C Giraud-Audine

T H Nguyen

M Amberg

B Lemaire-Semail

G Abba

R Bigot

Control of a multi-degree of freedom worktool for vibrations assisted forging

This paper addresses the control of a tool developed to superimpose vibrations along several directions on a piece during forging. Piezoelectric actuators are used to provide the required forces and speeds. Due to the minute displacements of the actuators, flexible hinges are used in a special arrangement in order realize the specified movements and to ensure controllability. The experimental results confirm the approach. 104 pt 1.444 in 36.7 mm 54 pt 0.75 in 19.1 mm 37 pt 0.514 in 13.1 mm 54 pt 0.75 in 19.1 mm

I. INTRODUCTION

In forging processes, a piece is forced into a shape given by dies. This requires huge forces which can be generated by an impact, or by moving steadily one of the dies. To reduce the necessary forces, the piece can be heated, or a lubricant can be used. Both solutions require supplementary operations, and energy. Vibrations have been known to influence material process during forming [START_REF] Blaha | Plastizittsuntersuchungen von metallkristallen in ultraschallfeld[END_REF] or even cutting [START_REF] Babitsky | Ultrasonically assisted turning of aviation materials[END_REF]. Some studies have demonstrated that applying ultrasonic vibrations superimposed to the movement of die can reduce the force, similarly to the previous solutions [START_REF] Siegert | Wire drawing with ultrasonically oscillating dies[END_REF], [START_REF] Huang | Influence of ultrasonics on upsetting of a model paste[END_REF]. More recently, it was shown that low frequencies vibrations with special or combined waveforms can achieve the same reduction of the forging force, with less power required [START_REF] Ly | Experimentally valided approach for the simulation of the forging process using mechanical vibration[END_REF]. This work addresses the control of a special active tooling that generates vibrations in different directions by combining several piezoelectric actuators. According to preliminary studies [START_REF] Khan | Effects of Vibrations on Metal Forming Process: Analytical Approach and Finite Element Simulations[END_REF], the tooling should be able to apply vibrations of arbitrary waveform along one direction while tilting the die around an arbitrary axis perpendicular to the first one to benefit from enhanced reduction of the effects. First, the mechanical design and the specific power supply is described. Then the modelling is addressed. In the third part, using a systemic representation that encompasses the different subsystems of the tooling in a unified approach, the design the control structure is addressed. Finally, experimental results are presented in the last part.

II. DESIGN

A. Mechanical Design

For this application, the piezoelectric actuators have several advantages : high stiffness, large force, and high dynamics. However, the displacement range is limited to tens Fig. 1: Vibrating tooling using three piezoelectric stack actuators of µm, therefore special attention must be paid during the design to avoid mechanical play. This motivates the use of flexure hinges combined in such ways that they realize the desired degrees of freedom (DOF) [START_REF] Ryu | Optimal design of a flexure hinge based XYθ wafer stage[END_REF] or magnification [START_REF] Choi | A magnification device for precision mechanisms featuring piezoactuators and flexure hinges: Design and experimental validation[END_REF]. During the design, attention must be paid to the rigidities that should be as small as possible along the desired DOF and very large for the other DOF, and the parasitic motions that may result from the imperfections of the hinges or from the kinematic are negligible [START_REF] King | The design and characteristics of piezomotors using flexure-hinged displacement amplifiers[END_REF]. The proposed mechanism (fig. 1) is based on three flexible links shifted by a 120°along a circle in the plane of the tooling holding the die (plate cf. fig 1b). The main bending direction of the link being perpendicular to this plane this defines the translation DOF. The rotations are obtained thank to the torsions of the flexible links which, thanks to their Margin requirements for the other pages Paper size this page A4 special arrangement combine and give large compliances around two perpendicular directions within the plane of the die. The plate is supported at three points by three piezoelectric stack actuators 1 (fig. 1a) which provide the necessary rigidity to support the forging force along the vertical axis, and that impose the attitude of the tooling plane thanks to punctual contact realized using spherical tips.

B. Power Supply

Piezoelectric devices have a very capacitive nature, resulting in large reactive currents. Several designs have been proposed for high power application, that take advantage of the resonance [START_REF] Li | Design of Power Supply for Driving High Power Piezoelectric Actuators[END_REF], [START_REF] Tran | Design a power inverter and transformer for piezoelectric actuator[END_REF]. However, the piezoelectric devices used her need some DC polarization which complicates the design [START_REF] Goenaga | Contactless Power Transfer System for High Power Piezoelectric Actuators in Aeronautical Applications[END_REF]. For multiple actuators, resonant power supply is hindered by the disparities in capacitances and the need for nonsinusoidal waveforms. To avoid the use of a transformer, the power supply is realized using an off-the-shelve inverter, a half bridge rectifier is connected directly to the piezoelectric actuators (fig 2). This configuration take advantages of the current reversibility of the inverter to realize a boost DC to DC conversion in order to charge the bus capacitor. To do so, the duty ratios of the inverter are set to a constant value generating a lower voltage than the DC supply voltage. The diodes thus conduct and the converter is equivalent to three boost in parallel and a bus voltage of nearly 1000 V can be achieved. When the duty ratios m k , k ∈ 1, 2, 3 are varied and maintained at values such that is greater than the DC voltage U dc , the diodes stop conducting, and the inverter operations take place. The two modes can be applied alternatively, that is inverter operations are switched off to charge the DC bus capacitor when it reaches a minimum value, then switched back once the desired DC voltage is obtained, or can be mixed [START_REF] Giraud-Audine | A simplified power supply for piezoelectric actuators used in forging processes[END_REF].

III. DYNAMIC MODEL A. Kinematic

As already explained, the tooling plate motion is imposed by the actuator using spherical pins. This solution is only able to push against the piece, although this is not a real limitation because the forging force is very large, and press the plate against the spherical pins. The diameters of the sphere are calculated in order to transmit 5500 N without noticeable deformations compared to the 40 µm stroke of the piezoelectric actuators. Thus, to model the kinematic, it is assumed that the plate remains in contact with the tips, and that their deformations are negligible. Besides, considering the compliances of the guiding (see III-C), displacements in the x and y directions and rotation around the z axis (cf. 1b) are second order of magnitude compared to the 1

Piezomechanik

HPSt 1000/15-8/60 : maximum force 5500 kN,maximum displacement 80 µm for a -200 V/1000 V supply voltage other displacements and therefore not considered. With those assumptions, the plane position is entirely defined by the pin positions. A straightforward calculation gives the relationship between the tip speed and the speeds at the center of the plate O :

  v p1 v p2 v p3   vp =    0 0 1 1 1 0 0 0 R -R 2 - √ 3R 2 0 0 0 0 -R 2 - √ 3R 2 0    A         v x v y v z ω x ω y ω z         v O (1)
where v k and ω k k ∈ x, y, z denote the translational and rotational speeds2 measured at the center O within the reference frame, while v 1 , v 2 and v 3 are the translational speeds along z at the contact points C 1 , C 2 and C 3 , which are located on a circle (radius R, center O). Moreover, considering that the friction is small compared to the normal load, the generalized forces at the end of the tip can be written as follow :

F Si = 0, 0, F iz , 0, 0, 0 (2)
Thus, following the screw theory, the components of the generalized forces and moment at point O are :

F O =         0 0 0 0 0 0 1 R 0 1 -R 2 - √ 3R 2 1 -R 2 √ 3R 2 0 0 0         A   F 1z F 2z F 3z   fp (3)
The power of the actuators is calculated by :

P = f p v p = f p Av O = (A f p ) v O = F O v O (4)

B. Power Supply

The frequency range of the device is below 100 hz. The actuators can therefore be modelled considering the quasistatic piezoelectric equation. For piezo-actuator k, considering fixed-free mechanical operation, the tip displacement w p k = v p k dt and the total electrical charge Q p k = i p k dt are linear functions of the actuator voltage u p k and the force F z k applied by the actuator as follows :

F z k = -k s w p k + N u p k (5a) Q p k = N w p k + C p u p k (5b)
where k s is the short-circuited rigidity of the actuator, N is the force factor resulting from the piezoelectric conversion and C p is the free capacitance of the actuator. Deriving (5b) with respect to time, one can see that the current in

C 0 u 0 i 0 L b i p1 C p i m1 U dc i s1 L s i b1 u m1 u p1
Fig. 2: schematic of the power supply the piezoactuator has two contributions. One is due to the dielectric through the free capacitance, the second is a source describing the charges transfer inside the piezoelectric material due to the strain. The later is called the motional current. For quasistatic operations it is small compared to the reactive current due to C p . Considering the case when u p k > U DC , the diodes are non conducting. The inverter switches are controlled by a pulse width modulation (PWM) with a 30 kHz carrier. Considering the 3 kHz cut-off frequency of the L b -C p branch, a mean model of the inverter is considered :

i 0 (t) = 3 k=1 m k (t)i b k (t) u m k (t) = m k (t)u 0 (6)
The voltage of piezoactuator k is then :

