Elio Keddisseh
email: elio.keddisseh@irit.fr

Marcos Serrano
email: marcos.serrano@irit.fr

Emmanuel Dubois
email: emmanuel.dubois@irit.fr

Keywords: Multi-display environments, Pen-based input, Bimanual input. CSS concepts Human-centered computing → Interaction design Environement multi-ecrans, Interaction Bimanuelle

Une approche bimanuelle basée sur un stylet pour l'interaction dans des environnements multi-écrans

Introduction

Multi-display environments (MDEs) are now common and have advanced fairly quickly over the last few decades. One major factor contributing to this evolution is the variety of displays that exist and can be combined (e.g. electronic paper, tabletops, personal tablets, non-rectangular displays [START_REF] Serrano | Investigating Text Legibility on Non-Rectangular Displays[END_REF], etc.). Another factor that explains the use of MDEs is the advantages they bring, such as increasing user productivity and usability [START_REF] Colvin | 31-53 Productivity and Multi-Screen Displays 54-60 An Essential Guide for Sound Health Communication Campaign Development: A Review of Effective Health Risk Messages: A Step-by-Step Guide Lindsey Polonec[END_REF], and the ability of creating shared workspaces [START_REF] Wallace | Investigating teamwork and taskwork in single-and multi-display groupware systems[END_REF]. Moreover, MDEs can adopt many topologies [START_REF] Saidi | TDome[END_REF] such as scattered displays in a room (meeting context), organized matrix (design, gaming) or horizontal setups (office). As a consequence, MDEs are used in many contexts, such as in meeting rooms [START_REF] Chiu | Manipulating and annotating slides in a multi-display environment[END_REF], control rooms, shared workstations [START_REF] Shen | UbiTable: Impromptu Face-to-Face Collaboration on Horizontal Interactive Surfaces[END_REF] and entertainment systems [START_REF] Nacenta | 1 Inventing the Future of Multi-Display Environments[END_REF]. Moreover, in some of the aforementioned contexts, such as control and meeting rooms, users need to be able to take notes. Due to the benefits multimedia notes can have over a traditional paper [START_REF] Chiu | NoteLook[END_REF] and the benefits of a pen over a keyboard [START_REF] Mueller | The Pen Is Mightier Than the Keyboard[END_REF], such users tend to use a pen tablet to take notes, thus complexifying even more the MDE environment.

With that diversity in MDEs setups and contexts, researchers have tackled the challenge of how to facilitate some frequent tasks in MDEs, such as monitor reaching [START_REF] Benko | Multi-monitor mouse[END_REF] (the ability of selecting a display among the others), input redirection [START_REF] Johanson | PointRight[END_REF] (redirect input channels to different displays) and output redirection [START_REF] Nacenta | A comparison of techniques for multi-display reaching[END_REF] (object transfer between displays). To better perform these tasks, researchers have either proposed new interaction techniques using existing input devices (pen [START_REF] Rekimoto | SyncTap: An Interaction Technique for Mobile Networking[END_REF]- [START_REF] Aliakseyeu | Bubble radar[END_REF]) or modified existing devices to adapt to one of these tasks (such as the Multi-Monitor Mouse [START_REF] Benko | Multi-monitor mouse[END_REF] for display switching and Touch Projector [START_REF] Boring | Touch projector[END_REF] to interact with displays through a smartphone). However, most of the proposed techniques were not adapted to realistic usage situations [START_REF] Nacenta | A comparison of techniques for multi-display reaching[END_REF] and are tackling only part of the MDE tasks [START_REF] Saidi | TDome[END_REF]. For instance, in a control room context (Figure ), where the user is sitting in front of a matrix of monitors, combining his pen tablet for annotations by his side, with keyboard and mouse to interact with a MDE results in a homing (device acquisition) time cost.

In this context, we explore the potential benefit of bimanual interaction to support common MDE tasks while preserving manual annotation with the dominant hand using a pen tablet. To this end, we propose the combination of TDome, a multi-DOF dome-like shaped mouse [START_REF] Saidi | TDome[END_REF] specifically designed for MDEs, with a pen tablet. In this paper, we detail the concept, our implementation and the envisioned studies that will be carried to assess the usability of such an approach.

