).

However, this distance consists of a constant value of the security distance (d s ) and the distance (d x ) that varies with respect to the change in the axial displacement (x) between the FODS probe and gratings. If the diameter of the illuminated surface (Φ z ) is less than the grating step length (l) the displacement measurement will be valid for a single probe.

As explained earlier, the FODS will be employed in its linear zone because of its high sensitivity and resolution. Due to the sensor characteristics in this zone the sensor probe will be placed very near to the gratings. However, in order to avoid any collision between the sensor probe and the gratings during experimentation, the security distance (d s ) need to be fixed. Taking in account the diameter of the FODS probe, equation (4.5) provides the basic criterion in order to select the security distance with respect to the inclination of the grating step (α) [Prel 06].

d s > Φ 2 tan α (4.5)

Influence of the FODS probe dimensions

The selection of the FODS probe dimensions is one of the important task in the geometric optimisation of the gratings. From equation (4.5), it can been seen that, for a fixed value of the security distance (d s ) between the sensor probe and the grating step, the diameter of the FODS probe is inversely proportional to the tan(α). So, by increasing the grating step angle (α), the diameter of the FODS probe needs to be reduced accordingly. However, in reality the selection of the FODS probe diameter (Φ) is not a free choice as it depends on several design/fabrication parameters (e.g., numbers, diameter, arrangement, metallic protection of the fibres, etc.,) in commercially purchased fibers.

In order to realize a long range displacement sensor, the FODS probe used in this work consists of Ø2 mm. With these sensor probe diameter, it was concluded in an earlier study conducted at Roberval laboratory, that for a minimum security distance (d s =30 µm), a maximum grating step angle (α) of 3.81 • can be achieved. For this grating step angle, a 15 nm lateral resolution (R α ) was reported for 1 nm axial resolution (R axial ) of the FODS in [Prel 06]. Indeed, in order to improve the lateral resolution of the sensor, the grating step angle (α) needs to be increased. However, for a fixed value of the security distance (i.e., 30 µm) the increase in the grating step angle (α) imposes limitation on the distance (d) between the FODS probe and the grating step.

Figure 4.7 represents the comparison between the sensor probe employed with two types of the gratings having parameters (α 1 , l 1 ) and (α 2 , l 2 ) where (α 1 <α 2 ) and (l 1 >l 2 ).

Assuming that the grating with length (l 1 ) provides a maximum grating step angle of (α 1 ) with FODS probe (Ø 1 =2 mm) as presented in case (a), the maximum perpendicular distance (d 1 ) between the sensor probe and the grating step will be limited to a value of 130 µm due to the working range of the FODS in linear zone (see sub section 4.1.1.1). Now, if the FODS probe is used with the grating having length l 2 , the grating step angle (α 2 ) will lead to a distance (d 2 ) for the same security distance (d s ) to avoid any collision between the FODS probe and grating (see case (b), figure 4.7). However, the value of this distance (d 2 ) will be greater than distance (d 1 ) and as a result the diameter of the illuminated zone (Φ z ) will become larger due to the increase in the distance (i.e., d 1 →d 2 ).

This will lead to a smaller or invalid measurement length over grating step length (l 2 ) due to the grating step angle (α 2 ).

In order to solve this problem, Khiat et al.[Khia 07], proposed to reduce the diameter of the commercially purchased FODS probe. By this way, the sensor probe can easily be placed at the same distance (d 1 ) in front of the grating step with parameters (α 2 , l 2 ) as shown in the case (c) of the figure 4.7.

Φ < Φ 2 1 Φ 2 Φ = 2 m m 1 Φ = 2 m m 1 d 1 d 2
Grating with length l 1 Grating with length l (l < l )

Reduction of the FODS probe diameter

In order to reduce the diameter of the FODS probe, conventional machining approach was selected to reduce the thickness of the steel cladding material that encapsulates the fiber bundle [Khia 07]. However, the machining of the FODS probe described in section 4.1 was not possible as the thickness of the metallic part of the FODS probe was very small (see figure 4.8(a)). So, a new FODS probe has been purchased from OMRON manufacturers. This new sensor consists of seven PMMA fibers each having 175±10 µm diameter and numerical aperture 0.46. Furthermore, the thickness of the metallic part of this new probe allowed us to remove 500 µm from both sides of the probe as depicted in the fig- With this new FODS probe, the functioning of the sensor remains the same as described in the section 4.1. The fiber located at the center of the probe acts as an emission fiber and the other six fibers situated around the emission fiber are the reception fibers.

However, due to the larger number of the reception fibers in the sensor probe and change in the diameter of the fibers in the bundle, an experiment was carried out to determine the range of the linear zone by moving away a flat mirror in front of the new FODS probe (similar to the case presented in figure 4.2). The range of the linear zone of the new FODS was found to be 170 µm. However, after applying a linear fit it has been concluded that for a linearized zone of 130 µm the sensor delivers a maximum sensitivity of 88 mV/µm with a linearity error less than 1%. Based on this information, during geometric model simulation the maximum value of the distance (d) between the FODS probe and grating step has been fixed to 130 µm.

FODS signal overlap criteria

According to the working principle of the long range sensor, a single FODS probe will lead to signal discontinuation (see figure 4.9(a)). A set of two FODS probes are needed in this case. However, it is not necessary that the application of two FODS probes will provide continuous signal measurement. For example, in the figure 4.9(b) it can been seen that, even with two FODS probes, there is a signal interruption which leads to the discontinuity in the displacement measurement. This is due to the relative distance between the two probes with respect to the grating step. To achieve continuity, a signal overlap (x o ) is needed to properly switch between the two sensors as shown in the figure 4.9(c). In addition, it is necessary that in the overlap zone both sensor should provide valid measurement. So in this scenario, the relative distance (δ E ) between the two sensor probes (see figure 4.9(d)) has been selected using equation (4.6).

δ E = (n + 1 2 ) l (4.6)
where, the term n represents a number of the grating step. This parameter is added to avoid the placement complication of the two FODS probe on adjacent grating steps due to their diameters. Moreover, it can been seen in the figure 4.9(d), that the relative distance between the FODS probes (δ E ) has been defined with respect to the centre of the grating step length to obtain a symmetrical overlap zone at the start and end of the

Selection of the bottom grating angle

The value of the bottom angle (δ) of the grating depends on the fabrication procedure adapted to realize the gratings. In practice, this angle can be selected in two different ways for the same grating step angle (α) as shown in the figure 4.10. However, in the second case (when δ > 90 • , see figure 4.10(b)) the real length of the grating (l r ) becomes smaller as compared to the first case (when δ < 90 • , see figure 4.10(a)). This reduction in real length (l r ) is due to increase in the transition zone length, ∆l=h r cos(δ-90 • ), where a single FODS probe illuminates two adjacent grating steps at the same time. In addition, this increase in the transition zone length (∆l) can not be neglected and as a result, in order to achieve valid signal overlap, the distance between two FODS probes (δ E2 ) needs to be increased by a factor ∆l cos(α) as compared to the case where δ < 90 • .

Taking into account the fabrication constraints (e.g., machining tolerance, residual radii at the bottom of the grating due to the tool tip, etc.), in our study, the selection of the bottom angle of the grating has been carried out using criteria, δ ≤ 90 • , as shown in the figure 4.10(a). The main advantage of this approach is that the useful length (l) depends on the height (h) and angle (α) of the grating even if l r > l. So, the residual length of the grating (∆l) can easily be discarded with respect to the case presented in

Simulation results

By taking into account all these geometrical constraints, a simulation in MATLAB R has been carried out for the FODS probe having 1 mm diameter. A 30 µm security distance (d s ) along with 30 µm signal overlap criteria have been selected on the basis of earlier studies in [Prel 06, Khia 07]. Furthermore, during simulation a condition has been employed that if the overlap zone x o is less than 30 µm or the distance (d) between the sensor probes and grating step increases beyond 130 µm (i.e., outside the linear zone of the FODS), the output solution for the theoretical resolution result is set to zero. This condition was adapted for the purpose of simplification in order to facilitates the analysis of the output solutions. that, for the optimal real length (l r = 653 µm) and height (h r = 96 µm) of a grating step, the maximum grating step angle (α) was found to be 8.29 • . In addition, the useful length (l) over a single grating step was computed to be 621 µm for the selected value of the bottom grating angle (δ=70.53 • ). Using equation 4.3, the theoretical limit of the resolution of the long range displacement sensor with these optimal geometrical parameters was computed to be 7 nm for a theoretical axial resolution of 1 nm.

Microfabrication of the planar grating

After determining the optimal geometric parameters of the grating, its fabrication has been carried out. According to the previous studies conducted in [Khia 07] at Roberval laboratory (UTC), it was decided to fabricate this grating via microfabrication. This fabrication technology was selected in order to achieve overall small dimensions of the planar grating with high surface quality (i.e., roughness and flatness parameters in the range of few nanometers) of the grating steps. These characteristics are very difficult to acquire via conventional machining techniques (e.g., shaping, milling, etc.) due to the fabrication constraints such as machine/tool tolerance, material handling, etc. In addition, microfabrication technology leads to the production of miniature components with dimensions from the scale of few micrometer to several millimeter with high accuracy and micrometer level fabrication tolerances. Furthermore, the parallel fabrication (also known as "batch processing") vastly reduce the fabrication cost thus making it more economical solution as compared to conventional fabrication techniques with mechanical tools.

Microfabrication technology is based on collection of different technologies such as lithography, etching, polishing, etc., to fabricate micro components. It has been widely used in the microelectronics industry to realize micro components such as Integrated Circuits (ICs) over the past sixty years. However, this technology demands precise positioning/machining tools for pattern processing, etching solutions for realizing three dimensional structures and most importantly the dust free fabrication environment (known as "clean rooms") in order to avoid any contamination during microfabrication process.

In order to meet these standards, in this work the microfabrication of the planar grating has been carried out at the Institute für Mikrotechnik3 , Technische Universität (IMT-TU)

Braunschweig, Germany which specializes in this technology.

In general, to realize 3D microstructure, the whole microfabrication process can be described as shown in figure 4.13. Initially, the material selection (in the form of wafers) is usually carried out as the machining of different materials demands different fabrication techniques. For example, materials such as glass, aluminum, copper, etc., cannot be machined with respect to their atomic structure whereas, silicon can be machined with respect to its crystallographic orientation. In addition, the choice of the microfabrication techniques is usually carried out with respect to the need of the three dimensional shapes in the selected material.

Once the microfabrication technique and the material are defined, a mask with desired patterns is designed and fabricated. Afterwards, the wafers are prepared for machining by adding different inorganic layers (e.g., silicon dioxide (SiO 2 ), silicon nitride (Si 3 N 4 ), etc.,) that serves as masking layers. In addition, the desired pattern is transferred via photolithography using the developed mask. The transferred pattern is developed and sacrificial layers are removed to expose the desired areas for machining. Next, the wafers are etched using chemical solutions to form 3D shape in the wafers, once the desired structures are achieved, a post processing of the wafers are carried out which includes verification of the desired 3D structure, removal of sacrificial layers, etc. In the end, the specimens (refers to three dimensional structures) are coated if needed and cut from the wafer with the help of precise cutting tools.

Material selection & choice of microfabrication approach

Finishing (e.g., metal coating, specimen cutting, etc.)

Mask designing and its fabrication

Post processing (e.g., validate the geometric parameters, etc.)

Wafer processing (e.g., patterning, mask transfer, etc.)

Etching of the wafer (Realization of 3D structures) FIGURE 4.13: Schematic layout of the overall microfabrication process

In the following text, the presented micro fabrication steps are discussed in detail in order to realize planar gratings at IMT-TU Braunschweig.

Selection of the material and micromachining approach

In our study, a grating has been machined into silicon material. This material is selected due to its low sensitivity to temperature change (2.6×10 -6 • C) and high melting point temperature (1413.85 • C) which makes this material more interesting as most of the microfabrication process (e.g., deposition of sacrificial layers, etc.) is often performed at high temperature (between 80 • C and 180 • C). Due to these listed or non listed characteristics, silicon material is used in many electronic devices such as diodes, transistors, etc., for their important electrical properties.

Classification of silicon material

Silicon material is classified into three different types depending upon its crystalline form as depicted in figure 4.14. The simplest form of the silicon is known as the amorphous form in which the atoms are randomly oriented. The polycrystalline form consists of randomly oriented grains. However, in each grain the orientation of the atoms are along single direction (see figure 4.14(b)). The third form of the silicon which is mostly used in microfabrication is known as monocrystalline form. In this form, the atoms of the silicon material are perfectly oriented along single direction which allows it to be machined

Micromachining of silicon material

Micromachining of the SCS material is usually carried out by removing the silicon material from the substrate via chemical process known as "etching". In this process, the etching agent such as a corrosive liquid (e.g., Potassium Hydroxide (KOH), etc.) or a chemically active ionized gas (known as plasma) is used to chemically react with the unprotected parts of the silicon substrate (see figure 4.16(a)). In literature, the etching with liquid and plasma are also referred as "wet etching" and "dry etching" technologies, respectively. In microfabrication field, both techniques are significantly employed.

However, wet etching approach is mostly preferred due to its low cost, simplicity and high degree of selectivity of silicon material over dry etching [Mado 02]. In this study, to realize three dimensional planar grating in SCS material, we have selected wet etching approach due to the above mentioned characteristics.

Wet isotropic/anisotropic etching

Based on the selected etching approach (i.e., wet etching) in the previous sub section, the removal of the silicon material can be carried out in two different manners. First approach consists of non-directional removal of material from the silicon substrate which is also known as "Isotropic etching". In this approach, the etching agent (usually aqueous acidic solutions containing HydroFloric acid (HF) with Nitric acid (HNO 3 ) reacts with the unprotected parts of the substrate in all directions with the same etching rate. Moreover, the wet isotropic etching is a diffusion limited process, so the only restriction in this etching approach is that the final structure will always be rounded (see figure 4.16(b)).

Mask design and its fabrication

After selecting the silicon wafer, the design and fabrication of the mask have been carried out for the photolithography process. Based on the dimensions for the planar grating computed via Matlab R simulation, the 2D structures of the grating have been designed

in the form of clear areas (w= 614.5 µm) and rectangular stripes6 (t=33 µm) as shown in figure 4.19. The value of the (w) parameter was computed using equation (4.7).

w = l • [cos(α)] -1 (4.7)
where, l is the useful length of the gratings step, α is the grating step angle.

The overall mask design has been optimized to achieve 32 planar grating specimens in single process during experimentation. In addition, a 14×14 mm 2 footprint dimensions for each planar grating was selected in accordance with the mobile part dimensions of the MPS designed in the previous chapter. The design presented in figure 4.19 has been realized with AutoCAD and was written on a blank mask using a mask writer machine (see figure 4.20(a), step 1). The mask used in our study consists of a pre-coated square glass plate with a layer of chrome and photoresist on one side. So, during mask writing process, the mask writer transfer the design by exposing the photoresist with a laser spot. The mask writing direction was carefully selected to achieve smooth edges along the length of the stripes (see figure 4.19).

In addition, some alignment structures have been designed in order to align the silicon wafer with respect to its crystallographic orientation during photolithography process.