L b C p d 2 u p k dt 2 + u p k = m k u 0 + L b di mk dt (k ∈ 1, 2, 3) (7)

C. Dynamic of the Flexible Guiding

The flexible hinges can considered as thin rods. Using the classical beam theory, it is then possible to relate the displacement of the tips of the hinges to the mechanical load at the tip ends [START_REF] Ciblak | Remote center of compliance reconsidered[END_REF]. The elasticity matrix at the center of the plate O is calculated according to the screw theory [START_REF] Khalil | Modeling, identification and control of robots[END_REF]. In the reference frame of fig. 1b, it writes :

K =         k 1 0 0 0 -k 2 0 0 k 1 0 k 2 0 0 0 0 k 5 0 0 0 0 k 2 0 k 3 0 0 -k 2 0 0 0 k 3 0 0 0 0 0 0 k 4         (8)
The various rigidity can be expressed from the geometry and the material properties of the hinges and are not detailed here. For the matter of interest in the scope of this paper it suffices to know that by construction :

k 1 k 5 k 3 k 4 .
The inertia matrix at the same point can be easily deduced from the inertia matrix of a cylinder using the parallel axis theorem :

M =         m 1 0 0 0 -m 2 0 0 m 1 0 m 2 0 0 0 0 m 1 0 0 0 0 m 2 0 m 3 0 0 -m 2 0 0 0 m 3 0 0 0 0 0 0 m 4         (9)
Assuming small displacement of the center of the plate , the motion equations are thus :

M ẅ + Kw = F O + F l ( 10
)
where w = [w x , w y , w z , α x , α y , α z ] is the generalized displacement of the center O of the plate, and F l = [0, 0, F l , M lx , M ly , 0] is the generalized force vector applied by the forged part onto the plate. It follows from the structure of the matrices that the tooling dynamic consists in four independent dynamic subsystems :

Σ 1 : m 1 -m 2 -m 2 m 3 ẅx αy + k 1 -k 2 -k 2 k 3 w x α y = 0 M y + M ly (11)
Σ 2 : m 1 m 2 m 2 m 3 ẅy αx + k 1 k 2 k 2 k 3 w y α x = 0 M x + M wlx (12)
Σ 3 : m 1 ẅz + k 5 w z = F z + F lz (13) Σ 4 : m 4 αz + k 5 α z = 0 ( 14
)
Σ 3 is the translational dynamic along the direction O z , while Σ 4 is the rotational dynamic around the same axis. The later is not controllable, while Σ 3 is controlled by the mean force applied by the actuators. Systems Σ 1 and Σ 2 are similar and show the cross coupling between rotation around the axis Ox (resp. Oy) with displacement Oy (resp. Ox). This results from the design where the flexible hinge neutral plane are not coincident with the orthocenter of the triangle defined by the contact points of the sphere with the plate.

D. Simplified Dynamic

In this section, the models of Σ 1 , Σ 2 are further simplified considering the different dynamics involved. Using a modal decomposition, each subsystem can be transformed in a new basis resulting in the new systems Σ i , i ∈ {1, 2} where the new state vectors have independent components. In this part, the discussion is based on Σ 1 , and can be straightforwardly applied to Σ 2 . The new system writes :

ẍ1 ẍ2 + λ 1 0 0 λ 2 x 1 x 2 = τ 1 τ 2 (15)
where λ 1 , λ 2 are the eigenvalues of the matrix Margin requirements for the other pages Paper size this page A4 matrix whose column are the eigenvectors. The input vector in the eigen basis is calculated by :

G = m1 -m2 -m2 m3 -1 k1 -k2 -k2
τ 1 τ 2 = P -1 m 1 -m 2 -m 2 m 3 -1 0 M y + M ly (16)
Hence, its component are proportional to M y -M ly . As already mentionned, the translational rigidities are larger by several orders of magnitude compared to the rotational rigidities. As a consequence, λ 1 λ 2 meaning that x 1 will have reached steady state much faster than x 2 the later being the so-called dominant mode. Replacing this assumption in 15 :

0 = -λ 1 x 1 + τ 1 ẍ2 = -λ 2 x 2 + τ 2 (17)
gives after some algebra, and casting the system back into the original coordinates, the system is reduced to :

A m 3 - p 12 p 22 m 2 αy + A k 3 - p 12 p 22 k 2 α y = M y -M ly (18) with A = 1 1+k2 p 22 m 2 -p 12 m 1 λ 1 p 22 (m 1 m 3 -m 2 2 )
, and p kl , k, l ∈ 1, 2 are the components of P.

IV. CONTROL

A. Macroscopic Energetic Representation

In order to design the control structure, the Energetic Mascrocopic Representation (EMR) is used [START_REF] Bouscayrol | Multi-converter multimachine systems: application for electromechanical drives[END_REF]. The EMR is a graphic representation, based on the equations of a system that highlights the power flows within a system. It relies on the fact that a subsystem composing a larger system interact with the others by reacting to the action it is submitted to. An important piece of information that is implicitly conveyed by this concept is causality which derives from the energy storages in the system. The worktool's EMR is depicted on fig 3 (orange blocks and green blocks). The diodes are supposed to be off because the strategy used consists in controlling the charge of the DC bus and the vibrations control as two separate phases. The energy storages, which states are defined by the integration of action variables imposed by other components, are represented by crossed box. Other blocks connect different component through constraints (e.g node currents or forces equilibrium), or represent conversion (e.g the piezoelectric conversion). Finally, sources can also be used to represent external interaction with the system (e.g voltage or force sources). The benefit of using the EMR is that the control structure can be systematically deduced by inversion of the gain in the system, and placing controllers to approximate the inverse of an energy storage. Applying the method to the system results in the maximal control structure, in the sense that it assumes that all the necessary variables are measured. The second outcome is that by subdividing the control to the control of the energy storage, physical limitations are easier to respect when designing the controller. Then, for obvious practical Fig. 4: Experimental set-up reasons, the designer task consists in simplifying the control structure, especially with regards to the measure availability, and design the controller accordingly. Following this approach, the resulting control structure is a cascaded control (fig 3 blue blocks), successively controlling the current supplied to the actuator, their voltage to finally achieve the desired speeds. The maximal control structure uses direct compensation (dashed arrows) to account for the constraint of the system (here to compensate the elasticities). For practical considerations, they are not implemented in this work although they could be estimated. Another simplification adopted in the experiment, was to by-pass the current control loop to avoid the difficulty of the current measurement which are particularly noisy (due to the capacitive nature of the load)s.

V. EXPERIMENTAL RESULTS

A. Experimental Set-up

The set-up developed in order to validate the control is presented on fig 4. the inverter is a semikron (1200 V, 60 A), the PWM is generated thanks to a EzDSP TMS320F2812 with a carrier frequency of 30 kHz. The duty ratio are transmitted through RS232. The communication maximum speed is 19200 bauds, and the length of the messages for a three-phase modulation requires 9 ascii characters resulting in a limited sampling time of 1201 Hz. Therefore, to avoid excitation of modes of the mechanical set-up, the transmitted duty ratio m k are interpolated using a first order hold. As a result, the duty ratio are updated at 30 kHz internally by the DSP, far above the mechanical resonance. The 10 mH inductances L b were chosen according to the theoretical capacitance of the piezo-actuators of 270 nF so as to have a cut-off frequency of ca 3 kHz. The control being limited at 1201 Hz, all measurement are filtered (600 Hz second order butterworth low-path filter) to avoid aliasing. For the electrical side, the voltages u 0 , u p k are measured. The vertical displacement w z , and the angles are calculated thanks to three vertical displacement measurements on the outer diameter of the plate regularly spaced 120°opposite to each hinge. To do so, magnet were fixed to the plate and hall sensors fixed to the tooling's bed were used. The control is executed by a DSPace 1104 board programmed using Simulink. It also provides a mean to define Margin requirements for the other pages Paper size this page A4 Fig. 3: EMR of the system (orange and green blocks refer to the system, blue to the control).

B. Voltages control

The main purpose of the flexible guiding rotations is to generate a rotating tilt of the plate that is superimposed to the vertical vibrations. It can be shown (this point will not be discussed in this paper for conciseness) that such a motion is obtained by applying three phased sinusoidal voltages. That follows from the design which is similar to magnetic alternative machines, and is somewhat visible from the matrix A (1). As a consequence, the control of voltages is performed in a rotating frame d, q, h [START_REF] Louis | Control of non-conventional synchronous motors[END_REF]. The dq components of the voltage control amplitude of the tilting, while the homopolar component generates the vertical waveform. In the process of transforming [START_REF] Ryu | Optimal design of a flexure hinge based XYθ wafer stage[END_REF] into the rotating frame cross coupling appears, but have little influence in the speed range of interest. On fig. 5a, the step response of the transfer function resulting from the model (including one order hold and antialiasing filter) with coupling neglected is compared to the measured one, and are in good agreement. It also validates the decoupling of the electrical and mechanical dynamics (through the motional current) since the later is not taken into account to calculate the transfer function. Based on this model, a proportional integral corrector is calculated. Fig. 6b compares open-loop step response with the theoretical and the actual response in closed loop on axis d (comparable results are obtained on the other axis by symmetry of the design). Good agreement of the closed loop is found, and validate the design. The control also prevents fluctuating voltage such as can be seen for open-loop at t =14 s (fig. 5b).