Related work

Some input devices were conceived for interacting with MDEs, yet none of these consider all major MDE tasks. For example, the multi-monitor mouse (M 3 ) simulates having one single cursor for every monitor in a multi-monitor setup, while using the mouse's side buttons to switch between screens. M 3 was evaluated for display switching in a multimonitor setup [START_REF] Benko | Multi-monitor mouse[END_REF] but does not tackle other MDE tasks.

Other interaction techniques were designed using existing input devices specifically for output redirection such as Pick'n Drop [START_REF] Rekimoto | Pick-and-drop[END_REF]: in this case it requires the user to touch the object with a digital pen to "pick it up" and touch again on the desired location to "drop it". However, this technique depends solely on the physical distribution of the displays in the MDE [START_REF] Nacenta | A comparison of techniques for multi-display reaching[END_REF] and requires the user to move in the MDE to reach the desired display. Another technique is Radar View that displays a miniature environment of the surrounding MDE once the user touches the object with a digital pen. The user then drags the object to the desired location on the mini map. Once the pen is released, the object is transferred to the desired location in the MDE. Nonetheless, this technique lacks the ability of sensing the physical environment: it has to reconfigure the virtual environment every time the physical environment is updated.

Recently, Saidi et al. have designed a novel device, TDome, to address the major MDE tasks [START_REF] Saidi | TDome[END_REF]. TDome is a half-sphere shaped mouse, topped with a touchscreen. Its bottomrounded shape provides 6 DOF (Rotation, Roll, Translation and Lift-Up (Figure ). The added touch screen on the top is used to (i) extend the device's gestures and to (ii) prevent any unintended physical manipulation. Moreover, TDome has the ability to sense the physical space making it independent from the MDE spatial setup. However, TDome was used and evaluated only with the dominant hand. Putting this in a control room context where users are already using the pen for annotations, they'll have to switch back and forth between TDome and the pen which will result in a homing effect as said earlier. Instead, in our work we explore how to use the 6 DOF of TDome in the non-dominant hand, in combination with a pen tablet in the dominant hand.

Additionally, researchers have used multi-DOF pens to design pen-tilt-based interaction techniques. For example, Tian et al. designed a menu selection interaction technique using a 'tilting' pen [START_REF] Tian | Tilt menu[END_REF]. 'Tilt menu' resulted in less than 10% error rate when the pie menu was divided in 4 or 8 sections. Moreover, Xin et al. evaluated a pen-tilt-based selection technique [START_REF] Xin | Acquiring and pointing[END_REF] and found that subjects committed the fewest errors when the angular width was 30°. Similarly to TDome [START_REF] Saidi | TDome[END_REF], a tilting pen allows efficient access to 6 commands. However, the multi-DOF pen was never tested in a MDE context.

TDome + Pen: motivation and design factors

Rational for the combination In the context of smart and control rooms, the pen is frequently used for annotations. It thus has to be handled in the dominant hand. We know that people are able to perform contextual coarse positioning tasks with the non-dominant hand while the dominant hand performs detailed interactions [START_REF] Guiard | Asymmetric division of labor in human skilled bimanual action: the kinematic chain as a model[END_REF]. Moreover, the non-dominant hand has at least the same performance than the dominant hand on coarse positioning tasks [START_REF] Kabbash | Human performance using computer input devices in the preferred and non-preferred hands[END_REF]. To complement the dominant hand interaction with the pen, the half-sphere shape of TDome and its 6 DOF could thus be used on the non-dominant hand to perform coarse positioning tasks. In our bimanual approach we therefore use TDome in the non-dominant hand to set context (e.g. reaching a display), and the pen in the dominant hand (Figure ) to perform a detailed interaction (e.g. positioning object in exact location), hence respecting Guiard's findings. In addition, the main functionalities of a keyboard -Typing and Accessing shortcuts -can be done with the pen and TDome respectively, thus, allowing us to exclude the keyboard from this technique and eliminating any homing time cost.

Using this bimanual approach, we designed several solutions to select a display in an MDE. This is a common and fundamental task, required prior to any other interaction in MDE environments. We adjusted the design of our interaction techniques in order to support display selection in three plausible perspectives, describing the setting of the user's interaction with regards to the selection in MDE environment:

(1) egocentric, (2) device centric and (3) cursor centric. We also considered two different displays topologies. We hereafter describe these two considerations.