Once the mask writing processing was completed, the exposed photoresist was developed using a chemical solution consists of a mixture of AZ 351B (50 ml) solution and water (250 ml) (see figure 4.20(a), step 2). After developing the photoresist, the chrome is etched using a chemical solution (composition: 51 g of Ceric ammonium nitrate Step 2

Photo resist development

Step 3

Chrome etching

Step 4

Photo resist removal

Step 1 defects (e.g., pin holes, scratches, contamination, etc.) under microscope. In step 2, different masking layers have been realized on the silicon wafer. First, a 300 nm thick layer of silicon nitride (Si 3 N 4 ) followed by a 300 nm thick layer of silicon dioxide (SiO 2 ) were realized using Plasma Enhanced Chemically Vapor Disposition (PECVD) machine on the both sides of the silicon wafer (see figure 4.21). After deposition of these layers, a layer of the positive photoresist (ma-P1215) was realized on both sides of the silicon wafer. For this process, 1 ml of the positive photoresist was spun on the top and bottom side of the substrate at 3000 rpm. The photoresist has been cured during each step by performing a soft baking for 1 min at 100 • C . This soft baking is necessary in order to avoid any damage (i.e., scratching) to the photoresist layer in the following step.

In step 4, the photoresist on the top side of the substrate was exposed to the Ultra Violet (UV) light for 8 seconds using the mask shown in the figure 4.20(b). During this process, the pattern of the mask is aligned to the crystal orientation of the silicon wafer. This is done by aligning the flat of the silicon wafer with respect to the alignment structures on the mask (see figure 4.20(b)). The wafer alignment process followed by photoresist exposure process has been carried out using a mask aligner/exposure machine (EV240). This machine is equipped with different systems such as optical alignment system, mask handling system, etc., in order to transfer the mask pattern on the wafer.

After exposing the photoresist to UV-light, it was then developed using ma-D331 developer solution (see step 4, figure 4.21). During this process, an exact image of the mask pattern forms on the silicon wafer as exposed photoresist dissolves in the developer solution. Moreover, the characteristics of the photoresist in the areas where it has been protected by the pattern of the mask (i.e., due to structured chrome layer) changes. The photoresist development time depends on several parameters such as saturation level of the ma-D331 solution, exposure time, structure dimensions, etc. In our case this time was found to be 25 seconds. After the development process, the structured photoresist was inspected under microscope for any irregularities such as improper transfer of the structure, over etching, etc. This inspection is necessary because if there is any problems regarding the development of the photoresist, it should be carried out again or else it can lead to improper etching in following steps and the silicon wafer may become unusable.

After the inspection, the developed silicon wafer is hard baked at 110 • C for 5 minutes.

After the development of the photoresist, Hydrofluoric acid (HF) solution (Concentration 40%, buffered 1:2) was used to etch the silicon dioxide layer (see step 5, figure 4.21). In this step, the photoresist acts as a masking layer, So the unprotected areas where SiO 2 layers is exposed to the HF solution undergoes chemical reaction. The etching of SiO 2 in HF solution is an isotropic process and the etch rate depends on the concentration of the etching solution as well as the etch depth (i.e., thickness of the SiO 2 layer).

In our case, the etch rate of the SiO 2 in the buffered HF solution was found to be around 46 nm/min. So, in order to etch 300 nm thick layer of SiO 2 layer the Silicon wafer was placed in the HF solution for 6 minutes and 30 seconds. After etching the SiO 2 layer, the substrate is rinsed with deionized water in Quick Dump Rinser (QDR) machine to remove all the traces of the HF acid. After properly rinsing the wafer, the it was dried using a spin dryer machine and an inspection has been performed to validate the etching of the SiO 2 layer.

After etching the SiO 2 layer, the photoresist has been removed using acetone and ethanol (see step 6, figure 4.21). The removal of the photoresist was necessary in order to avoid any contamination in the Phosphoric acid (H 3 PO 4 ) solution used for Si 3 N 4 etching.

In step 7, the Si 3 N 4 layer has been etched using 100% concentrated H 3 PO 4 solution at Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

SiO 2 ma P1215 - During the etching process, the solution has been constantly stirred using a magnetic stirrer and the height of the silicon grating steps has been measured using a surface profilometer machine. In addition, the profile of the etched surface has been carefully inspected. Upon finishing the silicon etching process, the wafer was rinsed and dried in order to eliminate the traces of TMAH solution. Afterward, the layers of the Si 3 N 4 and SiO 2 were removed using 40% concentrated HF solution (see step 9, figure 4.21). During this process, these layers dissolve into the HF solution thus leaving the etched silicon substrate behind. After removing Si 3 N 4 and SiO 2 layers, the silicon wafer was rinsed in QDR machine to eliminate the traces of HF solution using deionized water.

Mask

In step 10, the microfabricated silicon grating were coated with different metals (mostly gold, aluminum, chrome) to improve their surface characteristics such reflectivity index, roughness and flatness parameters [Khia 07]. This process was carried out using a Physical Vapor Deposition (PVD) machine. In this machine, the metal being deposited such as gold, aluminum, chrome, etc., on the silicon wafer is converted into vapor in a vacuumed chamber. The concept of the PVD sputtering (that has been carried out in IMT) is based on the ejecting the target material atoms (metal to be sputtered on silicon) with high-energy particles in vacuum environment. These atoms condensate on the surface of the wafer thus forms a fine layer of the metal. In MEMS, PVD sputtering is one of the most widely used techniques to deposit various metallic films on wafers such as platinum, tungsten, etc.

After metal sputtering process, the grating specimens from the wafer were cut using a diamond cutting machine. For this task, the final wafer was coated with 2 ml of the photoresist ma-1215 to protect the gratings from any particles or other contamination during cutting process. After cutting, the silicon grating specimens have been released from the silicon wafer and cleaned using Acetone and ethanol. After fabricating the silicon grating specimens, some analyses have been carried out in order to qualify it for the long range sensor application. In the following section, the descriptions regarding these analyses are presented.

Silicon grating analysis

The microfabricated silicon gratings have been examined using Zygo TM (New view 200) white light interferometric microscope at Roberval laboratory at UTC, France. Our main objective behind this analysis is to extract good quality silicon gratings. The quality of these gratings has been characterized by measuring the values of their surface roughness (R a ) and Peak-Valley (PV) parameters over each grating step (for details, see Annex B).

The PV parameter is the difference between the two extreme points of the surface which can also be interpreted as the flatness of the grating step. Furthermore, since the illuminated zone diameter (Φ z ) of the FODS probe (see figure 4.6) varies between 200 µm to 300 µm over a single grating step, these parameters have been analyzed for a length of 550 µm for each grating step. In the following subsection, some studies have been conducted in order to first, identify the influence of main etching parameters and second, to improve the surface characteristics of the silicon gratings. These studies have been carried out for silicon grating machined with TMAH solution.

Improvement of the grating surface characteristics

In practice, the optimisation of the surface roughness and flatness parameters using wet anisotropic etching technique is not an easy task as it depends on several etching parameters. However, the temperature and concentration (expressed in "%wt" ) of the etching solution are the two main parameters that often lead to different silicon etching rates. The solution was realized with following composition [Khia 07],

• 45.45% of Nitiric acid (HNO 3 )

• 27.27% of Hydrofluoric acid (HF), Concentration 40%

• 27.27% of Acetic acid (CH 3 COOH), Concentration 98%

• 0.5 ml Bromine (Br) for 100 ml of all three acids

This isotropic solution was used to treat the silicon grating at the silicon etch rate of 0.1 µm/min at 21 • C . In his study, the surface treatment of silicon grating realized with KOH solution was carried out for three etch duration such as 5 min, 7.5 min and 10 min.

From experiments, it was concluded that the isotropic polishing of the silicon grating lead to degradation of the surface (see figure 4.27(a)). In order to validate this effect at lower duration time (i.e.,< 5 min), we have used the same solution to treat the surface of the silicon grating fabricated with TMAH solution. Our objective was to polish the surface by removing few nanometers. So, four etch durations such as 0.5 min, 1 min, 2 min, 3 min were used to treat the silicon grating specimens (without metal coating) with average values of R a = 27 nm and PV=114 nm. During experimentation, it was observed that the irregularities on the silicon grating steps were reduced (see figure 4.28(b)), however after analysis it was concluded that the final surface quality degraded even on lower etch durations as shown in the figure 4.27(b).

At high etch duration (i.e., 3 min), the surface irregularities completely diminishes but it leads to high roughness and flatness values. As a result, it was observed that the final grating surface becomes less reflective even when coated with a 300 nm thick gold layer. From our results, it was concluded that isotropic polishing is not suitable in our application so, further studies regarding the isotropic polishing were not conducted. . This chamber is equipped with a pump mechanism to create a high vacuum (<10 -5 mbar). According to Hertz and Knudsen [Dani 04], when a pure substance is placed in a vacuum, it establishes its equilibrium state between solid or liquid phase and gaseous phase at pressure known as saturated vapor pressure. This characteristics is very important for evaporation process. At this pressure, the localized heating of the source metal (i.e., aluminium, gold, etc.), by focusing an electron beam on its surface, thermally releases the atoms from source metal which condensates on the substrate thus forming a metallic film. The thickness of this deposited film can be controlled by changing parameters such as temperature, heating time, etc.

For our application, we have deposited the silicon gratings that was etched with 25% TMAH+IPA solution at 80 • C solution with three different metals, i.e., chrome (Cr), aluminium (Al) and gold (Au). In order to compare the surface quality, the thickness of these metal layers have been kept same (i.e., 300 nm). After examining with the Zygo TM microscope, it has been observed that with the deposition of metallic layer, the silicon surface characteristics improves (see figure 4.22(b)). It can be seen that with 300 nm gold the grating surface roughness and flatness parameters are lower than with 300 nm coated layer of chrome or aluminium. So, on basis of these results and high coefficient of reflectivity (≈ 0.98), gold coating leads to further improvement of surface characteristics of the silicon grating.

Apart from the different surface improvement techniques, the final surface characteristics of the silicon grating also depends on the fabrication constraints such as temperature and concentration variation of the TMAH solution during etching process, presence

Conclusion regarding the silicon grating microfabrication

The microfabrication of the silicon grating for long range sensor application has been carried out in SCS material via wet anisotropic etching technique at IMT-TU Braunschweig.

Furthermore, these silicon gratings have been realized with 25% TMAH solution at 80 • C .

The analysis of the best grating achieved via this process revealed an average surface roughness and flatness values of 14.9 ± 4 nm and 72.8 ± 12 nm, respectively. In order to improve these values different techniques have been studied and it was concluded that the addition of IPA to TMAH solution at 80 • C leads to better surface quality. In addition, with the help of a 300 nm gold layer deposition, the average roughness and flatness values of the silicon gratings fabricated with 25% TMAH+IPA solution were found to be 9.35 ± 3 nm and 35.08 ± 7 nm, respectively.

Long range linear displacement sensor validation

After realizing the silicon gratings with microfabrication at IMT-TU Braunschweig, experiments have been carried out at Roberval laboratory at UTC Compiègne, to validate the long range displacement sensor. For this task, a 300 nm gold coated silicon grating with characteristics, R a = 9.35 ± 3 nm and PV=35.08 ± 7 nm was used with two FODS probes.

In addition, an experimental setup has been realized by fixing the silicon grating on top of a Newport tilt platform which is driven by two motorized linear stages (Newport MFA 25CC) in xy-plane (see figure 4.32(a)). Moreover, a mechanical support in aluminium was realized to hold two FODS probes over the silicon grating. In order to position the FODS probes (e.g., rotation about its axis or height adjustment) with respect to silicon grating, additional devices such as tilt stages, manual linear stages, etc., (no shown in the figure) have been used.

At first, the axial calibration of both FODSs have been carried out in order to determine their typical characteristics such as sensitivity, measurement range, etc. In order to do so, the grating has been levelled in xy-plane using a levelling mirror and laser. Then, both of the FODS probes have been adjusted perpendicularly with respect to the flat grating steps. After adjustment, the axial calibration has been carried out by moving away both FODS probes along axial direction with respect to their facing grating steps (see

FODS probe 1 FODS probe 2 Units

Calibration results of the both sensors along axial direction, i.e., α = 90 From the presented results it can be seen that both sensors exhibit a linear and a non linear zone. In the linear zone, the sensitivities of both sensors remain the same which means that the sensor probes are in front of the grating step. On the other hand, the non linear zone represents the output voltage due to the transition of the FODS probe between two adjacent grating steps. For better explanation, an enhanced view of the output voltage is presented in figure 4.35 in which the linear zones and non linear zones can easily be identified. In our study, the linear zones of the both sensors have been used

to validate the working principle of the long range sensor. These linear zones have been filtered within an output voltage range of 3.25 V to 8.75 V which represents the start limit and end limits of the linear zone of both senors.

Moreover, in order to switch between both FODS probes for continuous measurement, the signal overlap (see figure 4.35) between the linear zone provided by both sensors was found to be 37 µm. This signal overlap value is higher than the one computed via simulation (i.e., 30 µm) in section 4. represents the linearity error in the measurement over the long full length of the planar grating along y-axis. In figure 4.36(b), it can be observed that measurement error consists of periodic peaks. These peaks often appear due to the variation in the flatness of the grating steps as discussed previously in this chapter.

The accuracy of the long range sensor can be computed by the square root of the quadratic sum of different errors such as amplitude of the sensor noise (± 0.20 mV rms , see figure 4.33(b)), quantification noise (± 5 V/2 16 = ± 0.076 mV) and linearity error 0.83% (or ± 36.63 mV at full scale of 5.5 V, see figure 4.36(b)). After calculations, the RMS value of the uncertainty was found to be ± 36.63 mV. So, by taking into account the above mentioned average linear sensitivity (i.e., 12.63 mV/µm) for long range sensor, the uncertainty in the measurement was found to be ± 3 µm.

From the above text, the RMS noise value (± 0.20 mV rms ) with average linear sensitivity (12.63 mV/µm) over complete length of grating, were used to compute theoretical limit of resolution, i.e., 30.8 nm. This resolution value is 4.4 times more than the simulation result (i.e., 7 nm) as discussed in section 4.3.4. This deterioration in the resolution (measured with a linear fit) in comparison to the linear sensitivity that was achieved in the case of translation only along y-axis (i.e., 12.63 mV/µm). As discussed earlier in this chapter, the sensitivity of the FODS used in our study depends on the motion direction of the silicon grating. So, in the planar motion case, when the silicon grating is moved at an angle ψ=45 Moreover, the linearity error has been measured as shown in the figure 4.38(b)). It was found to be ± 0.93% (or ± 47.35 mV) for a the full scale output of 5.5V over each grating step. In the planar motion case, the new RMS value of the uncertainty was found to be ± 47.36 mV. So, with the measured linear sensitivity (S ψ =8.47 mV/µm) value in xy-plane, the uncertainty in the measurement was found to be ± 5.59 µm. In addition, by taking into account the RMS noise value (± 0.20 mV rms ) and the sensitivity of the sensor (S ψ ), the new limit of the resolution (R ψ ) of the long range sensor in xy-plane was found to be 47.22 nm. From these results, it has been concluded that in planar motion, the resolution of the long range sensor deteriorates with respect to displacement angle.

Uncertainty in the displacement measurement

In practice, the developed long range displacement sensor is sensible to certain physical phenomenons such as vibrations, temperature variations, etc., which can lead to uncertainty in the measured displacement. For example, due to the temperature variation, the dimensions of the silicon grating can vary because of the thermal expansion coefficient of silicon material. This can result in variation in the measured lengths with respect to the temperature change. During our experiments, the silicon gratings have been used at ambient temperature which did not influence the measured displacement. However, steep change in the temperature can significantly deteriorate the output of the long range sensor.

Thermal noise of the SPU consists of different electronic components. It can increase the sensor noise which can reduce the limit of the resolution of the sensor. Moreover, in chapter 3, it has been deduced that the mobile part of the MPS undergoes small vibrations. From the perspective of integrated MPS design, the influence of these vibrations will also introduce uncertainty in the displacement measurement via long range optical sensor. In future, these uncertainty aspects of the long range optical sensor will be further investigated to ensure high quality measurement.