C. Motion control

The purpose of the outer loop is to compensate for the imperfections and the disturbances such as the disparity of the actuators, the uncertainties on their locations and on the dimensions of flexible links. Besides, non-linearities of the piezoelectric materials will change the piezoelectric coefficient as the mechanical stress increases during forging [START_REF] Yang | Uniaxial stress dependence of the piezoelectric properties of lead zirconate titanate ceramics[END_REF]. It can be noticed from ( 11), ( 12) and ( 13) that the mechanical dynamic is already in a α, β frame. A rotation transformation casts the speeds in the same dqh frame of the voltages. Thus, to obtain a rotating tilt of the plate, the speed v d , v q should be constant. In practice, since we are only interested in the rotating speed, v q reference is set to zero, and v d directly imposes the desired speed. Pi controllers can be used. v h , the homopolar speed controls the vertical vibrations speed. The required waveforms are not limited to sine wave, but can be triangle, gaussian impulses etc. . . Moreover, the piezoelectric actuator will be compressed at (roughly) constant speed under the forging force. The control should not attempt to compensate this because the voltage would rapidly increase until saturation to maintain the mean position of the tip of the actuators. Indeed, looking at (5a), it can be seen that to keep w pk while F pk increases, implies a proportional rise of the voltage. Therefore, the control is applied on the dq axis, while the homopolar axis h remains in open loop.

VI. CONCLUSION

This paper has presented an original design for a worktool used in forging process. The components of this mechatronic systems have been explained, and models have been proposed. To design the control, the system is represented using a mutiphysic representation tool that respects causality and depicts the power transfer in the system. A control structure has been proposed, and simple controllers calculated. An experimental set-up has been realised, and the tests have confirmed the expected results.

  (a) Picture of the open tooling showing the actuator and the balls used to realize the spherical pin (b) Mounted tooling, the plate is supported by the actuators, flexible links are combined resulting in vertical displacement and two rotations out of the plane of the plate which will support the die.

  Comparison of the model and measured response to a voltage step.

  loop (simulation) Close loop (measured) (b) Closed Loop responses.

Fig. 5 :

 5 Fig. 5: Voltages control interfaces for adjusting gains or measure and visualise different variables of the process.

  On fig. 6 the open and closed loop response of v pd , v pq Margin requirements for the other pages Paper size this page A4 Open loop response in the dq frame.

Fig. 6 :

 6 Fig. 6: Speeds Control are compared. The speed are estimated by derivating the positions and then filtered in the dq frame. The control reduces the overshoot and the settling time. Some variations around the reference remain because the homopolar speed is not controlled.

1

  Laboratoire d'Electrotechnique et d'Electronique de Puissance (L2EP), Arts et Métiers Paristech, Centre de Lille, 8 bd Louis XIV, 59046 Lille, France christophe.giraud-audine@ensam.eu

2 Laboratoire de Conception, Fabrication et Commande (LCFC), Arts et Métiers Paristech, Centre de Metz, 4 rue Augustin Fresnel, 57078 Metz Cedex 3, France 3 L2EP, Université Lille 1, 59655 Villeneuve d'Ascq, France 4 LCFC, Ecole Nationale d'Ingénieurs de Metz, Metz Technopole, 57000 Metz, France

In the following, we will refer to the generalized speeds at a point defined as the vector gathering the translational (V ) and rotational speeds (Ω) at this point : v = [V Ω ] . Similarly, generalized forces concatenate the forces F and moments M at the considered point :F = [F M ]


Causal Ordering Graph and Energetic Macroscopic Representation are graphical descriptions to model electromechanical systems using integral causality. Inversion rules have been defined in order to deduce control structure step-bystep from these graphical descriptions. These two modeling tools can be used together to develop a two-layer control of system with complex parts. A double-drive paper system is taken as an example. The deduced control yields good performances of tension regulation and velocity tracking.

I. INTRODUCTION

Causal Ordering Graph (COG) has been introduced ten years ago [START_REF] Hautier | Le graphe informationnel causal[END_REF] [START_REF] Hautier | The causal ordering graph -A tool for modelling and control law synthesis[END_REF] to describe power electronics and electrical machines for developing their control. This graphical description uses integral causality to organize a causal graph of variables. The inversion of this graph yields the control structure of the system with measurements and controllers.

Energetic Macroscopic Representation (EMR) has been introduced in 2000 to describe complex electromechanical drives, especially multi-drives systems [START_REF] Bouscayrol | Multimachine Multiconverter System: application for electromechanical drives[END_REF]. EMR is based on action reaction principle, which organizes the system as interconnected sub-systems according to the integral causality. An inversion of this description leads to macro-control blocs.

In this paper, Causal Ordering Graph and Energetic Macroscopic Representation are coupled for a double-layer control of complex electromechanical drives. A double-drive paper system is chosen as an example. The global control of the system is deduced from EMR and the local velocity control of the band tension is deduced from the COG according to Hook's law. Simulation results highlight the interest of this double-layer control for increasing dynamics of actual systems without complex and advanced control methods.

II. CAUSALITY AND GRAPHICAL DESCRIPTION

A. Causal modeling

A System is composed of inputs and outputs. Its modeling consists in expressing outputs from inputs.

Electromechanical systems can be decomposed into elementary interconnected elements, which manage energy: dissipation, storage and transformation. All sub-systems can be modeled using differential equations with state variables. These variables are associated with energy and are dependent on inputs and time according to integral causality [START_REF] Hautier | Le graphe informationnel causal[END_REF][4] [START_REF] Rubin | The development of vehicular powertrain system modeling methodologies: philosophy and implementation[END_REF]. When inputs change, the state variables reach other steady states after transient states: outputs are always consequence of inputs.

The natural causality is the integral causality because it respects the energy flowing considering the state variables as delayed from their inputs. Integral causal modeling leads then to a more physical description. Derivative causality is sometimes used in simulation because it avoids expressing all elements according to the integral causality. Some association problems in complex systems are thus solved [START_REF] Paynter | Analysis and design of engineering systems[END_REF]. But derivative causality yields a longer computation time.

B. Causal Ordering Graph (COG)

The causal ordering graph is a graphical description based on the integral causality [START_REF] Hautier | Le graphe informationnel causal[END_REF] [START_REF] Hautier | The causal ordering graph -A tool for modelling and control law synthesis[END_REF]. On the contrary of Bond-Graph [START_REF] Paynter | Analysis and design of engineering systems[END_REF], COG doesn't authorize the derivative causality.

Two kinds of relationships are considered: rigid relationships without any time dependence between output and input. That means that an input change instantaneously leads to an output change. There is no delay. A rigid relationship is depicted by an orange balloon involving a double arrow inside: as there is no time dependence, input and output can be easily permutated. For example, the Ohm's law connects a current i R and a voltage u R through a rigid relationship using the resistance R (Fig. 1a):

R R i R u = or R R u R 1 i = (1)
Causal relationships are associated with time-dependence equations. According to the integral causality, the output is mandatory an integration of the input. This kind of relationship is depicted by orange balloons with a single arrow inside: output and input cannot be permutated and there is a delay between them. For example, the inductor relationship links the voltage u L and the current i L through a causal relationship using the inductance L (Fig. 1b).

L L u L 1 i dt d = or ) 0 ( i dt u L 1 i L L L + = ∫ (2)
All linear elements can be depicted using these two kinds of relationships connected by their inputs and outputs. EMR is a more macroscopic description, based on the action and reaction principle. All subsystems are connected by action and reaction variables, whose product yields the exchanged power. As for COG, internal descriptions of elements are defined according to the integral causality.

i R u R u L i L (a) (b)
Three kinds of elements are defined. Sources (green oval pictograms) are terminal elements, which deliver and/ or receive energy. Accumulation elements (orange rectangular pictograms) store energy, which leads to state variables. For example a capacitor stores potential energy, which is proportional to the square of its voltage u C ; this voltage is a state variable controlled by the upstream and downstream currents i up and i down (Fig. 2a):

) i (i C u dt d down up C - = 1 (3)
Conversion elements convert energy without energy accumulation. They are described by squares (electrical conversion), circles (electromechanical conversion) or triangles (mechanical conversion). For example a four-quadrant chopper is a conversion element, which modulates output voltage u chop from DC supply voltage V DC using the modulation ratio m chop , and reaction current i chop from the load current i load (Fig. 2b):

   = = load chop chop DC chop chop i m i V m u (4) i up u C u C i down (a) i up i down u C V DC i chop u chop i load (b) i chop V DC u chop i load m chop

Fig. 2: Accumulation (a) and conversion (b) elements of EMR

Moreover coupling devices are introduced to distribute energy [START_REF] Bouscayrol | Multimachine Multiconverter System: application for electromechanical drives[END_REF]. They are depicted by interleaved pictograms.