Display selection techniques EGO CENTRIC

This perspective requires the device's axis that sets the context (TDome in our case) to be aligned with the user's axis. When performing an interaction in this point of view, the cursor's initial position is the screen facing the user and it moves relatively to the user's position in the MDE. One implementation of this algorithm has been explored by Nacenta [START_REF] Nacenta | Perspective cursor[END_REF].

DEVICE CENTRIC

This perspective relies on the device's position in the MDE. We assume that it is a virtual device that can be fixed anywhere in the MDE. For example, the taskbar in Windows OS is on the bottom of the screen by default and the user is free to place it either on one of the sides or the top. In our case, the cursor's initial position will be fixed in a defined location in the MDE.

CURSOR CENTRIC This is the traditional approach of cursor detection, i.e. a cursor that can be displaced to the contiguous display. The starting point is always the display containing the cursor. This technique is efficient for selecting neighbor displays.

MDE topologies

A second consideration that drove our design is the MDE topology. We considered two different topologies that are relevant in the context of control or meeting rooms: (i) a matrix topology, where the user is sitting directly in front of 9 displays organized in a 3x3 matrix; (ii) an arc topology, where the user have displays next to him on each side in addition to a set of displays in front of him forming a semicircular form composed of 9 screens in total.

Display selection implementation

The general design approach of display selection technique in TDome + pen is a roll in the direction of the display with TDome followed by a pen tap on the tablet for confirmation which also represents the start of another task inside the selected display. For instance a roll in the north direction moves the display selecting cursor to the display in the north. If there is more than one display in that location, the amplitude of the roll determines what screen to be selected. To adapt the general technique to the perspective factors, we designed the following: . A slight roll to the east followed by a pen tap will select the next screen situated on the east [START_REF] Shen | UbiTable: Impromptu Face-to-Face Collaboration on Horizontal Interactive Surfaces[END_REF]. In Device centric, the cursor (device) is set at screen 1. To select the target display (screen 9), the user should perform a hard roll in the south east direction. In Cursor centric, the cursor starts at screen 4. To select the target display (screen 6) the user must go over screen 5. Therefore, they should perform a slight roll to the east, reset TDome to its original position and then another slight roll to the east.

To detect the pen's data, we are using a Wacom Intuos 3D tablet that allows capturing in real time the physical x and y coordinates on tablet, virtual x and y coordinates of connected monitors, pressure and the buttons states of the pen (pressed and released). To detect TDome's physical manipulations, the device holds an x-IMU composed of a gyroscope, accelerometer and magnetometer that detects the rolls and rotations of the device.

We prototyped a GUI using C# on visual studio that allows performing major MDE tasks with TDome. The GUI is made up from 9 panels representing the 9 proposed displays. Topology of the 9 display can be freely adjusted. Each panel contains one or more controls that can be selected, dragged inside the panel, and dragged and dropped in another panel.

For display selection [START_REF] Serrano | Investigating Text Legibility on Non-Rectangular Displays[END_REF], each panel can be highlighted when the user hover over it, followed by a validation gesture that change the panel's color. As for Output redirection (2) we implemented a drag and drop function that allows moving a control from one panel to another at the same location, followed by an adjustment to the exact target location. Input redirection (3) was prototyped by a cursor transfer to the new panel, whenever a new panel is selected.

With these implemented techniques, we are able to (1) use TDome + Pen to directly reach a display without the need of going through all existing displays between the starting point and the target; (2) to transfer objects from one display to another at an exact location using the two devices and without dragging it along the MDE; (3) to redirect the cursor to the selected screen immediately after selection and thus, removing time spent in MDE.

Conclusion and future work

In this work, we explore the use of TDome in the nondominant hand along with the pen in the dominant hand as a bimanual input technique to perform display selection in A first perspective to this work will consist of designing and implementing the interaction techniques for MDE tasks, including display selection, input redirection and output redirection, and compare TDome + pen with keyboard + pen. This comparison will allow us to (1) see if a multi-DOF mouse can be effective in the non-dominant hand, compared to keyboard shortcuts, and (2) evaluate bimanual interaction techniques for common tasks in MDEs. Moreover, after exploring the proposed design space, we can compare our technique with others from the literature on a real MDE setup and not on an MDE emulation.

Finally, concrete uses of this technique are expected to be developed in the context of control room and supervised situations such a as a teacher and multiple students running a simulation.