Conclusion

A high resolution non contact linear sensor for long range displacement measurement has been developed in this chapter. In the first part, the architecture and functioning of the long range linear displacement sensor has been discussed in detail. In order to achieve compact dimension for the long range linear sensor from the perspective to integrate it in the MPS prototype, the dimensions of different components of the sensor were optimized using a geometric model. In addition, the planar grating have been realized in silicon material using wet anisotropic etching technique with TMAH solution. To improve the surface roughness and flatness parameters of the silicon grating, different solutions have been discussed. However, it was concluded that a concentrated solution containing 25%

TMAH and IPA at 80 • C lead to better surface quality. Furthermore, the deposition of a 300 nm gold coating improved the surface roughness and flatness parameters. With this fabrication method, the best silicon grating obtained provided an average roughness and flatness values of R a = 9.35 ± 3 nm and PV=35.08 ± 7 nm, respectively.

After realizing the silicon grating, the experimental validation of the long range linear displacement sensor was carried out. For this task, the silicon grating has been employed with two FODSs. From the experimental results, it was concluded that the sensor is capable to measure the displacement at a range of 12.5 mm with a high resolution of 30.8 nm in xy-plane.

Chapter 5

Microfabrication of novel cross structure and sensor integration

This chapter presents the integration of long range sensor into the MPS prototype. In order to facilitate the integration of silicon grating and PMAs into the mobile part of the MPS prototype, first, a novel cross structure has been designed to reduce assembly errors. This structure has been realized with microfabrication technology with the aim to achieve compact dimensions. Later, different components of the MPS prototype have been assembled together and experiments have been performed to validate the various motion characteristics such as displacement range, resolution, etc.

Final MPS design layout and sensor integration

In this section, some design modifications have been carried out regarding the MPS prototype. One of the main objectives behind these modifications is to reduce/eliminate the assembly errors such as alignment errors between the PMAs situated along single axis in the MPS, air gap variation between PMAs and PEDCs, etc. These errors appeared because of the difficulty in handling the miniature PMAs and hemispherical glass beads during their manual assembly with Zerodur R cross structure. As a consequence, these assembly errors often lead to deterioration in the mobile part displacement over the fixed part of the MPS due to the generation of the non homogenous electromagnetic forces along a single or both axes (see section 3.1.2).

Moreover, in order to integrate the long range sensor into the MPS, our aim was to fix a set of silicon gratings on top of the mobile part along each axis (i.e., xand y-axis) to measure the long range displacement. Unfortunately, the addition of the silicon grating onto the Zerodur R cross structure will lead to an increase of 380 µm in the total height of the mobile part of the MPS. This additional height value represents the thickness of the silicon wafer in which silicon grating has been realized (see subsection 4.4.1.4). As a result, an air gap value greater than 380 µm is needed between PEDC (placed on the top side) and PMAs to avoid any collision between silicon grating and PCB during functioning of the MPS.

Taking into account the design/assembly constraints of the initial prototype, a novel cross structure design has been proposed as shown in isometric view of the MPS in fig- The proposed cross structure design has been realized with microfabrication technology in silicon material. This fabrication approach was selected due to its simplicity and ability to produce components with micro level fabrication tolerances. In our study, the cross structure has been realized with dry (or plasma) isotropic etching technique in silicon material. The description regarding the microfabrication of the silicon cross structure is presented in the following section.

Microfabrication of the novel cross structure

In this section, the microfabrication of the new cross structure in silicon material has been carried out. This material was selected due to its lower density (2329 kg•m -3 ), high strength1 (129.5 GPa) and low coefficient of thermal expansion (2.6×10 -6 / • C)

[Mado 02]. The lower density of the silicon material leads a light weight cross structure design which interns results in increase in the load carrying capacity of the mobile part in our application. Moreover, the microfabrication approach was selected due to the complication in realizing the small dimensions of the proposed cross structure design such as cross structure thickness (<1 mm), depth of cavities (380 µm), etc., with conventional machining.

For microfabrication of the cross structure, the selection of the silicon wafer was carried out irrespective of the its crystallographic plane orientation. The choice was made due to the high silicon etch rate (≈1.5-1.8 µm/min) characteristics of the Inductively Coupled Plasma (ICP) etching process to achieve structure with vertical side walls (see figure 5.1). So, a Ø100 mm, standard {100} oriented silicon wafer with both side polished was selected to realize the cross structure. This wafer type was selected due to its three times lower cost as compared to the one used to realize silicon grating in our study.

In addition, due to the height of the silicon grating, 0.8 mm thick silicon wafer was used to fabricate deep cavities. This thickness value was selected to avoid maximum height of the PMAs (i.e., 1 mm).

Design and development of the mask

After selecting the silicon wafer, the design and fabrication of the mask have been carried out for photolithography process. In our study, the silicon cross structure was realized in two steps to achieve cavities to hold the silicon grating. Initially the silicon wafer was etched from top side to reach desired etch depth and later it was etched from bottom side to realize through etched structures. For both of these steps, separate masks have been designed to transfer the desired cross structure pattern. Figure 5.2 represents the optimal designs for both masks used in top side and bottom side etching process. The designs of both masks are similar in shape with an exception that mask# 1 contains additional structures for cavities that will not be etched through during machining of silicon wafer.

In step 3, the mask presented in figure 5.2(a), was used to expose the photoresist layer to Ultra Violet (UV) light for 8 seconds. This process was realized with mask aligner/exposure machine. During this process, the wafer flat was first aligned with respect to the alignment structures on the mask. After exposure, the exposed photoresist was developed in ma-D331 developer solution for 25 seconds. After verifying the developed structures in the photoresist layer, the photoresist was cured for 5 min at 100 • C . Then, aluminum etching was carried out with aluminium etching solution2 at 35 • C . After etching the aluminium layer, the wafer was rinsed with deionized water in Quick Dump Rinser (QDR) machine and dried with spin drying machine. Then, the photoresist layer was removed using acetone and ethanol and wafer was again washed (see figure 5.4(a)). After drying the wafer, a 2 µm copper layer was realized on the bottom side (the side without structured aluminium) of the wafer with PVD metal sputtering machine (see step 5, figure 5.3).

This layer serves two purposes. First, it protects the bottom side from any contamination and second, due to high thermal conductively of the copper (401 W/(m•K)) it helps in cooling the wafer from the bottom side with liquid nitrogen, during ICP etching process.

In step 6, the silicon wafer is etched in ICP etching machine. During this process, the structured aluminium layer serves as mask and the plasma in the ICP machine reacts with the unprotected silicon material (on the top side on the silicon wafer). The silicon wafer was etched from the top side for 4 hrs at an average silicon etch rate of 1.6 µm/min (see figure 5.4(b)). After verification of the etch depth with Dektak profilometer, the aluminium and copper layers have been remove using aluminum etching solution in step 7. In the aluminum etching solution both copper and aluminum layers have been removed

until no traces of these metals were observed via naked eye inspection. Then, the silicon wafer was rinsed with deionized water in QDR and dried. At this point, the top face of the silicon cross structure in the silicon wafer can be observed.

From step 8 to step 11, the process has been repeated in similar fashion as described in step 2 to step 5, however during the exposure, mask # 2 (see figure 5.2(b)) was used.

During the alignment process, the etched alignment structures on the top face of the silicon wafer were used to align the mask and wafer. These etched alignment structures were used to achieve an overlap between the outer profile of the silicon cross structure between represents the final shape of the microfabricated silicon cross structure.

Aluminium

Step 1 Silicon

Step 3

UV Light

Step 4

Step 5

Step 6

Step 7

Step 9

UV Light

Step 10

Step 11

Step 12

Step 13

Step 14 structure profiles can easily be seen. Often, after ICP etching process, black silicon appear can be seen on the deeply etched silicon surface. This black silicon is also referred as silicon grass as shown in the figure 5.5(c). According to literature, the appearance of silicon grass is often linked to the oxygen flow rate during the ICP etching process which can be controlled by changing different control parameter such as pressure, gas flow rate, etc.

In our study, the influence of this silicon grass has been neglected due to their small height. In addition, it has been observed that this black silicon often diminishes during cleaning process of the final etched silicon wafer as shown in the figure 5.4(e). From figure 5.5(a) and (b), the supports can be easily seen. After dicing the silicon wafer with diamond cutting machine these supports are scratched with a diamond tip pen.

Final assembly and experimentation

After realizing the silicon cross structure, different components such as PMAs, glass beads, have been calibrated in similar fashion as described in section 3.2.2.2. After calibration, the displacement measurement resolution of FODS x and FODS y were found to be 15 nm and 12 nm, respectively. were found to be 0.21 and 0.18, respectively. For these parameters, the simulation result revealed a net displacement of 973 µm for a theoretically expected displacement of 1 mm along a single axis. Whereas from experimental results the displacement was found to be 978 µm. The small difference between the simulation and experimental results is mainly due to the dynamics of the MPS. From analysis it has been concluded that in comparison to our earlier prototype, the displacement loss due to friction is reduced by 11.78% in the new MPS prototype.

In order to evaluate the planar motion characteristics of the MPS. All four LMs have been injected with 0.8 A current. From the results it can be seen that, the trajectory of the profile is nearly repeatable. The small deviation between backward and forward motion is due to the characteristics of the the FODSs in their non linear zone. However, the maximum deviation in the trajectory was found to 7 µm. This less error indicates that the precise fabrication of the silicon From the result it can be seen that, the measured profile contains a drift effect. The drift effect is because the platform is not perfectly leveled with respect to the horizontal plane. Nevertheless, the error in the measured profile is very small.

In addition, to validate the motion in closed loop control, all four LMs have been injected with 0.8 A sinusoidal currents and the frequency of the injected current has been adjusted via PI control as described in section 2.5.3. For desired displacement trajectory, a sinusoidal signal with amplitude ±165 µm has been used to realize a circular profile of 330 µm. From the results presented in figure 5.8 the tracking error was found to be ± 2.8 µm. Ø1 mm) were used to measure the long range displacement. After the assembly, the sensor have been calibrated and average sensitives were found to be 11.37 mV/µm for x-axis sensor and 10.38 mV/µm for y-axis sensor with a linearity error less than 1% for both FODSs. Taking into the RMS noise values, the resolution of both sensor was found to be 43 nm and 69 nm, respectively. The degradation of the sensor resolution is mainly due to the difficulty of positioning the FODS probes in front of the silicon gratings in the cross structure.

In order to validate the concept, an experiment has been carried out in open loop control to measure long range displacement. This choice was made due to the difficulty in controller design. In future, the PI control will be modified to include the switching behaviour of the long range sensor. However, in this study we have decided to measure the output voltage with respect to the displacement performed by the mobile part. So, for this task along a single axis, PEDCs have been injected with 0.8 A currents with a sampling rate of 1 kHz. The objective was to realize the displacement at very slow speed (i.e., 10 µm/s) along both axis separately. In order to estimate the motion resolution of the MPS prototype, the long range sensor can be used. Since, each grating step provides a measurable length of 621 µm. So, with the help of the PI control, a step response test was conducted without signal switching between two FODSs. For this task, the frequency of the currents in PEDCs have been controlled in similar fashion as described earlier. From the results presented in figure 5.11 it has been concluded that the motion resolution of the MPS prototype is 1.367 µm with a standard deviation of ± 0.285 µm. This rotation is limited because of geometrical limit of the PEDCs and that of aluminium structure. In future, advanced image processing algorithms along with control models will be developed in order to control the rotation motion in real time with high resolution. Chapter 6

Conclusion and perspective

This chapter presents the conclusion by summarizing the works presented in the previous chapters. In addition, a number of perspectives for future research on the basis of the study presented in this thesis will be discussed.

General conclusion

The objectives of the work presented in this thesis concern the development a compact miniature positioning system with integrated sensor that should be able to deliver millimeter level displacement strokes in xy-plane in micro applications. In order to reach our objective, first, a survey has been conducted to evaluate different existing technologies. Based on this survey, electromagnetic based direct drive actuation technology was selected due to its characteristics such as high speed, ability to realize wireless mobile part of the MPS, etc.

After selecting the drive technology, a long range MPS concept has been proposed in chapter 2. The uniqueness of the proposed design lies in its simple design and ability to perform millimeter level strokes in xy-plane with minimum possible overall dimensions of the whole system. The functioning of the MPS has been explained for a single LM due to its symmetrical design. Afterwards, different solutions have been discussed in order to realize the miniature drive components such as planar coils and permanent magnet arrays. Based on these solutions, a permanent magnet array with 14 Permanent Magnets Array (PMA) assembled in North-South configuration have been proposed to realize a compact long range LM. In order to achieve continuous motion of the mobile part, a design of two phase Planar Electric Drive Coils (PEDC) has been proposed. After the description of the long range motion concept for a single LM, the solution is then extended to realize a miniature positioning system with a cross structure design.

After the description of the miniature positioning system, its modelling has been carried out. For the purpose of simplification, models have been developed for a single LM due to the symmetry of the MPS design. These models have been used to simulate the motion behaviour of the complete MPS prototype in open and closed loop control. From the simulation results, it has been concluded that the proposed MPS design can deliver millimeter level strokes in xy-plane.

In chapter 3, the proposed long range MPS design has been realized. In order to do so, the design layout and the description regarding the components used to realize the prototype have been discussed. Different solutions regarding the selection overall design parameters of the fixed and mobile part of the MPS have been carried out. In addition, analyses have been performed in order to qualify the MPS design for long range motion application by taking into account the influence of the magnetic field, vibration and the assembly errors generated over each LM. From these design and analysis, it was concluded that with an overall foot print size of 80×80 mm 2 of the fixed part, the prospered MPS is able to deliver a theoretical motion range of 10×10 mm 2 in xy-plane.

To verify the motion characteristics, experiments have been carried out in open loop control. Then, a PI control has been developed in order to control the motion of the mobile part by changing the frequency of the injected current in the PEDCs situated in the fixed part of the MPS. From these experiments, it has been concluded that the MPS is able to deliver variable stroke ranging from few micrometers to 2 mm with sub micrometer level accuracy. In addition, the MPS prototype can perform motion in xy-plane. It was also concluded that the maximum motion range of the MPS prototype was limited to 2 mm due to the fiber optic sensor used to measure the displacement range.

In order to solve the displacement measurement problem at long range (i.e., millimeter level), a high resolution non contact linear sensor has been realized in chapter 4. In the first part, the architecture and functioning of the long range linear displacement sensor has been discussed in detail. In order to achieve compact dimension for the long range linear sensor from the perspective to integrate it in the mobile part of the MPS prototype, the dimensions of the grating and sensor probe have been optimized using a geometric model.

To realize the long range sensor, its planar grating have been realized in silicon material by realizing a microfabrication process to etch the silicon gratings using wet anisotropic etching technique in TMAH solution. Furthermore, to improve the surface roughness and flatness parameters of the silicon grating, different solutions have been discussed and experimentally tested. From the results obtained after the analysis of the fabricated gratings, it was concluded that a concentrated solution containing 25% TMAH and IPA at 80 • C lead to good surface quality. In addition, the deposition of a 300 nm gold coating improves the surface roughness and flatness parameters. With this fabrication method, the best silicon grating obtained provided an average roughness and flatness values of R a = 9.35±3 nm and PV=35.08±7 nm, respectively.

After realizing the silicon grating via microfabrication, experiments have been carried out in order to validate the long range linear displacement sensor. For this task, the silicon grating has been employed with two FODSs. From the experimental results, it was concluded that the sensor is capable to measure the displacement at a range of 12.5 mm with a high resolution of 30.8 nm in xy-plane.