III. INVERSION-BASED CONTROL METHODOLOGY

A. Inversion Principle

The modeling of the system leads to express the output y(t) as a function of the input u(t) using integral causality.

The control structure has to define the adapted input to act on the system in order to produce the expected output (Fig. 3). In fact, the control has to express the tuning input u tun (t) as a function of the output set point y ref (t). Thus the control has to invert the power function of the system.

For defining the control structure, we have to find the algorithm to use and the measurement to do on the system. This inversion principle is applied to each sub-systems defined by COG or EMR. There are 3 basic inversion rules.

y(t) u(t)

System y ref (t) Control ? u tun (t) ? Fig. 3

: Inversion principle

Single-input rigid relationships -In this case a direct inversion can be used if the relationship is well defined. For example (Fig. 4.a):

) t ( y k 1 ) t ( u ) t ( ku ) t ( y ref tun = → = (5)
This inversion requires neither measurement nor controller.

Multiple-inputs rigid relationships -If we choose to act on one input to impose the output, the other inputs become disturbances. They have to be measured or estimated to define the tuning input u tun (t) from the output set point y ref (t). For example (Fig. 4.b):

) t ( u ) t ( y ) t ( u ) t ( u ) t ( u ) t ( y 2mes ref 1tun 2 1 - = → + = (6)
If no controller is required, disturbance input must be measured or estimated.

Single-input causal relationships -The direct inversion

of such a relationship leads to a derivation, which has a nonphysical causality. In order to solve this problem, an indirect inversion is made using a controller. In this case, the output has to be measured. For example, using a simple P controller with gain K p (Fig. 4c)

)] t ( y ) t ( y [ K ) t ( u ) ( y dt ) t ( u ) t ( y mes ref p tun - = → + = ∫ 0 ( 7
)
. In this third case, a controller and the measurement of the output are required.

Others relationships -For non-linear, or not welldefined rigid relationships, a direct inversion is not always possible. Controllers can be used too. Most of other relationship can be decomposed into the 3 basic relationships. Their control is thus a combination of the 3 basic control laws.

B. Maximum control structure

This control structure is obtained by a step by step inversion of the system decomposed into elementary sub-systems. Such a control is obtain by the following stages: 1. Decomposition of the system into elementary sub-systems. 2. Determination of the tuning chain: from the tuning input to the global output to be controlled. 3. Inversion step by step of the tuning chain using the previous inversion rules.

All variables are first considered as measurable. At this stage the control structure requires a maximum of controllers and sensors. For this reason, it is called maximum control structure. This control scheme is composed of cascaded loops, which enable limitation of internal variables.

This control can be obtained using COG or EMR. Generally, EMR is well adapted for complex systems. COG can be used to invert a sensitive part of EMR (see section IV).

It may be noted that other inversion rules are required for coupling devices, as distribution and weighting criteria [START_REF] Bouscayrol | Control Structures for Multi-machine Multi-converter Systems with upstream coupling[END_REF].

C. Practical control structure

The maximum control structure is not always adapted for a real time implementation. More practical control structures can be deduced using the following stages: 1. Simplifications of the control (merging of control blocs, avoiding explicit rejection of disturbance…).

Estimation of non-measured variables.

Finally, the controller can be tuned and the real time implementation can be done.

IV. APPLICATION TO A DOUBLE-DRIVE PAPER SYSTEM

A. Double-drive system for paper processing

The system is composed of an unwinding roll and winding roll (Fig. 5). A paper band is processed between both rolls.

Each roll is moved by an induction machine, which is supplied by a voltage-source inverter (VSI). Both power converters are supplied by a diode rectifier from the grid, but this common supplied is not considered in this paper. We assume that VSI are supplied by independent DC voltages.

There are two objectives for such a double-drive system. First, the tension of the band has to be regulated to a constant value for the quality of the paper processing. Secondly, the velocity of the winding roll has to be well managed for the quality of the final paper roll [START_REF] Koç | Modelling and robust control of winding systems for elastic webs[END_REF].

B. Graphical modeling of the double drive system

As a lot of drive applications have been already studied using COG and EMR, only the mechanical part is detailed. Global EMR is depicted in Fig. 6.

Electrical source -The equivalent dc voltage is assumed to be the electrical source (green oval pictogram), which provides the voltage V DC to the system. Induction machines and inverters -Their EMR can be summarized in three blocks. The first one is an electrical converter (square) associated with the voltage source inverter. The second one (rectangle) represents the equivalent stator windings in this frame. The last block deals with electromechanical conversion (circle), which yields the torque T im . Relationships of each element and details of EMR can be found in [START_REF] Bouscayrol | Hardware-in-the-loop simulation of a wind energy conversion system using Energetic Macroscopic Representation[END_REF]. It is just another way to describe the machine in the (d,q) frame from the same classical relationships.

Globally, the induction machine is connected to the inverter by the supplied voltage u vsi and reacts by the currents i im . The machine leads to impose the torque T im on the mechanical part, which reacts by the rotation speed Ω shaft .

Shafts and rolls

shaft roll im shaft f - T - T dt d J Ω Ω = ( 8
)
where J and f are the moment of inertia and the friction coefficient of the shaft, including the rotor and the driven roll, assuming rigid coupling. The rolls ensure the conversion from a rotational motion to a linear motion. They are mechanical converters (triangular pictograms), which yield the roll velocity v roll and torque from the shaft speed and the band tension T band :

T R T R v band roll roll shaft roll roll    = Ω = (9)
where R roll is the radius of the roll.

Paper bands -The band of paper has to be taken into account. It is modeled from simplified Hook's law [START_REF] Koç | Modelling and robust control of winding systems for elastic webs[END_REF]:

) v v ( T ) v v ( ES T dt d L roll roll band roll roll band 2 1 1 2 2 - - - ≈ (10)
with L the band length, S the band section and E the Young modulus of the paper. A paper band connects two drives with a non-linear elastic phenomenon. This leads to problems, which have to be solved by complex algorithms.

A COG is used to organize this complex relationship for control purpose. Intermediary variables are defined:

1 2 roll band v ) T (ES u + = (11) 2 roll band v ) T (ES w + = ( 12
)
w u y - = (13) y T dt d L band = (14)
This new description leads to three rigid and one causal relationships COG (Fig. 7). These simple equations can now easily be inverted (see section V).

w T band y v

roll2 u v roll1 v roll1 T band v roll2 T band (11) ( 13
) (12) (14)
Fig. 7: COG and EMR of the paper band

C. Inversion-based control of the double-drive system

We assume constant radius of rolls, constant inertia of shafts and constant elasticity. More advanced controls are used to take their variations into account [10] [11] [12], one of them is obtained by an extension of the EMR [START_REF] Djani | Extension of Energetic Macroscopic Representation to time-varying systems, applications to winder tension control[END_REF].

The Maximum Control Structure (MCS) of the doubledrive system is deduced from the EMR. Two tuning chains are defined. The first one leads to control the band tension T band from the switching orders of inverter VSI 1 s vsi1 . The second tuning chain lead to control the velocity v roll2 from the switching orders of inverter VSI 2 s vsi2 .

The MCS is obtained by an inversion step-by-step of the both tuning chains (Fig. 10). The first part is associated with the tension control using a tension controller, a speed controller, the machine and inverter controls. The second part leads to the roll velocity control with a speed controller, the machine and inverter controls.

Inversions of VSI and induction machines -Inverters

are inverted using a classical Pulse Width Modulation. Induction machines are inverted using a classical Field Oriented Control. More details are reported in [START_REF] Bouscayrol | Hardware-in-the-loop simulation of a wind energy conversion system using Energetic Macroscopic Representation[END_REF].