Figure 1 :Figure 2 :

 12 Figure 1: Control room setup "https://www.winsted.com/mark ets/oil-gas/"

Figure 3 :

 3 Figure 3: TDome + Pen

Figure 4 :

 4 Figure 4: Examples of Display selection technique in Ego, Device and cursor centric perspectives on Arc and Matrix topologies

Acknowledgment

This work is funded by the AP2 project (research grant AP2 ANR-15-CE23-0001).


Mario Bermudez

Hugo Guzman

Ignacio Gonzalez Prieto

Federico Barrero
email: fbarrero@us.es

Mario Javier Duran
email: mjduran@uma.es

Xavier Kestelyn
email: xavier.kestelyn@ensam.eu

M Bermúdez

H Guzmán

I González-Prieto

M J Durán

Comparative Study of DTC and RFOC Methods for the Open-Phase Fault Operation of a 5-Phase Induction Motor Drive

Keywords: Multiphase induction motor drives, Direct Torque Control (DTC), Rotor Field Oriented Control (RFOC), Open-phase fault operation

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The interest of the scientific community in the multiphase machine field is not new and has gained importance in recent times thanks to the development of modern microprocessors and power converters [START_REF] Levi | Advances in Converter Control and Innovative Exploitation of Additional Degrees of Freedom for Multiphase Machines[END_REF][START_REF] Barrero | Recent Advances in the Design, Modeling and Control of Multiphase Machines[END_REF]. High performance multiphase drives are now recognized like an alternative to conventional three-phase ones in applications where the reduction of the power per phase and a high fault-tolerant capability are required. The symmetrical five-phase induction machine is one of the most interesting multiphase machines, and control methods normally applied in high performance three-phase induction drives have been extended to five-phase ones to exploit their advantages.

Different speed and torque control methods have been proposed in recent research works for the development of high performance five-phase induction motor drives. RFOC method is the most common one, where the outer speed and torque controller is complemented with multiple inner current control loops [START_REF] Jones | A synchronous current control scheme for multiphase induction motor drives[END_REF] or with predictive current controllers [START_REF] Duran | Reduction of common-mode voltage in five-phase induction motor drives using predictive control techniques[END_REF][START_REF] Lim | FCS-MPCbased current control of a five-phase induction motor and its comparison with PI-PWM control[END_REF]. DTC and predictive torque control (PTC) techniques have been also presented like alternative control methods in the development of high-performance five-phase induction motor drives [START_REF] Zheng | A novel direct torque control scheme for a sensorless five-phase induction motor drive[END_REF][START_REF] Gao | Low-speed control improvements for a 2-level 5-phase inverter-fed induction machine using classic direct torque control[END_REF][START_REF] Riveros | Variable-speed five-phase induction motor drive based on predictive torque control[END_REF].

Most of these studies are focused on the normal operation of the drive, but the capability of the controllers to manage the faulty operation of the system without adding extra hardware has been also considered in the last years to increase the interest of the industry in multiphase motor drives [START_REF] Barrero | Recent Advances in the Design, Modeling and Control of Multiphase Machines[END_REF].

Different types of faults may appear in the electrical drive, including inverter and machine faults like short-circuits and open-circuits faults, being the fault tolerance against opencircuit faults the most analyzed case by far in the multiphase machine area [START_REF] Barrero | Recent Advances in the Design, Modeling and Control of Multiphase Machines[END_REF]. A common feature of the proposed openphase post-fault control schemes is the use of a RFOC method with the same outer PI speed controller than in normal operation, while the inner current control loops have been realized using different strategies [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF][START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF][START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF][START_REF] Guzmán | Comparative Study of Predictive and Resonant Controllers in Fault-Tolerant Five-phase Induction Motor Drives[END_REF]. For example, dual PI or resonant controllers are proposed in [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF] to follow oscillating reference currents, while a model-based predictive controller is used in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF][START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF]. Both controllers are compared in [START_REF] Guzmán | Comparative Study of Predictive and Resonant Controllers in Fault-Tolerant Five-phase Induction Motor Drives[END_REF], where the obtained results conclude that predictive control provides faster response and superior performance at low/medium speed operation being less resilient to fault detection delays and having higher current and torque ripples. This work compares the performance of DTC and RFOC controllers when facing an open-circuit post-fault operation in a symmetrical five-phase induction machine. The paper is organized as follows. Section II summarizes the behavior of the five-phase induction machine system during the open-phase fault operation mode when DTC controllers are applied. Then, how RFOC methods face the fault operation of the multiphase drive is detailed in Section III. Finally, Section IV shows simulation results where the ability of both methods managing the post-fault operation of the drive is studied, and the conclusions are provided in the last section.