In chapter 5, the integration of the long range sensor into the MPS prototype has been In our study, we used image processing technique to measure the maximum rotation that can be realized by the MPS. From the experiment, it was concluded that MPS is able to deliver a maximum rotation angle of ± 11 • .

Perspectives

The MPS design presented in this work has a fixed planar stroke (i.e., 10×10 mm 2 ). One of the perspective regarding the proposed MPS design is to further optimize its architecture to achieve larger strokes.

The rotation of the mobile is limited due to the length of the PEDCs. Based on the practical experience with the MPS prototype developed in this work, it was observed that the rotation of the mobile part in xy-plane does not entirely depend on the length of the PEDCs. So, in future it will be a good approach to redesign these coils and realize new models to simulate the rotation behaviour of the mobile part.

Concerning the payload capacity of the current MPS design which is limited to 11 grams, different solutions may be employed to increase its payload capacity. For example, by introducing another set of PEDC can increase the payload capacity due to the generation

  Barre d'aimants permanents, Actionneur électromagnétique, Système de positionnement, Bobines électriques, Entraînement direct, Capteur optique, Microfabrication, Gravure anisotrope du silicium, Dépôt de couches minces, Gravure à sec de silicium. List of figures 1.1 The schematic diagram of the functioning of a positioning system. . . . . 1.2 MPS mechanical design configuration (a) Serial kinematics (b) Parallel kinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Construction of (a) non-integrated (b) integrated positioning systems. . . 1.4 (a) Direct and (b) Converse piezoelectric effect [Bish 08] (c) Piezoelectric stack actuator [PI 12] (d) APA R and PPA, Courtesy of CEDRAT technologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 (a) xy stage [Cedr 11] (b) Silicon xy micro stage [Sabr 09] (c) PIMars TM [PI 12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 (a) Inchworm actuator principle [Benc 06] (b) Micro robot developed by Wu et al., [Wu 04] (c) PiezoWalk drive principle [PI 12](d) NEXLINE R actuator and N-512 Positioning stage [PI 12] . . . . . . . . . . . . . . . . . 1.7 (a) Stick-slip actuator principle (b) [Berg 03] (c) "SMARPOD" [Smar 11] . 1.8 (a) Friction-inertia drive principle (b) "Abalone" [Zesc 95] (c) [Nomu 07] 1.9 (a) Ultrasonic linear motor principle (b) [Mino 96] (c) [Devo 04] . . . . . 1.10 Thermal actuator principle (a) bimetal (b) bimorphe (c) Geometrically constrained single metal based actuator . . . . . . . . . . . . . . . . . . . . . 1.11 MEMS based xy-stages (a) [Lee 09] (b) [Lin 11] (c) µHexFlex [Culp 06] . 1.12 (a) Actuation principle (b) Single silicon leg (c) Micro conveyor [Ebef 00] 1.13 Distributed conveyance system [Chap 04] (a) Object in levitation and motion states (b) MEMS actuators assembly . . . . . . . . . . . . . . . . . . . 1.14 Light weight object handling table [Berl 00] (a) Experimental prototype (b) Schematic of a single pneumatic actuator . . . . . . . . . . . . . . . . 1.15 Conveyor system developed by A.Delettre et al., [Dele 11] (a) Sectioned view (b) Global view (c) Experimental prototype . . . . . . . . . . . . . . 1.16 Principle (a) Parallel-plate electrostatic actuator (b) An electrostatic comb actuator, [Malu 04] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17 MEMS micro stages (a) Liu et al., [Liu 07] (b) Sun et al., [Sun 08] (c) Ji et al., [Ji 10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.18 (a) Takahashi et al., [Taka 07](b) Kim et al., [Kim 03] (c) Ultra small 3DOF manipulator developed by Boudewijn de Jong [Jong 06] . . . . . . . . . . 1.19 (a) LIA principle (b) Dittrich et al., [Ditt 06] (c) Kumagai et al., [Kuma 12] 1.20 LIAs based MPS proposed by Jung et al. (a) [Jung 05] (b) [Jung 10] . . . 1.21 (a) LRA principle (b) Solution proposed by Lee et al., to control the pneumatic actuator [Lee 00] (c) Molanaar et al., [Mole 96] . . . . . . . . . . . 1.22 (a) Building blocks of the stator (b) Interaction principle (c) Schematics of the planar motor (d) Developed prototype Pan et al., [Pan 11] . . . . . . . xv List of figures 1.23 (a) EMA principle (b) Moving coil and fixed PMs construction (c) Moving PMs and fixed coil construction [Benc 06] . . . . . . . . . . . . . . . . . . 1.24 Positioning systems developed by (a) Hu et al., [Hu 06] (b) Yu et al., [Yu 10] (c) Nguyen et al., [Nguy 12] . . . . . . . . . . . . . . . . . . . . . 1.25 Maglev positioning systems developed by (a) Trumper et al., [Trum 98] (b) Holmes et al., [Holm 00] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.26 MPSs developed by Kim et al., [Kim 07] (a) Actuation principle and EMA structure (b) ∆-maglev stage (c) Y-maglev stage . . . . . . . . . . . . . . . 1.27 MPSs constructed with EMAs and compliant mechanism (a) Chen et al., [Chen 04] (b) Chen et al., [Chen 10] (b) Culpepper et al., [Culp 04] . . . 1.28 MPS developed by (a) Gao et al., [Gao 04] (b) Dejima et al., [Deji 05] . . 1.29 MPSs proposed by (a) Lu et al.[Lu 12] (b) Gloess et al.[Gloe 12] . . . . . . 1.30 Long range linear EMA and proposed solution to realize a 3DOF miniature conveyor [Benc 06] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.31 (a) Fiber optic displacement sensor principle (b) Sensor response . . . . . 1.32 Long range sensor (a) working principle [Prel 06] (b) Prototype [Khia 08] 1.33 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 (a) General layout of the positioning system (b) planar motion concept . . 2.2 (a) Electromagnetic actuation principle (b) Directions of the Lorentz force with different configurations of PM and conductor . . . . . . . . . . . . . 2.3 General layout of the long range LM . . . . . . . . . . . . . . . . . . . . . 2.4 (a) Halbach array configuration (b) North-South array configuration. . . . 2.5 Magnetic flux density on both sides of the NS array at an air gap d=170 µm 2.6 Different coil construction (a) Core based formation (b) Separated planar formation (c) Overlapped planar formation [Benc 06] . . . . . . . . . . . 2.7 (a) Two phase coil and cross sectional view (b) PCB model of a PEDC . . . 2.8 Working principle of the LM in four steps (a) PMA with respect to the conductors with currents "I 1 " and "I 2 " (b) Magnetic flux density "B z " relative to the position of the conductors (c) Magnetic flux density "B x " relative to the position of the conductors . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Contribution of currents in generation of translation force (a) two conductors (b) four conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 (a) Direction of motion by changing the phase of the current I 1 to -π/2 (b) Influence of the steady state currents . . . . . . . . . . . . . . . . . . . . . 2.11 Architecture with motion axes of the LMs coincides at (a) single point (b) multiple points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 (a) Unidirectional motion (b) Unidirectional motion with guidance (c) planar motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 (a) Small rotation (b) Restoring torque . . . . . . . . . . . . . . . . . . . . 2.14 Reduction of a single PM to equivalent magnetic charge distribution and its 2D representation in reference frame . . . . . . . . . . . . . . . . . . . 2.15 Reduction of the PMs in a PMA to equivalent magnetic charge distribution 2.16 Reduction of single PM into equivalent current distribution . . . . . . . . . 2.17 Comparison of the magnetic flux density components . . . . . . . . . . . . 2.18 Magnetic flux density measurement in rotation . . . . . . . . . . . . . . . 2.19 Comparison of the magnetic flux density components . . . . . . . . . . . . xvi 2.20 (a) Layout of the MPS with mechanical support (b) Detail view of a single LM with glass bead support . . . . . . . . . . . . . . . . . . . . . . . . . . 2.21 Detail description of a single LM attached to the cross structure . . . . . . 2.22 Schematic layout of the open loop control of a single LM . . . . . . . . . . 2.23 Currents I 1 and I 2 to realize forward and backward linear motion . . . . . 2.24 Open loop model of single LM . . . . . . . . . . . . . . . . . . . . . . . . . 2.25 Schematic layout of the closed loop control of a single LM . . . . . . . . . 2.26 Step response along x-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.27 (a) Sinusoidal displacement response (b) Displacement error along x-axis 2.28 Linear motion realized by the mobile part in xy-plane . . . . . . . . . . . . 2.29 Simulated results of circular motion realized by the mobile part in xy-plane 3.1 (a) Design layout of the MPS prototype (b) Detail view of the center . . . 3.2 Geometrical design and fabricated mechanical cross structure . . . . . . . 3.3 (a) Real view of a single PMA (b) Assembly approach (c) Implementation of top and bottom PEDCs over PMA . . . . . . . . . . . . . . . . . . . . . . 3.4 (a) Levitation force generated in linear and planar motion cases at different air gaps (b) Residual levitation force . . . . . . . . . . . . . . . . . . . . . 3.5 (a) Use of glass layer (b) Variable separation distance via point contact approach (c) Complete mobile part . . . . . . . . . . . . . . . . . . . . . . 3.6 (a) Fixed part dimensions along with partial view of the PMAs aligned to each PEDC (b) Rotation of the mobile part . . . . . . . . . . . . . . . . . . 3.7 Fabricated PCB (a) Bottom view (b) Top view . . . . . . . . . . . . . . . . 3.8 Assembly of the set of glass layer into the PCB through cavity . . . . . . . 3.9 Magnetic induction at the center of the mobile part . . . . . . . . . . . . . 3.10 Response of the cross structure with excitation frequency . . . . . . . . . . 3.11 Assembly errors in the mobile part . . . . . . . . . . . . . . . . . . . . . . 3.12 Magnetic induction measurement principle . . . . . . . . . . . . . . . . . . 3.13 Magnetic induction measurement (a) Schematic layout (b) Experimental setup with enhanced view of the Hall sensor and a single PMA . . . . . . . 3.14 Hall sensor calibration curves . . . . . . . . . . . . . . . . . . . . . . . . . 3.15 (a) Comparison of magnetic flux density (b) Magnetic flux density variation along both axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16 Pictorial view of the mechanical setup along single axis . . . . . . . . . . . 3.17 (a) Real view of the experimental setup (b) Top view, displacement measurement in linear motion case (c) Top view, displacement measurement in planar motion case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18 Schematic layout of the experiment . . . . . . . . . . . . . . . . . . . . . . 3.19 Voltage to current converter unit and its characteristic curve . . . . . . . . 3.20 (a) FODS probe (b) FODS signal processing unit . . . . . . . . . . . . . . . 3.21 FODS (a) Working principle (b) Characteristic curve, V out =f (∆d) . . . . . 3.22 Sensitivity curves both FODSs in (a) Linear zone (b) Non linear zone . . . 3.23 Linear displacement along x-axis . . . . . . . . . . . . . . . . . . . . . . . 3.24 Rectitude of the MPS in linear motion (a) Axial and lateral displacement (b) Real lateral displacement . . . . . . . . . . . . . . . . . . . . . . . . . 3.25 (a) xy-profile (b) Velocity response of the MPS . . . . . . . . . . . . . . . . xvii 3.26 Step response of the MPS (a) Short stroke (b) Long stroke . . . . . . . . . 94 3.27 Step train profile response along x-axis . . . . . . . . . . . . . . . . . . . . 95 3.28 Motion behaviour of the MPS with triangular profile along single axis . . . 96 3.29 (a) Linear motion in xy-plane (b) ± 50 µm circular planar trajectory . . . 96 4.1 Schematic layout of the architecture of the fiber optic displacement sensor 4.2 FODS working principle and its experimentally measured output voltage curve with respect to the position of the flat mirror . . . . . . . . . . . . . 4.3 FODS (a) sensitivity its linear zone (b) resolution [Prel 06] . . . . . . . . . 4.4 (a) Common configuration of the mirror and FODS probe (b) Tilted mirror configuration (c) Increase in the sensor range [Prel 06] . . . . . . . . . . . 4.5 Long range sensor concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Enhanced two dimensional view of a single grating step with FODS probe 4.7 Selection of the FODS probe for geometric modeling . . . . . . . . . . . . 4.8 (a) Old FODS probe with limited cladding material (b) New FODS probe with six reception fibers (c) Real view of the machined new FODS probe . 4.9 FODS signal(a) with single probe (b) with two probes without overlap (c) with two probes with overlap [Prel 06] (d) overlap distance setting . . . . 4.10 Bottom angle grating choices (a) 0 • <δ ≤ 90 • (b) 180 • >δ > 90 • . . . . . . 4.11 Limit of the sensor resolution as a function of the grating length and height 4.12 Theoretical results to represent the overlap between two FODS probe measurement based on the optimal dimensions computed via simulation . . . 4.13 Schematic layout of the overall microfabrication process . . . . . . . . . . 4.14 Different forms of the silicon material [Dech 06] . . . . . . . . . . . . . . 4.15 (a) FCC structure of the silicon (b) Different crystallographic planes in silicon crystal [Rive 04] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.16 (a) Silicon substrate with mask (b) Isotropic etching (c) Anisotropic etching 4.17 Etch rate as a function of etching solution (a) Temperature (b) Concentration [Marc 98] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.18 (a) Possible crystallographic configuration of the silicon wafer (b) Special case (1), α=8.29 • and δ=109.47 • (c) Special case (2), α=8.29 • and δ=70.53 • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.19 Layout of the mask with enhanced view of a single grating specimen . . . 4.20 (a) Fabrication steps of the mask (b) Real view of the fabricated mask . . . 4.21 Micromachining process to realize three dimensional planar silicon gratings 4.22 (a) Microfabricated silicon gratings (b) SEM image of the grating edge . . 4.23 An image of a single measurement zone on the gold coated silicon grating step measured using Zygo TM 200 interferometer machine . . . . . . . . . . 4.24 (a) Measurement zones (b) R a and PV values over each grating step . . . . 4.25 (a) Silicon etch rate at different TMAH concentration [Seid 90], Hill lock formation (b) with 5% TMAH solution (c) with 25% TMAH solution . . . 4.26 (a) R a and PV values of silicon gratings at different temperature (b) Etch rate and total etch time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.27 Isotropic polishing of silicon gratings etched with (a) 40% KOH solution at 80 • C (b) 25% TMAH solution at 80 • C . . . . . . . . . . . . . . . . . . . . 4.28 Silicon grating step surface quality (a) before treatment (b) after 0.5 min (c) after 3 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii 4.29 Silicon etched with 25% TMAH at 80 • C (a) without IPA (b) with IPA . . . 4.30 (a) R a and PV values over each grating step (b) Image taken over a measurement zone with Zygo TM interferometer machine . . . . . . . . . . . . 4.31 (a) Evaporation process in vacuum [Dani 04] (b) R a and PV values with different metal coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.32 (a) Experimental setup of the long range displacement sensor (b) Enhanced view of the FODS probes and gold coated silicon grating . . . . . . 4.33 (a) Calibration curves of the two FODSs along axial and lateral directions with respect to silicon grating (b) Sensor noise . . . . . . . . . . . . . . . 4.34 Output voltage response of the long range sensor . . . . . . . . . . . . . . 4.35 Zoom A: enhanced view of the output voltage signals . . . . . . . . . . . . 4.36 (a) Accumulated output voltage of both sensors probes (b) Linearity error 4.37 (a) Experimental setup (b) Limit of resolution, 30.8 ± 0.27 nm . . . . . . 4.38 Linear motion in xy-plane (a) Accumulated output voltage of both sensors probes (b) Linearity error . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 (a) Isometric view of the MPS prototype (b) Schematic layout of the new cross structure integrated with different components . . . . . . . . . . . . 5.2 Design layout of the (a) top side mask (b) bottom side mask . . . . . . . . 5.3 Microfabrication process of the silicon cross structure . . . . . . . . . . . . 5.4 Different views of the silicon wafer during microfabrication process (a) Top side with structure aluminium (b) Top side etched (c) Bottom side with structure aluminium (d) Top side with 2 µm copper layer (e) Through etched wafer with removed inner part (f) Real view of the microfabricated silicon cross structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 SEM images (a) Partial view of the etched cross structure (b) center view (c) Zoom view of silicon grass . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 (a) Experimental setup (b) Translation along y-axis . . . . . . . . . . . . . 5.7 (a) Linear xy-profile (b) Square profile in xy-plane . . . . . . . . . . . . . 5.8 Circular motion profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Integrated sensor and its enhanced view . . . . . . . . . . . . . . . . . . . 5.10 Open loop response along x-axis and y-axis . . . . . . . . . . . . . . . . . 5.11 Step response realized with long range displacement measurement sensor 5.12 Experimental setup to measure the rotation . . . . . . . . . . . . . . . . . B.1 Schematics of the working principle and real view of the Zygo TM 200 interferometer microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 Measurement of grating surface characteristics and analysis steps . . . . . C.1 Schematic layout and real view of the motorized linear stage . . . . . . . . C.2 Schematic layout of the linear stage control . . . . . . . . . . . . . . . . . xix List of tables 1.1 Characteristics of the presented positioning systems . . . . . . . . . . . . . 1.2 Drive choice in the multi-DOF miniature positioning systems . . . . . . . . 2.1 Generated electromagnetic force at different position during four steps . . 2.2 Static analysis of the electromagnetic force and torque for a single LM . . 3.1 Natural frequencies of the Zerodur R cross structure, [Benc 06] . . . . . . 3.2 Characteristics of the Hall sensor A1301 . . . . . . . . . . . . . . . . . . . 3.3 Comparison of the magnetic induction values at different air gaps . . . . . 3.4 Specification of the NI R DAQs used in the experiment . . . . . . . . . . . 3.5 Velocity response of the MPS prototype in open loop control . . . . . . . . 3.6 Position repeatability in 10 cycles square steps test . . . . . . . . . . . . . 4.1 Definition of the FODS probe and grating step parameters . . . . . . . . . 105 4.2 Characteristics of the two FODS probes used with silicon grating . . . . . . 132 B.1 Typical characteristics of the Zygo TM 200 interferometer microscope . . . . 159 C.1 Characteristics of the Newport motorized linear stage . . . . . . . . . . . . 162