Inversions of shafts -As a shaft is an accumulation element with integral relationships (8), a controller is required. Inversion of (8) yields the reference torque T im_ref using an explicit compensation of roll torque T roll :

roll_mes mes _ shaft ref _ shaft im_ref T ] - [ C T + = Ω Ω (15)
Where C[X ref -X mes ] is a controller, which could be PI, IP, PID or other type. A classical decomposition can be made using COG (Fig. 8). Most of accumulation elements are inverted by this way [START_REF] Bouscayrol | Hardware-in-the-loop simulation of a wind energy conversion system using Energetic Macroscopic Representation[END_REF]. A decomposition can be made using COG (Fig. 9). Most of conversion elements are inverted by this way [START_REF] Bouscayrol | Hardware-in-the-loop simulation of a wind energy conversion system using Energetic Macroscopic Representation[END_REF]. Inversions of paper band -The inversion of the paper band is more complex. The COG organizes the inversion of each decomposed relationship from [START_REF] Baumgart | Robust Lyapunov-based feedback control of non-linear web-winding systems[END_REF] to [START_REF] Giraud | Precise position control of a travelling wave ultrasonic motor[END_REF] to obtain:

Ω shaft ∆T T roll T im Ω shaft_ref ∆T ref T im_ref T im T roll Ω shaft T im _ref Ω shaft ref Ω shaft
Ω shaft v roll T roll Ω shaft Ω shaft ref T band v roll_ref v roll T roll T band Ω shaft ref v roll_ref
) T (ES u v mes _ band ref ref _ roll 2 1 + = (17) mes _ roll mes _ band est v ) T (ES w 2 + = (18) v roll1 i im1 ES s vsi2 e im1 u vsi1 i im1 V DC i vsi T im1 Ω shaft1 Ω shaft1 T roll1 T band DC bus s vsi1 v roll2 Ω shaft2 T roll2 T band i im2 ES e im2 u vsi2 i im2 V DC i vsi2 T im2 Ω shaft2 u vsi1_ref v roll1_ref T im1_ref Ω shaft1_ref i im1_ref T band_ref PWM FOC u vsi2_ref T im2_ref Ω shaft2_ref i im2_ref PWM FOC v roll2_ref controller
] T T [ C y mes _ band ref _ band ref - = (20)
In this case, the COG leads to one controller to define y ref , a compensation of w est and a compensation of T band . The influence of compensations is discussed in section D. EMR and inversion-based control can be directly transposed to Matlab-Simulink TM (Fig. 12). All controllers are PI controllers tuned with a pole placement. At first, the tension band is set at a constant value (Fig. 13). Then the velocity has a trapezoidal trajectory (Fig. 14) to start progressively. Using all compensations for the band control there are only few disturbances during velocity transient.

If the compensation of w est is avoided there is an important error for the band tension during velocity transient (Fig. 15). If this compensation is not made, a more complex controller is required [START_REF] Knittel | Decentralized robust control strategies with model based feedforward for elastic web winding systems[END_REF]. However the compensation of w est uses the measurement of the roll velocity v roll2 . But as in the actual process there is a great variation of the roll radius, this measurement is often required for the control of the velocity. In this case, the compensation of w est requires no supplementary sensor.

If the compensation of T is avoided (simplification of (17) in Fig. 11), there is no change in the band tension (Fig. 16). A simplification of the control can thus be made without breaking paper during transients.

V. CONCLUSION

The inversion-based control is deduced from integral causal modeling of the systems. Graphical descriptions as COG and EMR have been developed to systematically build controls using the inversion methodology. COG is devoted to detailed description of complex elements. EMR is associated to macroscopic modeling of an overall system. Both graphical descriptions can then be used to develop a two-layer control structure of an electromechanical system having sensitive elements. Such a two-layer control is applied to a double-drive paper process. EMR is used to organize the global control and COG is focused on the paper band controller. The inversion-based control deduced from these two graphical tools yields good performances of the tension regulation and the roll velocity tracking.

Inversion-based control have been successfully used in different applications for experimental results: piezoactuators [START_REF] Giraud | Precise position control of a travelling wave ultrasonic motor[END_REF], tool machine, hybrid vehicle [START_REF] Lhomme | Design and control of a supercapacitors storage system for traction applications[END_REF], polyphase machines [START_REF] Kestelyn | multi-phase system supplied by SVM VSI: a new fast algorithm to compute duty cycles[END_REF], automatic subway [START_REF] Verhille | Torque tracking strategy for anti-slip control in railway traction systems with common supplies[END_REF], wind energy conversion systems [START_REF] Bouscayrol | Hardware-in-the-loop simulation of a wind energy conversion system using Energetic Macroscopic Representation[END_REF]. In this application, the proposed approach yields an accurate control structure, taking into account the real physical behavior of the system and avoiding damage on the power components

Fig. 1 :

 1 Fig. 1: COG with rigid (a) and causal (b) relationships

Fig. 4 :

 4 Fig. 4: Basic inversions depicted by COGApplication to COG -In the COG description, the control sub-systems are depicted by blue oval pictograms. Direct inversion contains a double arrow inside and controller con-

Fig. 5 :

 5 Fig. 5: Paper processing system

  -A machine shaft is an energy accumulation element, which yields the rotation speed Ω shaft from the machine torque and the roll torque T roll:

Fig. 6 :

 6 Fig. 6: EMR of the double drive system

Fig. 8 :

 8 Fig. 8: EMR and COG of the speed control Inversions of rolls -A direct inversion of relationship (9) leads to the reference of rotation speed Ω shaft_ref from the reference of the roll velocity v roll_ref : v R 1 roll_ref roll

Fig. 9 :

 9 Fig. 9: EMR and COG of the roll inversion

Fig. 10 :

 10 Fig. 10: Maximum control structure of the double drive system

Fig. 11 :

 11 Fig. 11: EMR and COG of the band control

Fig. 12 :

 12 Fig. 12: Matlab-Simulink TM model of the paper system ACKNOWLEDGMENT This paper has been written by permanent staff of the L2EP control team, managed by Prof. Hautier, then by Prof. Lemaire-Semail. The authors thank all Ph.D. students, who have ensured the development of the methodology on various applications. The authors thank ENI Tunis and Université de Québec à Trois Rivieres for their collaborations on textile and paper band control.

Fig. 13 :Fig. 15 :Fig. 16 :

 131516 Fig. 13: Band tension with all compensations

Inversion-based control of electromechanical systems using causal graphical descriptions

  P. J. Barrre, A. Bouscayrol, Member, IEEE, P. Delarue, E. Dumetz, F. Giraud, J. P. Hautier, X. Kestelyn, B. Lemaire-Semail, Member, IEEE, E. Semail, Member, IEEE

	C. Energetic Macroscopic Representation (EMR)
	University of Lille, L2EP, USTL, 59 655 Villeneuve d'Ascq, France, Betty.Semail@polytech-lille.fr


Zaheer Khan

Hamed Ahmadi

Ekram Hossain

Marceau Coupechoux

Luiz A Dasilva

Janne J Lehtomäki

Carrier Aggregation/Channel Bonding in Next Generation Cellular Networks: Methods and Challenges

Keywords: Authorized shared access, carrier aggregation, channel bonding, heterogeneous networks, licensed access, opportunistic access, shared access, unlicensed access. I

To provide cellular systems with additional spectral resources, the wireless industry is considering the aggregation of frequency carriers in licensed, unlicensed, and shared access (SA) bands. In this article, we focus on reliable carrier aggregation/channel bonding (CA/CB) techniques, in which when CA/CB between the licensed, unlicensed and SA carriers is performed, the licensed carrier is used for the primary and secondary carriers, and the unlicensed and SA carriers are operated as additional secondary carriers. We provide a taxonomy of the use of CA/CB in cellular networks and highlight the differences between different CA/CB approaches. We make the case that although the licensed primary carrier can give reliable transmission of control signalling, due to the nature of unlicensed and SA bands, for the efficient aggregation of secondary carriers there is a need for new CA/CB methods. To illustrate our case for novel CA/CB methods, we provide examples for different network environments where intelligent CA/CB decisions can increase throughput as compared to the traditional CA/CB methods. Finally, we highlight challenges in the design of novel CA/CB techniques in unlicensed and SA bands.

to wireless systems at both the component and architecture levels. Techniques that can aggregate carriers simultaneously across different spectrum bands such as licensed, unlicensed, and shared access (SA) bands can also offer increased user data rates [START_REF] Lee | A survey of radio resource management for spectrum aggregation in LTE-advanced[END_REF]. Moreover, unlike the disruptive technologies mentioned above, they enable devices to co-exist seamlessly with existing wireless systems. In wireless networks, aggregation of carriers is enabled by carrier aggregation (CA) techniques and channel bonding (CB) techniques. CA techniques can aggregate multiple contiguous and non-contiguous carriers (in different spectrum bands) to be used together [START_REF] Lee | A survey of radio resource management for spectrum aggregation in LTE-advanced[END_REF]. In wireless networks, such as WiFi networks, CB techniques are used to combine multiple adjacent channels to form larger transmission bandwidths [START_REF] Deek | Intelligent channel bonding in 802.11n WLANs[END_REF], [START_REF]11ac: The fifth generation of wi-fi[END_REF]. CB approaches can be across different unlicensed spectrum bands, such as 2.4 GHz and 5 GHz bands.

It is worth noting that CA can also be leveraged in the context of millimeter wave (mmW) communications in the 30-300 GHz bands [START_REF] Rangan | Millimeter-wave cellular wireless networks: Potentials and challenges[END_REF]. However, for this, the specific propagation characteristics of mmW need to be taken into consideration. Due to their vulnerability to shadowing, mmW signals can rapidly change with small variation in user environment. Therefore, CA may need to be combined with macrodiversity schemes (e.g., simultaneous connectivity to multiple base stations) to improve communication reliability.