II. OPEN-PHASE FAULT OPERATION IN FIVE-PHASE INDUCTION

MOTOR DRIVES AND DTC CONTROLLERS If symmetrically distributed windings, uniform air gap, sinusoidal MMF distribution and neglectable magnetic saturation and core losses are considered, the normal five-phase induction machine can be modeled by a set of voltage equilibrium equations as it is stated in [START_REF] Bermúdez | Open-Phase Fault Operation of 5-Phase Induction Motor Drives using DTC Techniques[END_REF]. When an openphase fault appears (Fig. 1), the behavior of the system notably varies because the current in the faulty phase is zero and its voltage is given by the counter electromotive force (Back-EMF).

The model of the system must be then revised as it is shown in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF], where phase 'a' is assumed, without any lack of generality, as the faulty phase. In general terms and using the vector space decomposition (VSD) approach to refer the system into the well-known α-β-x-y stationary reference frame, non-circular α-β current components are obtained using the VSD normal transformation (T0), while circular α-β current components can be obtained using the modified VSD transformation shown in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF] and characterized by the TPCC matrix, see [START_REF] Levi | Advances in Converter Control and Innovative Exploitation of Additional Degrees of Freedom for Multiphase Machines[END_REF] and [START_REF] Barrero | Recent Advances in the Design, Modeling and Control of Multiphase Machines[END_REF]. The current components that contribute to the torque production (those mapped in the α-β plane) are sinusoidal in post-fault operation and the system can be modeled in open-phase fault operation using the modified VSD transformation from the matrix equations in phase coordinates (3)- [START_REF] Zheng | A novel direct torque control scheme for a sensorless five-phase induction motor drive[END_REF].

[ ]

                = 2 / 1 2 / 1 2 / 1 2 / 1 2 /
ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ T (1) [ ]             - - - - = 1 1 1
ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ PCC T (2) [ ] [ ]             + - -                         - - - - - - - - - - - - =             1 1 1 1 • 4 • 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 • 4 PCC r m s m e d c b PCC dc sz sy s s T dt di L dt di L S S S S T V v v v v α α β α (3) [ ] [ ] s PCC sz sy s s i T i i i i ⋅ =             β α (4) ] [ )] ( [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ r sr s ss s s s s s s i L dt d i dt d L i R dt d i R v ⋅ + + ⋅ = + ⋅ = θ λ (5) ] [ )] ( [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ s rs r rr r r r r r r i L dt d i dt d L i R dt d i R v ⋅ + + ⋅ = + ⋅ = θ λ (6)
where Si denotes the available power converter switching states (being Si = 0 if the lower switch is ON and the upper switch is OFF, and Si = 1 if the opposite occurs), [is] is the stator phase current vector, [vs] is the stator phase voltage vector, [λs] is the stator phase flux vector, the electrical parameters of the machine (stator and rotor resistances and inductances) are included into [R] and [L] matrices, ϑ is an electrical degree of 72º, θ represents the instantaneous rotor azimuth with respect to the α-axis of the stationary reference frame, phase 'a' is considered as the faulty open phase (isa = 0) and the lost control degree is modeled as isx = -isα. The reduction of the available power converter switching states (Si), from 2 5 =32 in pre-fault to 2 4 =16 in post-fault situation, is detailed in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF] and summarized in Fig. 2(a). [START_REF] Zheng | A novel direct torque control scheme for a sensorless five-phase induction motor drive[END_REF][START_REF] Gao | Low-speed control improvements for a 2-level 5-phase inverter-fed induction machine using classic direct torque control[END_REF]. Its extension to the open-phase post-fault operation of the multiphase drive is introduced in [START_REF] Bermúdez | Open-Phase Fault Operation of 5-Phase Induction Motor Drives using DTC Techniques[END_REF], and the proposed control scheme is shown in Fig. 3. The control action is provided using an outer PI closed-loop speed controller and two inner electrical torque and stator flux regulators based on a two-level stator flux and a three-level electromechanical torque hysteresis comparators. Eight active virtual voltage vectors are defined in the α-β subspace, each one corresponding to a different sector (see Fig. 2(b)), combining two available voltage vectors to obtain zero average volts-per-seconds in the y direction. The proposed DTC technique uses the look-up table shown in Table I, which determines the applied virtual voltage vector depending on the dλs and dTe error signals, the hysteresis comparators and the flux position. Notice that the stator flux and the torque in the electrical machine are estimated using two observers and the healthy stator phase currents. x-y β α-