FIGURE 1 . 1 :

 11 FIGURE 1.1: The schematic diagram of the functioning of a positioning system.

  the micro factory concept by developing a small fabrication unit (overall size 625×490×380 mm 3 ) which consists of a micro turning machine, micro milling machine, micro drill machine, etc., [Okaz 04]. This concept could be employed as a solution to reduce the unit production cost of the miniature components. In such desktop factories the positioning of the components or raw material for machining can be realized with miniature positioning conveyors [Benc 06].

  order to realize Miniature Positioning System (MPS) designs, the choice of mechanical structure, drive technology, sensor integration and fabrication technology have been extensively studied. This section discusses the current developments in the positioning systems. The descriptions regarding innovation into the positioning systems are mostly taken from [Ahme 05, Benc 06, Wim 06, Ratc 06, Hell 09, Joub 12].

FIGURE 1

 1 FIGURE 1.2: MPS mechanical design configuration (a) Serial kinematics (b) Parallel kinematics.

  FIGURE 1.3: Construction of (a) non-integrated (b) integrated positioning systems.

•

  FIGURE 1.4: (a) Direct and (b) Converse piezoelectric effect [Bish 08] (c) Piezoelectric stack actuator [PI 12] (d) APA R and PPA, Courtesy of CEDRAT technologies.

FIGURE 1

 1 FIGURE 1.5: (a) xy stage [Cedr 11] (b) Silicon xy micro stage [Sabr 09] (c) PIMars TM

FIGURE 1

 1 FIGURE 1.7: (a) Stick-slip actuator principle (b) [Berg 03] (c) "SMARPOD" [Smar 11]

  FIGURE 1.8: (a) Friction-inertia drive principle (b) "Abalone" [Zesc 95] (c) [Nomu 07]

  FIGURE 1.9: (a) Ultrasonic linear motor principle (b) [Mino 96] (c) [Devo 04]

FIGURE 1 FIGURE 1

 11 FIGURE 1.10: Thermal actuator principle (a) bimetal (b) bimorphe (c) Geometrically constrained single metal based actuator

  FIGURE 1.13: Distributed conveyance system [Chap 04] (a) Object in levitation and motion states (b) MEMS actuators assembly

FIGURE 1

 1 FIGURE 1.15: Conveyor system developed by A.Delettre et al., [Dele 11] (a) Sectioned view (b) Global view (c) Experimental prototype

  similarly charged objects respectively [Beeb 04]. The simplest design of these actuator consists of two facing surfaces called electrodes (figure 1.16(a)). The force is derived from the gradient of the electrostatic potential between the two electrodes. Electrostatic actuators provide contact less actuation but the main drawback of these actuators is their dependency on the electrode facing surface area and the air gap inbetween. This deeply effects the work range of these actuators which restrict their application in micromechanical positioning system designs [Benc 06].

FIGURE 1

 1 FIGURE 1.16: Principle (a) Parallel-plate electrostatic actuator (b) An electrostatic comb actuator, [Malu 04]

FIGURE 1

 1 FIGURE 1.18: (a) Takahashi et al., [Taka 07](b) Kim et al., [Kim 03] (c) Ultra small 3DOF manipulator developed by Boudewijn de Jong [Jong 06]

  For example, Dittrich et al., have developed an integrated planar motor for heavy miniature component conveyance (figure 1.19(b)). Four orthogonally arranged LIAs were used to realize 3DOF motion on a copper sheet. In order to compensate the weight of the planar motor (2.5 kg), air bearings have been used (details not provided). The planar actuator is able to carry 21.5 N load at maximum speed of 0.36 mm/s and is integrated with two optical sensors (resolution 63.5 µm). Similar approach have led Kumagai et al., to develop their 3DOF based planar actuator (figure 1.19(c)). They have used three LIAs in delta (∆) configuration. The core of the planar actuator was realized with 100 magnetic steel sheets resulting in a 4.8 kg total mass. The planar actuator travels over a 1.5 mm copper sheet and offers a payload capacity of 60 N with a maximum 12 m/s 2 acceleration. Three laser sensors were integrated in the planar actuator to provide displacement parameters (details not provided).

FIGURE 1

 1 FIGURE 1.19: (a) LIA principle (b) Dittrich et al., [Ditt 06] (c) Kumagai et al., [Kuma 12]

FIGURE 1

 1 FIGURE 1.20: LIAs based MPS proposed by Jung et al. (a) [Jung 05] (b) [Jung 10]

FIGURE 1 FIGURE 1

 11 FIGURE 1.21: (a) LRA principle (b) Solution proposed by Lee et al., to control the pneumatic actuator [Lee 00] (c) Molanaar et al., [Mole 96]

  followed in multi-DOF planar MPS based on EMAs. The electric coils are placed in the slider part and PMs are fixed on the stator side (figure 1.23(b)). The main advantage of this technique is the ability to extend the travel range of the MPS by adding more number of PMs to the fixed stator. Due to this reason it is mostly applied for MPSs dedicated for object conveyance purposes. In addition, the stator part for these MPSs are often constructed with PMs assembled in specific magnetic orientation to enhance the magnetic field strength (see figure 1.23(b) for Halbach configuration of the PMs). This is because the both sides of the PMs can not be exposed to current carrying coils which limits the per unit area electromagnetic forces generation for the levitation and translation of the mobile part. Based on this technique, Hu et al., Yu et al., and Nguyen et al., have developed their planar MPSs for conveyance application [Hu 06, Yu 10, Nguy 12]. The MPS developed by Hu et al., provides six degrees of freedom and is driven by three EMAs (figure 1.24(a)). The coils of these EMAs are embedded inside the ∆-shape platen that resulted in a 5.91 kg total weight. Moreover, the stator part is realized with PMs matrix to form a concentrated magnetic field. The positioner provides a travel range of 160 mm in a plane with a displacement resolution of 20 nm. The displacement measurement was carried out using three external laser interferometer sensors (resolution = 0.6 nm each). In similar fashion, Yu et al., and Nguyen et al., have developed their compact MPSs with two and six coils, respectively (figure 1.24 (b) and (c)). The overall weight of their platen resulted in 1.5 kg and 0.64 kg, respectively. The travel range of both MPSs is around 20 cm in a plane with the positioning resolution of 8 µm. These positioners are compact in design but in order to compensate the overall weight of the platen they are equipped with aerostatic bearings (details not provided).

  FIGURE 1.24: Positioning systems developed by (a) Hu et al., [Hu 06] (b) Yu et al., [Yu 10] (c) Nguyen et al., [Nguy 12]

  FIGURE 1.25: Maglev positioning systems developed by (a) Trumper et al., [Trum 98] (b) Holmes et al., [Holm 00]

  FIGURE 1.29: MPSs proposed by (a) Lu et al.[Lu 12] (b) Gloess et al.[Gloe 12]

  FIGURE 1.30: Long range linear EMA and proposed solution to realize a 3DOF miniature conveyor [Benc 06]

FIGURE 1

 1 Photodiode LED

PrelleFIGURE 1

 1 FIGURE 1.32: Long range sensor (a) working principle [Prel 06] (b) Prototype [Khia 08]

  Piezoelectric based actuation principle offers great variety of linear actuators from its application point of view. The MPS realized with piezoelectric actuators have a very fast response time and provide a nano metric displacement resolution. However, their direct application restricts their work strokes up to few hundreds of micrometers due to the very small relative deformation (0.1%) of the piezoceramic material [Cart 11]. Their application in step-mode operation (see section 1.3.1.2) offers MPSs with large displacement strokes but they are slow in nature. From integrated design perspective, the integration of feedback sensors is often difficult in MPS based on step-mode operation due to their design [Wu 04, Zesc 95].Thermal and electrostatic actuation technology is often adapted for MPS used in MEMS modules due to their small foot print size. MPS realized with thermal actuators have high power density but at macro/meso scale these actuators deliver slower response time. On the other hand, electrostatic actuators have very high frequency bandwidth but the generated force are relatively low as compared to other actuation principles [Karp 08]. However, the low current consumption characteristics of the electrostatic actuators makes them highly efficient. The main drawback of these actuators is their small working strokes in a single module due to their optimal design and functional limitations.Pneumatically actuated MPSs are clean and deliver strong output forces but due to the digital control of the air flow control unit their accuracy is limited as compared to other actuation technologies. Further, their scale down version is difficult to fabricate due to the complex design of the nozzles. However, their strong output force characteristics are often applied in electromagnetically actuated MPSs to achieve levitation and remove heat generated due to the current flow in conductor at the same time.Electromagnetic actuators are simple in design, easy to control and cost effective solution in most of the positioning systems [Gilb 96]. Further, their application at macro, meso and micro level scale have been well established as compared to other actuation technologies. These actuators demonstrate very high operation speeds as reported by

(

  FID), PiezoWalk Drive (PWD), Comb Drives (CD), Stick-slip actuator (SSA), ElectroMagnetic Actuator (EMA), Linear Induction Actuator (LIA), Linear Reluctance Actuator (LRA), Electric Heat Resistor (EHR), Diameter (Ø) Integrated inside the MPS (*), Displacement resolution (Res.), Actuator Type (A.T) several research groups [Gloe 12, Lu 12, Kim 07]. In order to realize contact less actuation, their ability to generate levitation and translation forces in a single module makes them more compact from their design aspect as compared to other actuation technologies. In addition, this technology results in high actuation forces, long strokes (displacement), low voltage control and bidirectional motion characteristics in MPSs [Voll 10, Mole 00]. From miniaturization point of view, MPSs realized with EMAs based actuation solution is mostly preferred by several researchers due to their flexible design, fabrication (see table 1.1). Further, the input energy required to realize the magnetic field in the case of LIAs and LRAs is no more needed in EMAs due to the PMs which reduces the energy consumption. In addition, these systems offers wire free mobile platforms which further enhance their ability to integrate external components such as sensors, etc. However, the miniaturization of this technology into the micro domain often lead to two kinds of problems. First, the difficulty of fabricating small electric coils and PMs and second reduction in output power due to the miniaturization. In order to solve the first problem related to fabrication of the miniature components for MPSs realized with EMAs, Micro System Technology (MST) have played an important role over the past few years. Currently, PMs and electric coils can easily be realized with small dimensions using micro fabrication technology. Concerning the reduction of output power due to the miniaturization of PMs and electric coils there exist alternate solutions to compensate the force losses due to the miniaturization of EMAs. One of the commonly adapted solution is to levitate the mobile part of the MPS via aerostatic bearings during motion such as in the cases [Deji 05, Gloe 12].

  FIGURE 1.33: Research objectives

  .1. Each LM is an electromagnetic actuator based on the "moving magnets and fixed coils" technique. The MPS consists of a mobile part and a fixed part. The mobile part consists of four orthogonally arranged Permanent Magnet Arrays (PMAs) that are fixed to the edges of a thin cross shaped platform, here called "cross structure". The fixed part consists of orthogonally arranged four Planar Electric Drive Coils (PEDC) in xy-plane. The combination of a single PMA and facing PEDC acts as an LM. By this way four LMs such as LM A , LM B , LM C and LM D , can be distinguished (see figure 2.1).

FIGURE 2

 2 FIGURE 2.1: (a) General layout of the positioning system (b) planar motion concept

FIGURE 2

 2 FIGURE 2.2: (a) Electromagnetic actuation principle (b) Directions of the Lorentz force with different configurations of PM and conductor

  FIGURE 2.3: General layout of the long range LM

FIGURE 2

 2 FIGURE 2.4: (a) Halbach array configuration (b) North-South array configuration.

FIGURE 2. 5 :

 5 FIGURE 2.5: Magnetic flux density on both sides of the NS array at an air gap d=170 µm

  FIGURE 2.6: Different coil construction (a) Core based formation (b) Separated planar formation (c) Overlapped planar formation [Benc 06]

"

  vias" as shown in the PCB model of the PEDC in figure 2.7(b).

  FIGURE 2.7: (a) Two phase coil and cross sectional view (b) PCB model of a PEDC

  figure 2.9(a)). In order to reduce this effect, W. J Kim[Kim 97] proposed to increase the number of phase currents facing Halbach array. This ensures the generated electromagnetic force overlap between the adjacent conductors and reduces the fluctuations during motion. A Similar solution can also be applied to NS array by introducing another set of current carrying coils (I 3 , I 4 ) with relative phase shift of π/4 on the top side of the PMA as shown in the figure2.9(b) for a single period of the PMA. The value of the phase shift depends on the number of input phase currents and the relative position of the coils. However, in real case scenario the relative position of these conductors may vary due to the fabrication or assembly errors. So, a corrective phase term "∆ϕ i " can be added to adapt these variations in the phase currents as presented in equation (2.5). Due to this conductor arrangement, the total translation force generated over a period of the PMA is the sum of the force contributed by each conductor.