Thanks to the smart device revolution, modern devices have enhanced hardware and also support for multiple network interfaces such as cellular and WiFi, which means they can use different protocols and operate over much wider bandwidths in different spectrum bands. This has created new opportunities and challenges to design enhanced CA/CB schemes that can be employed by a unified network across different types of spectrum for increased capacity. Broadly speaking, wireless spectrum can be classified into three different types: 1) licensed spectrum, in which a specific range of frequencies are for exclusive use in a defined geographic area; 2) unlicensed spectrum, in which a specific range of frequencies (such as 2.4 GHz and 5 GHz bands) allow license-exempt operation and are often available worldwide. Such spectrum use is subject to certain limitations, such as limits on power emissions; and 3) shared Access (SA) spectrum, in which in a defined geographic area, a specific range of frequencies (such as 2.3 GHz and TV bands) are allocated to one or more incumbent users, and additional users are allowed to use the spectrum in accordance with sharing rules. SA spectrum can be further subdivided into two types: a) opportunistic access (OA) spectrum (such as TV white spaces) in which a user can use the spectrum as long as she finds it free or she does not cause interference to the incumbent; and b) authorized shared access (ASA) spectrum (such as in the 2.3 GHz band) in which a secondary user requires specific authorization by the incumbent.

Recent tutorial articles and surveys have focused on radio resource management schemes for CA in licensed LTE-A networks [START_REF] Lee | A survey of radio resource management for spectrum aggregation in LTE-advanced[END_REF]. However, techniques designed for conventional CA in the licensed bands cannot be directly applied to perform CA in the unlicensed and the SA bands. Unlike in licensed bands, the unpredictability of the interference environment due to uncoordinated competing users in unlicensed bands needs to be considered by a network operator [START_REF] Deek | Intelligent channel bonding in 802.11n WLANs[END_REF]. Also, the number of utilized aggregated carriers needs to be adapted to the changing spectrum environment in SA bands. When multiple networks independently employ CA/CB, due to the heterogeneous strength of interfering transmissions on overlapping channels, issues such as adjacent-channel interference and channels with dynamic duty cycle patterns become significant. Moreover, not all spectrum bands are equal in terms of coverage or capacity.

Different from the works in the existing literature, in this article we review the recent research efforts relating to the implementations of CA/CB techniques that can be used by the operators to offer unified services in licensed, unlicensed, and SA bands. In particular, we identify challenges faced in the scenarios where multiple independent operators decide to combine channels simultaneously in the licensed, unlicensed, and SA bands to obtain wider bandwidth and higher throughput. To this end, we outline directions for future generation wireless networks in this research area. We provide a taxonomy of the use of CA in cellular networks, and highlight differences between the traditional coordinated CA techniques employed in licensed bands and the extension of CA/CB techniques to uncoordinated scenarios in the unlicensed and SA bands.

II. TAXONOMY OF CA/CB MODELS IN CELLULAR NETWORKS AND THE CONCEPT OF ANCHORING

Fig. 1 presents a CA/CB taxonomy consisting of two branches: "CA in traditional cellular networks", and "CA/CB: the next generation". Under CA in traditional cellular networks, the concept of CA was first deployed in high speed packet access (HSPA)-based cellular networks [START_REF] Lee | A survey of radio resource management for spectrum aggregation in LTE-advanced[END_REF]. However, HSPA-based cellular networks support only contiguous intra-band (same band) aggregation of only two carriers. Restrictions in HSPA-based cellular networks (in terms of aggregation of carriers) are relaxed by 3GPP in its LTE-A standard for cellular networks [START_REF] Lee | A survey of radio resource management for spectrum aggregation in LTE-advanced[END_REF]. Unlike HSPA, LTE-A allows coordinated aggregation of contiguous and non-contiguous carriers in both intra and inter-spectrum bands, to achieve high data rate transmissions using up to 100 MHz bandwidth [START_REF] Pedersen | Carrier aggregation for LTE-advanced: Functionality and performance aspects[END_REF]. CA for user terminals in both LTE-A and HSPA cellular networks is performed by central entities (such as base stations) that belong to the same operator. This is efficient for these networks as they operate in licensed spectrum, and hence, they have exclusive use of certain bands.

During the last two decades there has been mostly independent technological and market developments in WiFi and cellular networks. However, the past few years has seen a feverish level of activity in the area of cellular-WiFi integration. Two of the major activities that are ongoing are Hotspot 2.0, under the WiFi Alliance (WFA), and integrated small cell-WiFi networks under the Small Cell Forum [START_REF]Cellular-WiFi integration[END_REF].

At a high level, the ongoing efforts relating to cellular-WiFi integration under 4G may be seen as the design of techniques for managing data traffic in mobile operator networks in a smart manner. For example, two such techniques are radio interface offloading and network offloading. In radio interface offloading, traffic is dynamically routed to use the optimal radio interface to suit the particular application and user at hand, taking into account the connectivity cost, network congestion etc. In network offloading, intelligent routing of traffic within the backend networks is performed.

Advances in the next generation of networks will be more than cellular/WiFi integration using interface/network offloading [START_REF] Andrews | What will 5G be?[END_REF]. 5G networks will tie new air interfaces and spectrum together with enhanced versions of LTE-A and WiFi to provide simultaneous and efficient use of multiple radio access technologies. Also, unlike 4G networks, enhanced CA/CB capabilities will provide simultaneous use of licensed, unlicensed and SA bands for increased capacity [START_REF] Andrews | What will 5G be?[END_REF], [START_REF]More spectrum-especially for small cells[END_REF]. In other words, the cellular industry is preparing to adopt newer technologies in which a unified network offers services on licensed, unlicensed and SA bands by employing CA/CB schemes simultaneously in these bands [START_REF]More spectrum-especially for small cells[END_REF], [START_REF] Surampudi | LTE-advanced in white space: A complementary technology[END_REF]. The need to address the challenges related to the use of enhanced CA/CB schemes has led to the techniques which are presented in the second branch of the taxonomy in Fig. 1, and are also the main focus of this article.

In the second branch, "CA/CB: the next generation", three different approaches are presented. In the first approach, aggregation concepts are extended to a unified network offering simultaneous aggregation of carriers across licensed and unlicensed spectrum. From here, there are two broad categories of aggregation schemes: 1) A network using common core and integrated small cells offers the network service (using a technology such as next generation advanced version of LTE-A) on both licensed and unlicensed bands to create fatter data pipes [START_REF]More spectrum-especially for small cells[END_REF]; 2) WiFi is integrated into the operator network, which controls the WiFi interface and decides when and how to simultaneously use the unlicensed spectrum along with the licensed spectrum. In the latter approach, along with CA in licensed bands, CB is used in unlicensed bands.

Aggregation of carriers across licensed and SA bands are of two types: across licensed and OA spectrum bands (such as white the space bands between 50 MHz and 700 MHz), and across licensed and ASA bands (such as 2.3 GHz band) [START_REF] Xiao | Expanding LTE network spectrum with cognitive radios: From concept to implementation[END_REF]- [START_REF] Joshi | When channel bonding is beneficial for opportunistic spectrum access networks[END_REF]. Finally, in the third category, aggregation concepts are extended to both unlicensed and SA bands [START_REF]More spectrum-especially for small cells[END_REF].

To provide the best use of CA/CB across all available spectrum resources in the next generation cellular networks, the decision of whether or not to utilize a particular band for CA/CB, and when to utilize it, needs to be made according to a more complex set of principles than existing CA methods for licensed bands. Operators therefore need a toolbox including different CA/CB options so that the right option may be selected for every given scenario. In Fig. 2, we illustrate three methods that can be utilized for the extension of CA/CB in LTE-A, which are further explained in Sections III and IV. For the extension of CA in unlicensed and SA bands using a unified cellular network, licensed spectrum is still of paramount importance, as it provides the foundation for an operator to offer wireless services that is reliable and has predictable performance. Due to this reason, when a network operator employs the extension of CA in the unlicensed and SA bands, it is more appealing that the control signaling always happens on the licensed band, where the quality-of-service (QoS) is ensured. This means no matter what the channel condition in the unlicensed or an SA band is, the crucial signaling information is always communicated properly between the network and device. In [START_REF]More spectrum-especially for small cells[END_REF], this concept is referred to as "anchoring in licensed spectrum".

III. CA ACROSS LICENSED AND SA BANDS: METHODS AND CHALLENGES

Under this approach, the aggregation of carriers in licensed and SA bands can be utilized for broadband wireless service.