DTC control technique has been very recently applied to five-phase induction motor drives in normal operation

7 V1(9)
V2 [START_REF] Bermúdez | Open-Phase Fault Operation of 5-Phase Induction Motor Drives using DTC Techniques[END_REF][START_REF] Riveros | Variable-speed five-phase induction motor drive based on predictive torque control[END_REF] V8(11,1) V7 [START_REF] Lim | FCS-MPCbased current control of a five-phase induction motor and its comparison with PI-PWM control[END_REF][START_REF] Jones | A synchronous current control scheme for multiphase induction motor drives[END_REF] V4 [START_REF] Duran | Reduction of common-mode voltage in five-phase induction motor drives using predictive control techniques[END_REF][START_REF] Yepes | Parameter identification of multiphase induction machines with distributed windings-Part 1: sinusoidal excitation methods[END_REF] V9( 15) V5( 6

V2 V3 V4 V5 V6 V7 V8 V1 -1 V8 V1 V2 V3 V4 V5 V6 V7 0 V0 V9 V0 V9 V0 V9 V0 V9 -1 +1 V4 V5 V6 V7 V8 V1 V2 V3 -1 V6 V7 V8 V1 V2 V3 V4 V5 0 V9 V0 V9 V0 V9 V0 V9 V0 III. RFOC MANAGING OPEN-PHASE FAULT OPERATION IN FIVE- PHASE INDUCTION MOTOR DRIVES
Other conventional three-phase control techniques have also been extended to the five-phase induction motor drive case, including also the open-phase fault operation. This is the case of the RFOC structure where different schemes have been proposed [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF][START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF][START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF][START_REF] Guzmán | Comparative Study of Predictive and Resonant Controllers in Fault-Tolerant Five-phase Induction Motor Drives[END_REF]. The controller is based on an outer PI closedloop speed control and an inner fault-tolerant regulation considering proportional resonant (PR) regulators or finitecontrol set model-based predictive current controllers (PCC for now on). Fig. 4 shows a scheme of RFOC controllers applied in five-phase induction machines when the open-phase fault operation is also considered.

The speed and flux control is implemented in the d-q reference frame using conventional PI controllers. The dcurrent reference is set to a constant value while the q-current reference is determined using the speed error and a PI-based controller. Considering that the y-current component does not contribute to torque production, it is set to zero in order to minimize losses and improve the efficiency of the system [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF][START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF][START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF]. As a consequence, it is not possible to achieve the maximum post-fault torque. The maximum reference currents in the α-β subspace can be obtained, using the five-phase drive maximum current ratings and imposing a rotating circle-shaped MMF, as follows: The transformation into the α-β-x-y planes is done using T0 in [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF] (RFOC with PR controllers) and with TPCC in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF][START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF] (RFOC with a PCC type current control method). The α-β current components are then mapped in the rotating d-q reference by means of the Park transformation and the position estimator that estimates the instantaneous rotor azimuth θ with respect to the α-axis:

      ⋅       - =       sq sd s s i i i i ) cos( ) sin( ) sin( ) cos( θ θ θ θ β α (8) dt i i sd r sq r          ⋅ + = * * τ ω θ (9)
The sinusoidal nature of the post-fault x-y current references in RFOC methods results in the necessity of using PR regulators instead of conventional PI ones to control the oscillating terms. PR regulators are implemented in [START_REF] Tani | Control of multiphase induction motors with an odd number of phases under opencircuit phase faults[END_REF] adding the outputs of two independent PI controllers, rotating in the direct and the inverse direction of the field-oriented reference frame, tracking positive and negative sequence currents and driving to zero the total tracking error. The feed-forward terms (ed and eq) were included in the control scheme to improve the controller performance, where the rotor-flux estimator is based on the speed measurement and the d-current component, as shown in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF].