[

  FIGURE 2.11: Architecture with motion axes of the LMs coincides at (a) single point (b) multiple points

  FIGURE 2.13: (a) Small rotation (b) Restoring torque

  FIGURE 2.14: Reduction of a single PM to equivalent magnetic charge distribution and its 2D representation in reference frame

FIGURE 2 .

 2 FIGURE 2.15: Reduction of the PMs in a PMA to equivalent magnetic charge distribution

  FIGURE 2.16: Reduction of single PM into equivalent current distribution

FIGURE 2

 2 FIGURE 2.17: Comparison of the magnetic flux density components

FIGURE 2 .

 2 FIGURE 2.19: Comparison of the magnetic flux density components

FIGURE 2

 2 FIGURE 2.20: (a) Layout of the MPS with mechanical support (b) Detail view of a single LM with glass bead support

  in a PMA with each PM having dimensions 1×1×6 mm 3 and remanent magnetization B r =1.43 T as shown in figure2.21. The PEDC was modeled with an array of 50 conductors separated by a distance (d a ) of 500 µm and with each having length (L c ) of 20 mm. These conductors represent the two phase coils with currents I 1 and I 2 flowing through them with a relative phase difference of π/2. The pitch of a single coil turn is 2 mm which is equivalent to the period of the PMA (2π).

FIGURE 2

 2 FIGURE 2.21: Detail description of a single LM attached to the cross structure

FIGURE 2 .FIGURE 2

 22 FIGURE 2.22: Schematic layout of the open loop control of a single LM

FIGURE 2 FIGURE 2

 22 FIGURE 2.25: Schematic layout of the closed loop control of a single LM

  FIGURE 2.27: (a) Sinusoidal displacement response (b) Displacement error along x-axis

experimentation

  have been carried out in order to simulate the motion behaviour of the MPS. A three dimensional magnetic flux distribution model has been presented along with Lorentz force computation model. In addition, the mechanical modeling has been carried out which integrates both electromagnetic force computation model and friction forces computation model due to the mechanical support. At the end, the developed analytical models have been used to evaluate the dynamic performances of the MPS in open loop control. For precise positioning, a PI control was adapted to realize a closed loop control model. From the simulation, the developed models have been evaluated by subjecting the MPS to different motion scenarios in open loop and closed loop control.In this chapter, the development of the MPS prototype and it's assessment to realize planar motion have been carried out. In the first part of this chapter, the detail design layout of the MPS and construction of it's components will be discussed. In addition, different design and fabrication solutions adapted to realize two parts based compact MPS will be presented. In the second part of this chapter, experimentations have been carried out in order to examine the different motion characteristics of the MPS in open and closed loop control. Different linear and planar motion trajectories have been realized to examine the dynamic behaviour of the complete system.

  FIGURE 3.1: (a) Design layout of the MPS prototype (b) Detail view of the center

Figure 3

 3 Figure 3.3 (a) represents the real view of a PMA.

FIGURE 3

 3 FIGURE 3.3: (a) Real view of a single PMA (b) Assembly approach (c) Implementation of top and bottom PEDCs over PMA

Figure 3 .

 3 Figure 3.4(a), represents the generated levitation force in two motion scenarios of the mobile part, i.e. linear motion along single axis and planar motion in xy-plane. For both cases, the residual levitation forces (F net =F z -W) have been computed using the total weight of the mobile part (W = 82.50 mN) as shown in figure 3.4(b). From analysis, it has been concluded that for worst motion case scenario when only two LMs are used to compensate the total weight of the mobile part, the separation distance between the PMA and PEDC must be less then 140 µm to avoid the adherence effect during motion. In planar motion case scenario, all four LMs are used so at separation distance of 140 µm between

  FIGURE 3.5: (a) Use of glass layer (b) Variable separation distance via point contact approach (c) Complete mobile part

FIGURE 3

 3 FIGURE 3.6: (a) Fixed part dimensions along with partial view of the PMAs aligned to each PEDC (b) Rotation of the mobile part

FIGURE 3

 3 FIGURE 3.7: Fabricated PCB (a) Bottom view (b) Top view

  FIGURE 3.8: Assembly of the set of glass layer into the PCB through cavity

FIGURE 3 . 9 :

 39 FIGURE 3.9: Magnetic induction at the center of the mobile part

FIGURE 3 .

 3 FIGURE 3.10: Response of the cross structure with excitation frequency

Figure 3 .

 3 Figure 3.11(b) represents angular misalignment error ∆α (degrees) of a single PMA along an axis. The appearance of this error is linked to several parameters such as fabrication tolerances of the PMs, improper machining of the cross structure edge, uneven thickness of the bonding resin between the PMA and the cross structure, etc. The presence of this error results in non uniform distribution of the magnetic field over the conductors in the PEDC. As a result, during motion the auto alignment feature of the LMs will tend to

FIGURE 3

 3 FIGURE 3.14: Hall sensor calibration curves

FIGURE 3

 3 FIGURE 3.15: (a) Comparison of magnetic flux density (b) Magnetic flux density variation along both axes

FIGURE 3

 3 FIGURE 3.16: Pictorial view of the mechanical setup along single axis

  FIGURE 3.17: (a) Real view of the experimental setup (b) Top view, displacement measurement in linear motion case (c) Top view, displacement measurement in planar motion case

  MPS prototype. So, by taking into account different parameters such as resistance of the each coil in the PEDCs, maximum output of the PCI-6733 DAQ, etc., the converters used in our experiment are able to generate ±3 A for a voltage range ±10 V with a frequency bandwidth of 50 kHz (see figure3.19(a)). These converters have two input voltage channels (to feed PCI-6733 DAQ output voltage) and two output current channels to inject currents into each coils in a single PEDC. Two pairs of such converters were used in order to drive all four LMs individually.In addition, to examine the output current generated over a single channel, a ramp of input voltage signal with an increment of 0.25 V was applied for a load of 2Ω. Figure 3.19(b) represents the output current generated over each channel which indicates that the voltage to current conversion is linear with a linearity error less then 1%.

  FIGURE 3.19: Voltage to current converter unit and its characteristic curve

FIGURE 3

 3 FIGURE 3.20: (a) FODS probe (b) FODS signal processing unit

FYF

  FIGURE 3.22: Sensitivity curves both FODSs in (a) Linear zone (b) Non linear zone

Figure 3 .

 3 Figure 3.23 represents three cycles of repeated motion of the mobile part along x-axis between position A and B. In addition, the experimental result has been compared with the simulation results. The mean value of the simulated and experimental positions A (B) were found to be 66.67 µm (955.85 µm) and 65.01 µm (928.59 µm), respectively. The large difference between experimental and simulated results at position B is because of the low sensitivity of the FODS in zone (2) of the sensor.

c)FIGURE 3

 3 FIGURE 3.23: Linear displacement along x-axis

FIGURE 3

 3 FIGURE 3.25: (a) xy-profile (b) Velocity response of the MPS

  computational time, programming and experimentation. So, instead of using the global gain values for the PI controller, an approximation was carried out by selecting different gain values such as (K P = 0.077, K I = 0.010) for x-axis and (K P = 0.085, K I = 0.012 ) for y-axis in a manner to avoid any overshoot. a) Square step response: At first, the step response of the MPS has been realized for two cycles at short stroke within the range of the linear zone of the FODS x . The results obtained have been compared with the simulation results and a good agreement was found (see figure3.26(a)). Afterward, for the same gain values, the step responses of the MPS in long strokes (i.e. 0.5, 1, 1.5 and 2 mm) were carried out by using the FODS x in its non linear zone (see figure3.26(b)). The average settling time was computed to be 0.921 s (5%) for long strokes and 0.256 s (5%) for short stroke.

FIGURE 3

 3 FIGURE 3.26: Step response of the MPS (a) Short stroke (b) Long stroke

FIGURE 3 .

 3 FIGURE 3.27: Step train profile response along x-axis

FIGURE 3 .

 3 FIGURE 3.28: Motion behaviour of the MPS with triangular profile along single axis

FIGURE 3

 3 FIGURE 3.29: (a) Linear motion in xy-plane (b) ± 50 µm circular planar trajectory

FODS

  probe) and a reflective target surface as shown in figure 4.1. The SPU consists of the electronic circuitry which controls a Light Emitting Diode (LED) to generate a light at 670 nm wavelength and a Photo Diode (PD) with a detection zone of 1 mm 2 to convert the collected light via reception fibers into the electrical signals. The fiber optic cable consists of five multimodes PolyMethyl MethAcrylate (PMMA) fibers (purchased from OMRON 1 manufacturers) which are combined in a Ø 2 mm steel probe. In the FODS probe, the emission fiber (Ø 486 ±10 µm) is located in the center whereas, the reception fibers (each having Ø 240 ±10 µm) are symmetrically located around the emission fiber (figure 4.1). The numerical aperture of both types of fibers in the FODS probe is 0.46 [Khia 08].

FIGURE 4 . 1 :

 41 FIGURE 4.1: Schematic layout of the architecture of the fiber optic displacement sensor

FIGURE 4

 4 FIGURE 4.2: FODS working principle and its experimentally measured output voltage curve with respect to the position of the flat mirror

  figure 4.3(a)) is often reduced to minimize the linearity error. The slope of the best linear fit (i.e., change in the output voltage (∆V) with respect to the change in the distance (∆d) between the flat mirror and the sensor probe) represents the sensitivity of the sensor. Furthermore, the sensitivity of the sensor can be mathematically written as in equation (4.1). The FODS used in our study delivers a 60 mV/µm sensitivity over the range of 130 µm with 0.67% linearity error.

  FIGURE 4.3: FODS (a) sensitivity its linear zone (b) resolution [Prel 06]

  figure 4.4(a) and (b)). From the results it can be seen that in common configuration (i.e.,

FIGURE 4

 4 FIGURE 4.4: (a) Common configuration of the mirror and FODS probe (b) Tilted mirror configuration (c) Increase in the sensor range [Prel 06]

FIGURE 4 . 5 :

 45 FIGURE 4.5: Long range sensor concept

FIGURE 4 . 7 :

 47 FIGURE 4.7: Selection of the FODS probe for geometric modeling

  ure 4.8(b). The new width dimension of the sensor probe was obtained as 1 mm. A further reduction of the metallic part was avoided in order to leave some metallic protection to hold the fiber bundle intact after machining as shown in the figure 4.8 (c).

FIGURE 4

 4 FIGURE 4.8: (a) Old FODS probe with limited cladding material (b) New FODS probe with six reception fibers (c) Real view of the machined new FODS probe

FODSFIGURE 4

 4 FIGURE 4.9: FODS signal(a) with single probe (b) with two probes without overlap (c) with two probes with overlap [Prel 06] (d) overlap distance setting

FODSFIGURE 4

 4 FIGURE 4.10: Bottom angle grating choices (a) 0 • <δ ≤ 90 • (b) 180 • >δ > 90 •

  figure 4.10(b). As a result, to achieve valid signal overlap, the distance between two FODS probes (δ E ) remains the same. For our simulations, the value of the bottom angle of the grating (δ) was kept 70.53 • . This value corresponds to the crystallographic orientation of the slow etching planes (i.e., {111} plane) of the silicon when planar grating is realized via microfabrication in single crystal silicon substrate. The choice regarding the selection of this angle (δ) is discussed in the section 4.4.1.4.

Figure 4 .

 4 Figure 4.11 represents, the theoretical lateral resolution (R α ) of sensor with respect to the length (l) and height (h) of the grating step. From the results it has been concluded

FIGURE 4 .

 4 FIGURE 4.11: Limit of the sensor resolution as a function of the grating length and height

FIGURE 4 .

 4 FIGURE 4.12: Theoretical results to represent the overlap between two FODS probe measurement based on the optimal dimensions computed via simulation

  figure 4.14(b) with marker (a flat or a notch) to identify the crystallographic orientation of the silicon crystal.

FIGURE 4 .

 4 FIGURE 4.15: (a) FCC structure of the silicon (b) Different crystallographic planes in silicon crystal [Rive 04]

FIGURE 4 .

 4 FIGURE 4.16: (a) Silicon substrate with mask (b) Isotropic etching (c) Anisotropic etching

FIGURE 4

 4 FIGURE 4.17: Etch rate as a function of etching solution (a) Temperature (b) Concentration [Marc 98]

FIGURE 4 .

 4 FIGURE 4.19: Layout of the mask with enhanced view of a single grating specimen

[(NH 4 ) 2

 2 Ce(NO 3 ) 6 ] + 324 ml of Perchloric acid [HClO 4 ]). This solution etched the chrome in the areas where it is not protected by the developed photoresist (see figure4.20(a), step 3). After etching the chrome, the mask has been rinsed and inspected under microscope to verify the structures. After verification, the photoresist is removed with the help of acetone and ethanol (see figure4.20(a), step 4). The finished mask consists of transparent and non-transparent (covered with chrome) areas as shown in the figure4.20(b).

(

  FIGURE 4.20: (a) Fabrication steps of the mask (b) Real view of the fabricated mask

FIGURE 4

 4 Photoresist exposure

  Figure 4.22(a) represents three different planar gratings, each having dimensions 14×14×0.38 mm 3 and coated with 300 nm thick chrome, aluminium and gold material, respectively. To provide a better view of the grating steps, figure 4.22(c) represents the Scanning Electron Microscope (SEM) image of the edge of the gold coated grating. In this figure the grating step (i.e., the slowest etch plane {111}) and different parameters such as height, angle and length can be clearly identified.

FIGURE 4

 4 FIGURE 4.22: (a) Microfabricated silicon gratings (b) SEM image of the grating edge

Figure 4 .

 4 Figure 4.23 represents an image of a single measurement zone via Zygo TM (New view 200) microscope. The roughness and PV parameters in this zone were found to be 15 nm and 95 nm. From figure 4.23, it can be seen that the grating surface is not uniform which means that the values of these parameters will vary over each grating step. So, in order to estimate the average roughness and PV values of the complete planar grating, each grating step has been analyzed separately over its length by taking into account different measurement zones (see figure 4.24(a)).

FIGURE 4 .

 4 FIGURE 4.23: An image of a single measurement zone on the gold coated silicon grating step measured using Zygo TM 200 interferometer machine

FIGURE 4

 4 FIGURE 4.24: (a) Measurement zones (b) R a and PV values over each grating step

FIGURE 4

 4 FIGURE 4.25: (a) Silicon etch rate at different TMAH concentration [Seid 90], Hill lock formation (b) with 5% TMAH solution (c) with 25% TMAH solution

  Figure 4.26(a) represents the variation of R a and PV values. It can been seen that at lower etching temperature the etch rate of the silicon is very low (see figure 4.26(b)) which results in high roughness and flatness values.However, at higher temperature the silicon etch rate is very high and the resulting surface provides lower roughness and flatness values. In addition, the total etch time required to completely etch the silicon grating steps is decreased. From these measured results, we concluded that at 80 • C , the average surface roughness and PV values always remain less than 20 nm and 90 nm, respectively (see figure4.26(a)). At this concentration and temperature of the TMAH solution the average silicon etch rate and total etching time were found to be 0.37 µm/min and 3.5 hours, respectively.Chemical polishing: One of the techniques to achieve a flat surface is to perform chemical polishing after anisotropic etching. Since, the solutions used in the chemical polishing process exhibit isotropic etch characteristics (i.e., the solutions do not etch the silicon material with respect to its crystallographic orientation (see subsection 4.4.1.3)) they can be used to remove the sharp peaks on the final etched silicon surface [Boge 67]. Earlier,

FIGURE 4 .