A. Extension of CA in Opportunistic Access (OA) Spectrum Bands

TV white space spectrum is one of the candidates for OA-based SA. TV white space spectrum refers to the lower frequency bands between 50 MHz and 700 MHz. Due to the dynamic nature of white space, the devices in a white space-based network must be aware of its availability. To address this challenge, the extension of CA to white space spectrum can be achieved with an anchor in the licensed spectrum in two different configurations: 1) active scanning and 2) geo-location databases [START_REF]11ac: The fifth generation of wi-fi[END_REF], [START_REF] Surampudi | LTE-advanced in white space: A complementary technology[END_REF], [START_REF] Salameh | Spectrum bonding and aggregation with guard-band awareness in cognitive radio networks[END_REF].

i) Active scanning: In active scanning of the spectrum, the eNodeB (anchored in the licensed spectrum) decides which of the available channels to aggregate and use. In this approach, the LTE UEs would be sensing the spectrum and sending periodic reports to the eNodeB informing it about spectrum availability.

The eNodeB would then collate the reports and evaluate whether a change is necessary in the CA configuration, or if the UE ought to continue transmitting and receiving in the same aggregated channels.

ii) Geo-location database:

The second deployment model is to have the eNodeB communicating with a geo-location database and allocating/aggregating the available channels to the UEs in its cell. This approach is favored as there is no additional complexity added at the UE or the eNodeB for dynamic radio sensing and evaluation. Here, the LTE UE acts as a Mode I device and the eNodeB acts as a fixed device and communicates with the geo-location database once every 24 hours.

B. Extension of CA in Authorized Shared Access (ASA) Spectrum Bands

Operators are planning to utilize ASA in bands such as the 2.3 GHz band. Along with macro cells using licensed bands, ASA is well suited for small cell deployment with low power scenarios as the radio propagation is mostly suitable for local area coverage [START_REF]More spectrum-especially for small cells[END_REF]. In any given place and at any given time ASA spectrum is used by either the incumbent user or by the ASA licensee operator. A novel aspect of ASA is that in order to use the ASA bands the operator needs an agreement with the incumbent, based on a sharing framework that outlines the terms of shared use, in which geographical areas to operate, technical conditions for the protection to the incumbent user, and how to vacate the spectrum, if needed.

The difference between OA usage and ASA usage is that since the licensees are known and limited in number, both the incumbent and secondary users can be certain of adequate protection.

Most of the existing literature suggest the use of an ASA geo-location database by a network operator, which instructs the relevant base station to start aggregating the ASA channels that are free at a given time.

However, the problem of competition among multiple uncoordinated base stations that belong to different operators and can perform CA has not been extensively studied. Next we describe a CA deployment model that is developed in [START_REF] Ahmadi | Carrier aggregation as a repeated game: Learning algorithms for efficient convergence to a nash equilibrium[END_REF] and can be utilized for performing CA in spectrum bands (including ASA bands) where multiple uncoordinated networks compete for the aggregation of carriers with minimized interference.

C. A Model for Autonomous Aggregation

We consider that N independent networks operate in the same geographical area and they are notified by a geo-location database that there are B non-overlapping channels available for dynamic usage such as in ASA bands. Each non-overlapping channel has K b carriers in which networks can operate. We consider that each network n can autonomously aggregate a maximum number of M n carriers and all networks support both contiguous and non-contiguous CA. Since non-contiguous CA may suffer from out-of-channel (OOC) interference in adjacent frequency channels and also some overhead due to additional guard bands [START_REF] Salameh | Spectrum bonding and aggregation with guard-band awareness in cognitive radio networks[END_REF], contiguous CA is preferred by a network and we take this into account in our model. When a CA decision is made, the terminals supporting CA between the underlying licensed band (used for control signalling) and the aggregated carriers start operating in the CA mode.

We can model this CA competition as a non-cooperative game denoted by G = (N , A,r). In this game, N denotes set of players which are the wireless networks. The set of possible actions is denoted by A = {A 1 , . . . , A N }, where A n is the set of available actions of the n th network, and r represents the payoff function. We can define the payoff function in a way that combines the two main aspects of the CA problem: the interference experienced as result of the transmissions of neighboring networks and the cost incurred for inter-band CA. When a network decides to select a set of carriers then its payoff is given as:

r n (a) = 1 M n ∑ c n ∈a n ( 1 - γ c n γn ) - (nbands(a n ) -1)δ N B n ,
otherwise, its payoff is zero, where γ c n is the interference measured in channel c n and normalized in the range of [0, 1], and γn is the maximum interference that player n can tolerate on a channel (also normalized in [0, 1]). The function nbands(a n ) returns the number of bands that player n accesses when she selects action a n ∈ A \ , and δ is a parameter that each network can tune to reflect its degree of flexibility in performing CA. The game G is repeated and the networks can change their aggregation decisions, i.e., they change the carriers that they have aggregated.

In our model, each network is not aware of the aggregation decisions of other networks. Each network is able to sense and estimate the level of interference on the available carriers. Each network employs a randomized best response dynamic algorithm [START_REF] Ahmadi | Carrier aggregation as a repeated game: Learning algorithms for efficient convergence to a nash equilibrium[END_REF] that utilizes this sensing/estimation information to reach a stable configuration in which no network has an incentive to unilaterally deviate from its CA selection.

In game theoretic terms this is called a Nash Equilibrium (NE). In Fig. 3, we show the performance of the randomized best response dynamic algorithm for autonomous CA in terms of probability of convergence to reach a stable configuration (Nash Equilibrium) under different network scenarios. Fig. 3 shows that by using the randomized best response dynamic algorithm, after only 200 iterations all the studied network scenarios converge to an NE with probability 1. Our results also show that when the number of iterations is less than 200, it is still possible that the network converges to a stable configuration; however, it is not always guaranteed. Figure 3 also shows that more complex scenarios, i.e., having more players (autonomous wireless operators) and larger action set (number of carriers that an operator can aggregate), require a higher number of iterations for the network to converge to a stable configuration. Reliable availability of opportunistically aggregated spectrum Availability of a particular CA configuration is not always guaranteed (as the incumbent may return to a channel).

Different physical properties of various channels

White space spectrum (such as in TV bands) has excellent propagation characteristics. On the other hand, the SA spectrum under ASA models targets higher bands where radio propagation is mostly suitable for local area coverage.

Independent non-correlated incumbent activity on different channels

Non-correlated incumbents transmit at different times on different channels. When such channels are aggregated they can reduce the total channel utilization time.

Dynamic CA techniques

As the number of free channels and also the number of contending users can change with time, this requires dynamic CA techniques that take into account such network features.

Reliable control

SA can be unreliable with unpredictable performance. Hence, to inform the user nodes about change in spectrum utilization, reliable control is required.

Physical layer constraints

For instance, if the same transmit power is utilized over twice as many (aggregated) channels, the data rate can double, but the range can reduce.

D. Challenges in the SA Bands

Much of the existing literature concentrate on designing methods for aggregation of carriers for coordinated network scenarios operating in licensed spectrum bands. However, under the extension of aggregation of channels in SA bands the problem of CA/CB has been explored very little. The available spectrum in SA bands at different frequency ranges can be heavily fragmented and without novel aggregating/bonding techniques the secondary devices in SA systems cannot efficiently make use of available spectrum. In Table I, we list some of the challenges in combining channels in the SA spectrum ranges when uncoordinated users are present.

IV. CA/CB ACROSS LICENSED AND UNLICENSED BANDS: METHODS AND CHALLENGES

The bandwidth and number of non-overlapping channels available are key factors when it comes to determining the effectiveness of autonomous CA/CB schemes for the aggregation of carriers in licensed and unlicensed spectrum. For instance, in the unlicensed band at 2.4 GHz, only three non-overlapping 20

MHz channels are available, whereas the 5 GHz band has up to 500 MHz of spectrum with more than 20 non-overlapping channels of 20 MHz bandwidth. Moreover, in the 5 GHz band, a network also does not share the spectrum with widely used devices that utilize Bluetooth and cordless phone technology and also equipment such as microwave ovens. This implies less interference.

Licensed Plus Unlicensed Using Small Cells

In this scenario, a heterogeneous network operator deploys small cells in unlicensed bands that use the modified version of the same technology (such as LTE-A or its future versions) that is used in the macro cell (which operates on a licensed band) to co-exist with WiFi systems [START_REF]More spectrum-especially for small cells[END_REF]. In principle LTE-A offers a good opportunity for utilizing CA in both 2.4 GHz and 5 GHz bands due to its ability to utilize flexible bandwidths of different sizes for component carriers (CCs) (such as 1.4, 3, 5, 10, 15 or 20 MHz).

The main idea behind this scheme is that when suitable carrier(s) are available in the unlicensed band, then a user's primary component carrier (PCC) in the licensed band is aggregated with these secondary component carriers (SCCs) in the unlicensed band. Control signalling (such as ACK/NACK and channel quality indicator [CQI]) is carried on the PCC. A listen-before-talk scheme is utilized before transmission on aggregated channels in the unlicensed aggregated carriers so that the interference with WiFi systems is avoided. In addition, the unlicensed spectrum is used on an "on demand" basis, meaning that only the small cells that have active users are able to transmit in the unlicensed band, and do not transmit at all at other times. This is possible because of a mandatory "anchor" in the licensed band.