 4 FIGURE 4.26: (a) R a and PV values of silicon gratings at different temperature (b) Etch rate and total etch time

FIGURE 4 FIGURE 4

 44 FIGURE 4.27: Isotropic polishing of silicon gratings etched with (a) 40% KOH solution at 80 • C (b) 25% TMAH solution at 80 • C

  FIGURE 4.29: Silicon etched with 25% TMAH at 80 • C (a) without IPA (b) with IPA

FIGURE 4

 4 FIGURE 4.30: (a) R a and PV values over each grating step (b) Image taken over a measurement zone with Zygo TM interferometer machine

  FIGURE 4.31: (a) Evaporation process in vacuum [Dani 04] (b) R a and PV values with different metal coating

  figure 4.6(b)). The output voltages from both sensors have been plotted with respect to the axial displacement and linear fits have been applied as shown in the figure 4.33(a).From figure, with the help of linear fits, the sensitivities of the FODS 1 and FODS 2 were found to be 87.98 mV/µm and 82.85 mV/µm, respectively. The difference between the sensitives of both sensors is due to various factors such as deterioration of the PhD and its coupling with the reception fibers in the SPU, etc.

FIGURE 4 .

 4 FIGURE 4.32: (a) Experimental setup of the long range displacement sensor (b) Enhanced view of the FODS probes and gold coated silicon grating

  FIGURE 4.33: (a) Calibration curves of the two FODSs along axial and lateral directions with respect to silicon grating (b) Sensor noise

  After calibrating both FODSs, the silicon grating was displaced with the help of the motorized linear stage situated along y-axis (see figure4.32(a)). In order to avoid any vibrations due to the motion of the linear stage, the translation speed was kept 1 µm/s.The experiment was carried out in open loop by measuring the output voltage response of both FODSs using a LabView R software.

  FIGURE 4.34: Output voltage response of the long range sensor

  figure 4.35) which results in motion of the silicon gratings along y 1 -axis. In practice, this

  Figure 4.36(b),

FIGURE 4 .

 4 FIGURE 4.36: (a) Accumulated output voltage of both sensors probes (b) Linearity error

  FIGURE 4.37: (a) Experimental setup (b) Limit of resolution, 30.8 ± 0.27 nm

FIGURE 4

 4 FIGURE 4.38: Linear motion in xy-plane (a) Accumulated output voltage of both sensors probes (b) Linearity error

  FIGURE 5.1: (a) Isometric view of the MPS prototype (b) Schematic layout of the new cross structure integrated with different components

  the bottom and top face to for through etching. Once the mask pattern is transferred into aluminum layer and a 2 µm copper layer is realize as shown in the figure5.4(c) and (d), the dry isotropic etching was carried out on the bottom face of the silicon wafer in ICP etching machine (see step 12, figure5.3). The silicon wafer was etched until the structures are through etched. Upon finishing, the aluminium and copper layers are removed with aluminium etching solution (see step 13, figure5.3). At this point the silicon cross structure profile is through etched. After cleaning the wafer in QDR, the silicon cross structure has been released from the rest of the silicon wafer with diamond cutting machine. The inner parts of the cross structure have been removed by breaking the small cross structure supports with diamond pen as shown in the figure5.4(e). Afterwards the cross structure is rinsed with ethanol and dried. The isometric view in step 13, figure 5.3

FIGURE 5. 3 :

 3 FIGURE 5.3: Microfabrication process of the silicon cross structure

FIGURE 5

 5 FIGURE 5.4: Different views of the silicon wafer during microfabrication process (a) Top side with structure aluminium (b) Top side etched (c) Bottom side with structure aluminium (d) Top side with 2 µm copper layer (e) Through etched wafer with removed inner part (f) Real view of the microfabricated silicon cross structure

  and a mirror cube have been assembled together. An experimental setup has been realized to validate the new cross structure deigns as shown in the figure 5.6(a). To hold the fixed part of the MPS, an aluminum structure with dimensions 130×130×10 mm 3 has been fabricated. Two FODS probes have been installed to measure the displacement performed by the mobile part in xy-plane. Both of the FODSs (i.e., FODS x and FODS y )

Figure 5

 5 Figure 5.6(b) represents the linear response of the silicon cross structure based MPS along y-axis in open loop control. An amplitude of 0.8 A for the injected currents were used in the PEDCs to generate electromagnetic forces.Figure 5.6(b) represents the sim-

  Figure 5.6(b) represents the simulated response (computed via model presented in section 2.5.2) and experimentally measured response of the MPS. For simulation results the new values of the total weight (i.e., 4.7 gms) of the mobile part have been used. In addition, since the glass beads are not the similar to the one used earlier with Zerodur R cross structure, the new friction values have been experimentally determines using inclined plane technique. The new values of the static friction coefficient (µ static ) and dynamic friction coefficient (µ dynamic )

  Figure 5.7(a) represents the linear profile in xy-plane.

  FIGURE 5.6: (a) Experimental setup (b) Translation along y-axis

FIGURE 5 .

 5 FIGURE 5.7: (a) Linear xy-profile (b) Square profile in xy-plane

Figure 5 .

 5 Figure 5.7(b), represents the real motion profile. From the result it can be seen that,

FIGURE 5 . 8 :

 58 FIGURE 5.8: Circular motion profile

Figure 5 .

 5 Figure 5.10(a), represents the accumulated voltage along x-axis. This measurement has been carried out over 7 mm displacement range. Theoretically, the travel range of the MPS prototype is 10 mm, but due to the relative distance between two FODS probes

FIGURE 5

 5 FIGURE 5.10: Open loop response along x-axis and y-axis

FIGURE 5 .

 5 FIGURE 5.11: Step response realized with long range displacement measurement sensor

FIGURE 5

 5 FIGURE 5.12: Experimental setup to measure the rotation

  carried out. In order to facilitate and reduce assembly errors during manual assembly of the various components of the MPS, a novel cross structure in silicon material has been developed via ICP etching technology. For fabrication, two mask designs have been used to etch a standard silicon wafer in two steps, i.e., from top side and bottom side.The detail microfabrication layout has been realized and silicon cross structure has been fabricated. From the result, it has been concluded that the new cross structure eliminates the PMA assembly error thus reduce the displacement loss by 11.78% as compared to conventionally fabricated Zerodur R cross structure.At the end some additional experiments have been carried out to evaluate the motion behaviour of the mobile part in xy-plane. In addition, open loop tests have been carried out to verify the functionality of the integrated long range sensor. With PI control, a displacement resolution of 1.37 µm has been achieved via measuring with long range silicon sensor. At the end, a rotation test has been carried out to measure the maximum rotation range of the MPS. The rotation of the mobile part in our case is mainly limited due to the aluminum fixture that has been developed to mount the fixed part of the MPS.

  Indirect drive technology and direct drive technology. Indirect drive technology is based on the mechanical conversion of the rotary motion (often generated by the rotary motor) into linear mo-

tion [Ahme 05]. The positioning systems based on this technology have the driving part (i.e. actuator, motor) indirectly coupled with the driven part (i.e. stage or platform) via flexible or rigid mechanical coupling elements such as belts, lead screw, gear train, etc. Positioning systems based on indirect drive technology have high load driving capacity and simple control but they suffer from issues like backlash, low efficiency, low accuracy, etc.,[Ratc 06]. The problems like these are unacceptable, especially when the positioning systems are to be used for micro applications where high precision is one of the essential parameters. The alternate solution is direct drive technology in which the motion generated by motors is directly transmitted to the driven part [Joub 12]. These drives eliminate the need of the mechanical coupling elements thus making them more compact and suitable for micro applications demanding high precision and accuracy [Hell 09]. Moreover, a direct drive solution reduces the number of components, simplifies assembly and thus reduces the overall cost of the positioning system.

table Contact pads

 Contact FIGURE 1.17: MEMS micro stages (a) Liu et al., [Liu 07] (b) Sun et al., [Sun 08] (c) Ji et al., [Ji 10] stage in xy-plane. A displacement of ±12.5 µm was reported by the authors. In addition, a bottom electrode of 1 mm 2 was fabricated under the center stage. The bottom electrode

	Glass substrate		Movable	Piezoresistor
	Tethering beams Comb actuators	4mm	Bending flexure	Folded beam	Sensing electrode Driving	comb actuators Center stage Tethering
					electrode	beams
	Actuator suspension beams Bottom electrode	4mm	Piezoresistor Glass substrate	Comb actuator	Silicon substrate capacitors Sensing	Anchors Suspension beams
	(a)		(b)			(c)
	and center stage acts as parallel-plate actuator. By this means Liu et al., have realized a
	3.5 µm displacement in z-axis. The open loop repeatability of the stage was reported to
	be 17.3 nm along all three axes. External optical microscope with a digital camera (reso-
	lution: 2.58 nm) and an optical interferometer (resolution: 7.1 nm) was used to measure
	planar and vertical displacement, respectively. The device is compact in nature but due
	to its small size it does not integrate the positioning measurement sensors.
	Similar kind of design has been proposed by Sun et al., [Sun 08]. They have de-
	veloped an integrated micro xy-stage with a 2×2 mm 2 movable table (figure 1.17(b)).
	The stage is integrated with displacement measurement sensors. They have used double-
	sided bulk-micromachining technology to fabricate their stage. The micro device is com-
	posed of four comb actuators and piezoresistors with a full Wheatstone bridge circuit that
	is used for displacement measurement. The integrated micro stage is able to deliver a
	±10 µm displacement along a single a axis.
	Ji et al.[Ji 10], have developed a micro positioner (figure 1.17(c)) for nano appli-
	cations. The device is integrated with four orthogonally arranged comb-drive actuators
	and capacitive sensors to measure in-plane displacement. The actuation force from comb
	actuators is transmitted to the 520×520 µm 2 center stage through 700 µm long tethering
	beams. The positioner has a average range from ±6.64 µm.
	Takahashi et al.[Taka 07], have developed an xy-stage mechanism for the 2D lens
	scanner based on electrostatic actuation principle (figure 1.18(a)). The stage has a small
	footprint (2×2 mm 2 ) compared with an integrated silicon lens (dia 1 mm). The overall
	device is dual layer design utilizing comb actuators with a double-gimbal structure to
	Liu et al.[Liu 07], have developed a 3DOF based nanopositioing stage (figure 1.17(a)). perform 2D motion. It was fabricated in silicon-on-insulator (SOI) and offers a maximum
	It was micro fabricated using DRIE technology in a 500 µm thick Pyrex substrate. Four lateral displacement of 19 µm in the x-directions and 23 µm in the y-directions.
	orthogonally arranged comb drive actuators have been used to actuate a 1×1 mm 2 center

.5.3 Electro-Magnetic Actuator (EMA)

	ability to withstand hostile operating conditions in industries. The stator of the planar
	motor was realized with small sheets assembled together to form building blocks. These
	building blocks are put together to realize the stator part of the planar motor. The motor
	was integrated with optical encoders (resolution=1 µm) to measure the planar displace-
	ment.
	1.3Another approach to realize actuation for positioning systems based on electromagnetic
	principle is to use EMAs. The principle of EMA is based on the generation of Lorentz
	force. It originates due to the direct interaction between a current carrying electrical
	conductor and a magnetic flux density prevailing around the conductor (figure 1.23(a)).
	In comparison with LIAs and LRAs, EMAs are simple in design and are simple to control
	due their linear current-to-force relationship [Mole 00]. The construction of EMA consists
	of a movable slider and a fixed stator. According to the literature, two design solutions
	are mostly used to realize MPS based on EMAs. The first approach is "moving coil and
	fixed PMs technique" (figure 1.23(b)) and the second one is "moving PMs and fixed coil
	technique" (figure 1.23(c)).
						Motion direction
		Current				Magnetic
				Levitation force	field	Stator	Slider/rotor
						(fixed PMs)	(movable coils)
		Magnetic
	Force	field	Translation	S
		direction	force	N	(b)	Direction of
				Airgap		Motion direction	magnetization
		Current carrying conductor		Permanent magnet	Stator (fixed coil)	Slider/rotor (movable PMs)
				(a)		(c)
	FIGURE 1.23: (a) EMA principle (b) Moving coil and fixed PMs construction (c) Moving
					PMs and fixed coil construction [Benc 06]

Table 1 .

 1 1: Characteristics of the presented positioning systems

	Ref.	A.T	DOF	Dimensions	Max. Stroke	Res.	Sensor
				MPS based on smart material actuation principle
	[Cedr 11]	MAPA	2	50×50×20 mm 3	25×25 µm 2	2 nm	*Capacitive
	[Sabr 09]	MAPA	2	45×40×1.4 mm 3	80×60 µm 2	-	*Capacitive
	[PI 12]	MAPA	3	150×150×25 mm 3	300× 300× 300 µm 3	-	Capacitive
	[Wu 04]	PIWA	3	20×20×12 mm 3	Theoretically infinite	14 µm	none
	[PI N512]	PWD	2	-	6×6 mm 2	15 nm	none
	[Zesc 95]	FID	3	38×38×9 mm 3	6×6×6 mm 3	10 nm	none
	[Smar 11]	SSA	6	Ø110×45 mm 2	20×20×10 mm 3	1 nm	*Encoder
	[Nomu 07]	FID	3	28×28×1.65 mm 3	-	17 nm	none
				MPS based on thermal actuation principle
	[Lee 09]	EHR	2	2×2 mm 2	41×41 µm 2	-	Camera
	[Lin 11]	EHR	2	8.8×8.8×0.2 mm 3	25×25 µm 2	-	Camera
	[Culp 06]	EHR	6	Ø3 mm	8.4×12.8×8.8 µm 3	0.1 nm	Camera
	[Ebef 00]	EHR	3	15×15 mm 2	-	-	Camera
				MPS based on Pneumatic actuation principle
	[Chap 04]	-	3	35×35 mm 2	Same as dimensions	-	-
	[Berl 00]	-	3	30.5×30.5 mm 2	Same as dimensions	-	-
	[Dele 11]	-	3	120×120 mm 2	Same as dimensions	-	-
				MPS based on electrostatic actuation principle
	[Liu 07]	CD	3	4×4×0.5 mm 3	±12.5, 3.5 µm	-	Camera
	[Sun 08]	CD	2	-	±10 µm	-	*Piezoresistor
	[Ji 10]	CD	2	3.75×3.75 mm 2	±6.64 µm	-	*Capacitive
	[Taka 07]	CD	2	2×2 mm 2	19×23 µm 2	-	Camera
	[Kim 03]	CD	2	17×17 mm 2	36×36 µm 2	-	Laser
	[Boud 10]	CD	3	-	±10 µm, θ=2 µm	-	Camera
				MPS based on electromagnetic actuation principle
	[Ditt 06]	LIA	3	4.6×4×2 cm 3	≈ facing surface area	31.75 µm	*Optical
	[Kuma 12]	LIA	3	Ø180 mm	≈ facing surface area	-	*Optical
	[Jung 05]	LIA	3	30×30×20 mm 3	-	-	*Laser
	[Jung 10]	LIA	3	-	10×10 mm 2	-	Interferometer
	[Pan 11]	LRA	2	340×350 mm 2	100×180 mm 2	-	*Optical encoder
	[Hu 06]	EMA	6	95.25×190.5 mm 2	160×160 mm 2	20 nm	Interferometer
	[Yu 10]	EMA	6	170×152×53 mm 3	220×200 mm 2	10 µm	*Hall sensor
	[Nguy 12]	EMA	3	185.4×157.9 mm 2	15.2×20.32 cm 2	8 µm	*Hall sensor
	[Trum 98]	EMA	3	-	80×69×17.5 mm 3	5 nm	Interferometer
	[Holm 00]	EMA	2	-	25×25×0.1 mm 3	10 nm	*Interferometer
	[Kim 07]	EMA	6	80×69×17.5 mm 3	0.3×0.3×0.5 mm 3	5 nm	Interferometer
	[Kim 07]	EMA	6	115×127×112.7 mm 3	5×5×0.5 mm 3	4 nm	Interferometer
	[Chen 04]	EMA	2	-	100×100 µm 2	20 nm	*Capacitive
	[Chen 10]	EMA	3	100×100×100 mm 3	1×1 mm 2	5 µm	*Optical
	[Culp 04]	EMA	6	-	100×100×100 µm 3	23 nm	Camera
	[Gao 04]	EMA	3	260×260×23 mm 3	40×40 mm 2	20 nm	*Encoder
	[Deji 05]	EMA	5	720×720×60 mm 3	200×200×0.01 mm 3	-	*Multiple
	[Lu 12]	EMA	6	559×320×5.7 mm 3	260×60×2.5 mm 3	0.5 µm	Interferometer
	[Gloe 12]	EMA	3	-	100×100×0.1 mm 3	5 nm	*Capacitive+optical
	[Benc 06]	EMA	3	100×100×20 mm 3	5×5 mm 2 , ±8 •	200 nm	Fiber optics

Acronym used in the table

Mechanically Amplified Piezoelectric Actuator (MAPA), Piezo InchWorm Actuator (PIWA), Friction Inertia Drive

TABLE 1

 1

	Principle		Smart material		Thermal Electrosta c Pneuma c		Electromagne c
	Actuator types	Piezo-stack actuator	Mechanically amplified actuator	Stepping mode actuator	Ultrasonic motor	Bimorph actuator	Comb drive	-	Induc on actuator	Reluctance actuator	Lorentz force actuator
	Stroke size (>1 mm)	100 µm ~~~~~~~~~~~S	300 µm	> 1 mm	>1 mm	41 µm	36 µm	>> 1 mm	>>1 mm	>>1 mm	> 1 mm
	Resolution (< 1 µm)	2 nm	2 nm	10 nm	20 nm	1 nm	1 nm	10 µm	10 µm	10 µm	5 nm
	Response time (< 1ms)	Very fast	Very fast	Moderate	Very fast	Slow	Fast	Slow	Fast	Fast	Fast
	Output force	Moderate	Large	Moderate	Moderate	Very large	Very low	Large	Very large	Moderate	Low
	Design complexity	Moderate	Moderate	High	High	Moderate	Very high	High	High	High	Low
	Sensor integration	Easy	Easy	Difficult	Difficult	Difficult	Moderate	Moderate	Easy	Easy	Moderate
	Speed (> 1 mm/s)	Very fast	Very fast	Slow	Fast	Slow	Fast	Slow	Very fast	Very fast	Very fast
	Miniaturization Very easy	Easy	Moderate	Moderate	Difficult	Moderate	Moderate	Very hard	Moderate	Moderate
		trong advantage		Weak drawback	Strong drawback

.2: Drive choice in the multi-DOF miniature positioning systems

TABLE 2 .

 2 1: Generated electromagnetic force at different position during four steps

	Position	1	2	3	4	5	6	7	8	Total force
	Currents	-I 1	-I 2	+I 1	+I 2	-I 1	-I 2	+I 1	+I 2	translation	levitation
	Step 1	+I 1 Bz	+I 2 Bx	+I 1 Bz	+I 2 Bx	+I 1 Bz	+I 2 Bx	+I 1 Bz	+I 2 Bx	4I 1 Bzl	4I 2 Bxl
	Step 2		+I 2 Bz	+I 1 Bx	+I 2 Bz	+I 1 Bx	+I 2 Bz	+I 1 Bx	+I 2 Bz	4I 2 Bzl	4I 1 Bxl
	Step 3		+I 2 Bx	+I 1 Bz	+I 2 Bx	+I 1 Bz	+I 2 Bx	+I 1 Bz	+I 2 Bx	3I 1 Bzl	4I 2 Bxl
	Step 4			+I 1 Bx	+I 2 Bz	+I 1 Bx	+I 2 Bz	+I 1 Bx	+I 2 Bz	3I 2 Bzl	3I 1 Bxl

TABLE 3 .

 3 1: Natural frequencies of the Zerodur R cross structure, [Benc 06]

TABLE 3

 3

.3: Comparison of the magnetic induction values at different air gaps

  Specification of the NI R DAQs used in the experiment The PCI-6733 card is used as an output device to feed the voltage signals (generated via Labview R interface) to the voltage-to-current convertors. Whereas, PCI-6036E card has been used as an input device to treat the input voltage signals attained by the FODS.

	R	Analog	Analog	Resolution Sampling Application
	DAQ card input ports output ports		frequency
	PCI-6733	0	8	16 bit	1 MHz	Output
	PCI-6030E	16	2	16 bit	200 kHz	Input
	TABLE 3.4:

TABLE 3 .

 3

6: Position repeatability in 10 cycles square steps test

  .6. The description of these parameters are provided in table 4.1.

		Fiber optic probe	Φ		Illuminated surface Emitted light
				Φ e
		FODS security				R axial
		distance limit				α
			x	d s	β	R α
		Grating Top edge limit		d x		α	δ	Grating edge
		h		Φ z
		Grating				FODS probe
		bottom edge limit	δ		l	axis
				Grating displacement direction
	FIGURE 4.6: Enhanced two dimensional view of a single grating step with FODS probe
	Symbol Definition		Symbol Definition
	Φ e	Emission fiber diameter			h	Height of the grating step
	Φ	FODS probe diameter			l	Length of the grating step
	β	Half angle of the numerical aperture	d s	Security distance
	α	Angle of the grating step		d x	Distance: probe/ step = x•sin α
	Φ z	Diameter of the illuminated zone	δ	Bottom angle of the grating step

TABLE 4 .

 4 1: Definition of the FODS probe and grating step parameters

  180• C . During this process, the structured SiO 2 layer serves as masking layer. So, the areas where Si 3 N 4 layers is not protected by SiO 2 are etched. The etching rate of the Si 3 N 4 layer is very slow (≈6 nm/min) in the H 3 PO 4 solution. It takes around 45 minutes to etch the 300 nm thick Si 3 N 4 layer. After etching is finished, the wafer was rinsed, dried and an inspection under the microscope has been carried out to verify the structures etched in the Si 3 N 4 layer. At this point the silicon surface of the wafer is exposed to realize grating (see step 7, figure 4.21). In this work, our main objective regarding the fabrication of silicon grating is to achieve further lower values for the described parameters. So, we have decided to realize silicon grating with 25% TMAH concentrated solution. During this process, the Si 3 N 4 layer serves as masking layer. The silicon etching has been carried out for 4 hours with an average silicon etch rate of 0.37 µm/min.

	In order to etch silicon, two alkaline solutions (i.e., KOH and TMAH) are mostly used
	in microfabrication field due to their lower environmental pollution and better surface
	smoothness [Bisw 06]. However, in the study conducted by Dr. Ali Khiat, it was concluded
	that silicon etching with TMAH solution leads to smaller values of surface roughness
	(19 ± 3 nm) and flatness (70 ± 13) as compared to silicon etching with KOH solution
	[Khia 07]. Photoresist
				removal
				H PO 3	4
				(Si N etching) 3 4
				Silicon
				etching
	ma-D331	l	h	40% HF (SiO and Si N 2 3 4
	(Development			removal)
	of the exposed
	photoresist)

TABLE 4

 4

	•

.2: Characteristics of the two FODS probes used with silicon grating

  • in xy-plane, the theoretical linear sensitivity (S ψ ) of the long range sensor can be computed with the help of lateral sensitivity of the sensor, i.e., 12.63×cos ψ=8.93 mV/µm. The measured value of the sensitivity (8.47 mV/µm) is very close to the computed value. The small difference is due to the fact that the motion of the silicon grating have not been carried exactly at angle of 45 • in xy-plane. So, in order to identify the real angle, the measured value of the sensitivity (8.47 mV/µm) was used to compute the real displacement angle (i.e., 47.88 • ).

The authors have measured the change in displacement using moonie angle (θ max =

• ) of the amplification structure [Sabr 09]. 2 http://www.physikinstrumente.com

http://www.smaract.de

The term "Linear" represents single degrees-of-freedom of motion i.e. translation

http://www.supermagnete.de

Honeywell, 101MG7, http://www.radiospares-fr.rs/

http://www.cadsoftusa.com/

http://www.multi-circuit-boards.eu/

http://www.allegromicro.com/

http://www.ia.omron.com/

Common configuration represents when the flat mirror is displaced perpendicularly from the FODS probe surface, see sub figure 4.2

http://www.imt.tu-bs.de/

Single Crystal Silicon (SCS) is referred to Monocrystalline silicon

http://www.silchem.de/

The optimal value of the rectangular stripes width (t=33 µm) was selected after experimentation.

Type A uncertainty is equal to the standard deviation divided by the square root of the number of measurement [Khia 07].

hill lock formation represents the appearance of small pyramids on the surface during anisotropic etching of silicon

Silicon is an anisotropic material and its Young's modulus value varies along its different crystalline planes, i.e., 129.5 GPa (100 plane), 168 GPa (110 plane), 186.5 GPa (111 plane), [Mado 02].

100 ml of the aluminium etching solution consists of 73% Phosphoric acid (H

PO

), 3.1% Nitric acid (HNO 3 ), 3.3% Acetic acid (CH 3 COOH) and 20.6% deionized water (H 2 O)

http://www.newport.com/

List of abbreviations

used to translate the PMA (attached to the cross structure) beneath the Hall sensor.

In order to drive/control the linear stage, the command signals were generated using LabView R software. These signals are sent to the dedicated Newport controller which generates corresponding driving voltage for the linear stage. Similarly, the output voltage generated by the Hall sensor is acquired using the analog channels of the National Instrument data acquisition modules (NI R PCI-6030E) in real time. These voltage data were processed and stored using Labview R software.

In practice, the described components have been assembled together to realize the experimental setup. Both, Hall sensor and the PMA have been insulated from the metallic components using non-magnetic supports (1) and (2) as shown in figure 3.13(a). This insulation is necessary in order to avoid any kind of disturbances during experimentation such as magnet-metal attraction, thermal variation, etc. Further, the Hall sensor was fixed to a manual linear stage (Newport, UMR 5.16) using a mechanical support to adjust the air gap "d" between the PMA surface and Hall sensor along z-axis (see figure 3.13(b)). An additional glass wafer was fixed on top of the non-magnetic support (2) in order to avoid any free suspension of PMAs due to the small surface area of the non-magnetic support

(2). This is done in order to avoid the scenario in which, small vibration (generated by to the data to acquire a relationship with respect to displacement. Further, the expressions obtained have been used to construct the relationship between output voltages in terms of the applied magnetic field as shown in figure 3.14(b). A linear fit is then applied in order to determine the sensitivity of the Hall sensor which was found to be 25.13 V/T

(2.513 mV/Gauss). The value of the sensitivity is in good agreement with the Hall sensor manufacturer value (see table 3.2).

The precision error of the Hall sensor measurement was carried out by measuring the magnetic induction of the reference PM at the air gaps provided by the fabricator.

However, the measurement for the first air gap value (i.e., d = 0.25 mm) could not be carried out as the Hall element in the sensor is located 0.5 mm inside the sensor package (see data sheet of A1301). For the rest, the measured values of the magnetic induction are presented in the table 3.3. The results show a very good agreement between the measured and reference magnetic induction values with a very small precision error of ≈

1.1 mT. The influence of this error can easily be neglected. Hall sensor and PMA surface was selected to avoid any physical contact during measurement. After adjusting these parameters, the mobile part of the MPS is translated for 18

b) Magnetic induction measurement of the

In these mask designs, some additional supports have been included to support the etched cross structure in silicon wafer from falling during etching process (see 5.2).

( After designing both of the masks in AutoCAD R software, these two dimensional designs have been transferred on the blank masks that consist of a square glass plate which is pre-coated with chrome and photoresist layers on one side. This process was carried out with mask writing machine by exposing the photoresist layer with a laser spot. After writing process, the photoresist layer of the masks have been developed in similar fashion as described in section 4.4.2 in the previous chapter. The dimensions of the structures and profiles were verified under the microscope. After verification of the masks, the fabrication of the silicon cross structure has been carried out. The description regarding the microfabrication process is described in the following section.

Microfabrication process

The microfabrication of the cross structure in silicon material has been carried in 14 steps as shown in the figure 5.3. Initially, the silicon wafer was cleaned and coated with a 600 nm thick aluminum layer on one side. This process was carried out via metal sputtering process in PVD machine. This material serves as a protection mask during dry etching process that is carried out in an ICP machine. After the aluminium deposition, a layer of the photoresist was realized on top of it, by spinning 1 ml of positive photoresist (ma-P1215) at 3000 rpm in order to transfer the mask pattern via photolithography technique (see step 2, figure 5.3). A soft baking for 1 min at 100 • C was carried out to avoid any kind of damage such as scratching during the mask alignment process in the next step. of more electromagnetic force. Alternatively, this solution can also be employed to reduce the power consumption. In future, benefits of applying a second set of PEDCs on top of the mobile part need to be carried out. In addition, the sandwich structure based MPS design could help in levitation of the mobile part which can significantly improve the dynamics of the system due to elimination of the friction that appears because of the mechanical contact between the mobile and fixed parts.

The integration of the long range sensor has been manually carried out. Though, this solution seems suitable as silicon grating has been realized in a silicon wafer with special crystallographic orientation. However, the direct fabrication of the silicon gratings on the cross structure, is possible if the etching is preformed in silicon wafer with 111 crystallographic orientation at 45 • . This approach will reduce the fabrication time and will eliminate manual assembly errors. The main complication that need to be assessed is to realize a hybrid microfabrication process that should integrate wet anisotropic etching followed by ICP etching process.

In future, the work presented in this thesis will be extended to realize compact smart actuation platform for micro factories. In addition, from the control aspect, a dedicated control will be developed in order to reduce the complexity of the displacement measurement with long range linear displacement sensor.

Appendix A

List of publications

The work presented in this thesis has been published and presented in the following international journals and international conferences.

• Muneeb Ullah khan, Nabil Bencheikh, Chritine prelle, Frédéric Lamarque, Tobias Beutel and Stephanus Büttgenbach, "A long stroke Electromagnetic XY positioning stage for micro applications, IEEE Transaction on Mechatronics, vol. 17

Appendix B Measurement of the silicon grating surface characteristic

In chapter 4, section 4.5, the surface analysis of the micro fabricated silicon grating has been carried out using white light interferometer machine Zygo TM (New view 200) at Roberval laboratory UTC. The measurement principle this machine consists of passing a white light through optical system and create interference fringes on the surface of the specimen that is being analyzed. These fringes are recorded with a help of CCD sensor.

The objective lens is mounted on a vertical piezoelectric actuator which saves the interferogram at each altitude. Based on the saved information, a three dimensional topography of the observed surface is realized and displayed. Similar to all optical measurement techniques, there is no contact between the surface of the sample which avoids the deterioration of the surface during measurement. Table B.1 represents the characteristics of this Zygo TM microscope. In order to examine the microfabricated silicon gratings, it has been placed beneath the objective lens of the Zygo TM 200 machine. After leveling the grating steps with respect to the objective lens, the surface scan has been carried out. During analysis steps to examine the roughness and flatness parameters of the grating steps, the raw profile obtained via scanning the surface has been filtered using a plane form. This process is often carried out in order to remove any ambiguity concerning the leveling error of the grating step in horizontal plane. Different surface filtering options (e.g., plane form, cylindrical form, spherical form, etc.) can be carried out, however, since our grating steps are theoretically flat so we have selected the removal of a plane form for filtering process in order to re-