There are two main deployment modes for aggregating unlicensed spectrum: 1) supplemental downlink (SDL) mode and 2) time-division duplex (TDD) mode.

1) SDL mode:

In the SDL mode, unlicensed spectrum will only be aggregated for the downlink, so that the data rates and capacity are greatly increased in the downlink, keeping the uplink as is. This can be beneficial, especially to address the typically heavy traffic in the downlink.

2) TDD mode: In the TDD mode, the unlicensed spectrum will be aggregated for both downlink and uplink, just like a typical LTE TDD system, and it works like a typical LTE TDD carrier aggregation.

The advantage here is the flexibility to adjust the amount of resources between the uplink and downlink.

When CA is utilized in the 5 GHz band, to protect radars using the 5 GHz spectrum, it is also a mandatory regulatory requirement to use Dynamic Frequency Selection and Transmit Power Control (DFS/TPC).

B. Licensed Plus Unlicensed Using WiFi

Currently, the way WiFi is utilized is suboptimal in the sense that the decision to utilize WiFi for communication and also the decision to whether or not utilize CB is made independent of real-time information about all the available resources (such as available licensed and unlicensed channels). To overcome this problem and to achieve maximum gain from the efficient utilization of both licensed and unlicensed spectrum bands, CA across the licensed and unlicensed band (using WiFi) is controlled by the network operator. In this approach when CA is utilized across an unlicensed band, then a user's PCC is always in the licensed band. When the operator finds a good radio link using WiFi, then it is the network operator that decides on channel selection/bonding decision for secondary carriers. In the following, we describe the existing CB methods for secondary carriers.

Bonding in the 2. [START_REF] Deek | Intelligent channel bonding in 802.11n WLANs[END_REF] [START_REF]11ac: The fifth generation of wi-fi[END_REF]. To ensure fairness among heterogeneous CB users, a network that is using CA/CB across licensed and unlicensed bands needs to determine not only when unlicensed channels are available for CB but also how many are interference free around both the initiator and the responder nodes (see examples in Fig. 4). It can be seen in Fig. 4 that in this enhanced protocol, CB is allowed only on those channels which are found interference-free by both the initiator and the recipient of communication.

C. Challenges in the Unlicensed Bands

It is worth noting that the increased complexity brought about by the addition of aggregation opportunities in unlicensed bands require more efficient CA/CB techniques. In Table II, we list some of the challenges faced by a network operator in combining channels in the unlicensed spectrum ranges when uncoordinated users are present.

Reduced coverage range

When using CB if the same transmit power is utilized over twice as many (bonded) channels, the data rate doubles, but the range can reduce.

Multiple uncoordinated nearby APs

Need to avoid multiple uncoordinated nearby APs over bonded channels. Due to uncoordinated APs, a single overlapping channel can affect the wider bandwidth of this AP.

CB decision using RSSI

Recent measurements in [START_REF] Deek | Intelligent channel bonding in 802.11n WLANs[END_REF] show that if RSSI is above the minimum input sensitivity of a bonded channel, then a bonded channel always performs better than a single channel given that interference is not very high.

Selection of modulation and coding scheme (MCS) along with rate adaptation

Proper selection of MCS along with rate adaptation can maximize the benefits of CB.

Channel leakage due to neighboring user transmissions

To utilize CB efficiently it is important that neighboring users with strong signal strengths should bond orthogonal channels.

Knowledge of the physical rates of competing links Knowing the physical rates of competing links, i.e., the links that are in carrier sensing range, helps in making a good bonding decision.

V. CONCLUSION

Carrier aggregation/channel bonding (CA/CB) between licensed, unlicensed, and shared access (SA)

carriers is an innovation in the next generation cellular networks. This has the potential to offer increased user data rates, while enabling clients to co-exist efficiently with existing cellular systems. In this article, we have discussed different techniques where CA/CB is performed between licensed, unlicensed, and SA carriers. Despite the similarity that (for reliability) almost all the CA methods in different bands need a licensed PCC to control secondary carriers, there are unique challenges to CA due to the different types of spectrum utilization regimes. For instance, due to multiple overlapping WiFi channels and also several other uncoordinated users using frequency bands of different sizes (for example the 802.15.4 uses 2 MHz), efficient CA between licensed carrier and unlicensed carriers (in the 2.4 GHz band) can be challenging. On the other hand, the 2.4 GHz band is very close to the 2.5 GHz LTE band. This implies that modification of the RF circuits will be easier in devices to aggregate carriers in the 2.4 GHz band using the LTE air interface. CA/CB between licensed and unlicensed carriers in the 5 GHz band provides more opportunities due to the availability of many non-overlapping channels; however, to efficiently utilize wider bandwidths, a user needs to avoid this bandwidth to overlap with other uncoordinated users, all potentially on different channels. This is due to the reason that multiple uncoordinated media access control (MAC) over a single overlapped channel can affect the wider bandwidth of this user.

In the scenarios where CA/CB is performed between licensed and SA carriers, it is important to aggregate those carriers that are more reliable in terms of availability. This is due to the reason that at a given time instant, SA bands are mostly fragmented and the availability of a particular CA/CB configuration is not always guaranteed. Taking these different challenges into account, due to the dynamic nature of unlicensed and SA carriers, and also due to the presence of uncoordinated users in these carriers, careful design of new CA/CB techniques is required for the next generation cellular wireless networks.

  For instance, when N = 3, B = 4, M = [4 4 4], K = [3 3 3 3], it takes 200 iterations for the network to converge to a stable configuration whereas when N = 3, B = 3, M = [2 2 2], K = [2 2 2] it takes only 100 iterations for the network to converge.

Fig. 1 .

 1 Fig. 1. CA/CB taxonomy and different spectrum band utilization for aggregation in traditional and next generation networks.

Fig. 2 .

 2 Fig. 2. Next generation CA/CB toolbox. PCC denotes primary component carrier and SCC denotes secondary component carrier.

Fig. 3 . 1 RTS=

 31 Fig. 3. Convergence probability of the randomized best response dynamic to an NE for different scenarios. K shows the number of carriers in each band and M shows the number of carriers that each user can aggregate.

Fig. 4 .

 4 Fig. 4. Examples of enhanced RTS/CTS channel bonding protocol: a) When access point (AP) 1 is bonding to communicate in the absence of interference; and b) When AP 1 is bonding to communicate in the presence of interference.

TABLE I A

 I SUMMARY OF CHALLENGES IN THE DESIGN OF CA/CB TECHNIQUES IN SA BANDS

	Challenges in SA bands	Reasons
		Aggregated carriers from licensed and SA bands can have
	Inter-carrier load balancing (ICLB) issues	different bandwidths and propagation conditions which in turn
		can yield different capacities and can give rise to ICLB issues.
		Use of fixed guard bands to mitigate adjacent channel inter-
	Autonomous guard band assignment algorithms	ference is no longer relevant in CA scenarios where multiple
		operators independently perform CA decisions.

  GHz ISM bands: CB of 40 MHz in 2.4 GHz brings real challenges in terms of both collision avoidance and fairness. Due to the presence of uncoordinated users, maintaining accurate physical carrier sensing and virtual carrier sensing on two 20 MHz subchannels in parallel incurs additional overhead costs. To address this challenge, in 40 MHz CB, a primary 20 MHz channel and a secondary 20 MHz channel are defined. When a user wants to transmit using a 40 MHz band, it performs usual carrier sensing on the primary channel and it performs a carrier sensing for a shorter duration on the secondary channel to make sure it is clear too. If clear, the packet is transmitted using a 40 MHz band; otherwise, the device can either: 1) transmit in the primary 20 MHz channel; or 2) back off again, and then recheck if the full 40 MHz bandwidth is available[START_REF]11ac: The fifth generation of wi-fi[END_REF]. APs that use 802.11a or 802.11n. This scenario leads to the nodes having different virtual carrier sensing, hence they can transmit at different times on the different subchannels, this can lead to different overlapping transmission times on bonded channels. Currently, IEEE 802.11ac defines an enhanced RTS/CTS protocol for CB of multiple channels by uncoordinated users

	Bonding in the 5 GHz ISM bands: Using 802.11ac, up to eight 20 MHz contiguous channels can be
	bonded. It is required in the 802.11ac standard that a cellular network bonding 40 MHz (or 80 MHz
	and so on) should also allow 802.11a or 802.11n clients to associate. For instance, there can be nearby
	other uncoordinated

TABLE II A

 II SUMMARY OF CHALLENGES IN THE DESIGN OF CA/CB TECHNIQUES IN THE UNLICENSED BANDS

	Challenges in unlicensed bands	Reasons
	Dynamic frequency selection (DFS)	DFS in the 5 GHz band should avoid incumbents such as domain weather radar (if present).

This work was funded by Academy of Finland, National Science Foundation, USA, Natural Sciences and Engineering Research Council of Canada (NSERC), and Science Foundation Ireland.