sd r m r m r r i L j dt d • • 1 τ λ ω τ λ =         - + (10)
When the PCC technique is applied, the measured speed and stator currents are used with all available voltage vectors and the post-fault drive model to predict the stator current evolution for the next sampling period (k+1). The estimated stator current that minimizes a predefined cost function J defines the next voltage vector to be applied, which is the optimum voltage vector to be applied, Si optimum (k+1). Different cost functions can be defined, although the most common one considers the difference between the reference and the predicted stator currents, as it is shown in [START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF] where different weighting factors are defined for α-β-x-y coordinates (A, B, C and D parameters). In [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF] and [START_REF] Guzmán | IGBT-gating failure effect on a fault-tolerant predictive current controlled 5-phase induction motor drive[END_REF] C is zeroed because the xcomponent stator current is isx = -isα (it cannot be regulated independently from the α-component stator current), while A, B and D are set to one.

) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( * * * * + - + + + - + + + - + + + - + = k i k i D k i k i C k i k i B k i k i A J sy sy sx sx s s s s β β α α (11)
IV. OBTAINED RESULTS RFOC and DTC control methods are implemented in a five-phase induction motor drive modeled using a Matlab/Simulink environment. The electrical and mechanical parameters of the multiphase induction motor drive (see Table II) are obtained from a real system using different identification techniques [START_REF] Yepes | Parameter identification of multiphase induction machines with distributed windings-Part 1: sinusoidal excitation methods[END_REF][START_REF] Riveros | Parameter identification of multiphase induction machines with distributed windings-Part 2: time-domain techniques[END_REF]. Figs. 5 to 9 summarize the obtained results, where a DC link voltage (Vdc) of 300 V is used. Fig. 5 compares the speed responses of the system using DTC and RFOC controllers in the open-phase fault operation when the reference speed is first changed from 500 to 300 rpm, and then from 300 to 400 rpm. A load torque of 25% of the nominal one is used. Although similar speed responses are obtained (upper plot), a detailed analysis of the responses (lower figures) shows that the DTC controller (red traces) generates larger overshoots and poorer responses than the RFOC controllers with PCC technique (green traces), while offers similar responses than RFOC with PR controllers (blue traces). All the control techniques offer a similar performance when a change in the load torque is applied, as it is shown in Fig. 6, where the load torque is changed from 0 to 25% of the nominal one at 500 rpm. However, the speed responses when a reversal test is done (from 500 rpm to -500 rpm in Fig. 7) show again slightly better performances when RFOC method with PCC current controllers are used. These results prove that RFOC methods are not clearly superior to DTC techniques from the system performance perspective. Nevertheless, notice that the computational cost is much higher using RFOC methods, particularly if PCC technique is applied, which favors the real-time implementation of the DTC technique in modern microprocessors.

Fig. 8 shows the evolution of the stator currents in stationary frames using DTC and RFOC controllers in the open-phase fault operation when the reference speed is 500 rpm. The applied load torque is 25% of the nominal one. Again, the obtained results using the DTC controller, Fig. 8(c), are worst that the obtained using RFOC techniques, Figs. 8(a) and 8(b). The harmonic content (amplitude of the ripple in the circular plots) is superior using DTC in the α-β and x-y plane.

Notice that the PR current controller offers the best performance in this test, Fig. 8(a). Fig. 9 depicts the evolution of the stator currents in stationary frames but using an applied load torque of 56% of the nominal one. The same conclusions are reached, showing that the DTC controller presents the worst response among the applied controllers. Notice that higher current ripples appear in this test comparing with the previous one, being this a consequence of approaching the maximum load torque that the speed controller can manage in the open-phase fault operation (about 64% of the nominal one, as it is shown in [START_REF] Guzmán | Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques[END_REF]). V. CONCLUSIONS Multiphase motor drives have been recently used in applications where a high fault-tolerant capability is an important requirement of the system. The symmetrical fivephase induction motor drive is one interesting multiphase drive, and high performance controllers have been developed based on the RFOC method to take advantage of this faulttolerant capability. DTC techniques have been also proposed in very recent times, but there is a lack of comparison studies of the closed-loop system performance using DTC and RFOC controllers when facing the open-phase fault situation. This paper presents this comparison analysis for the first time, showing that DTC controllers are a viable alternative to RFOC methods in symmetrical five-phase induction motor drive. Although the DTC technique generates slightly poorer system performance than using RFOC methods with PCC current controller, its simpler implementation can make DTC an interesting alternative in particular applications.

i sa i sb i sc i sd i se -2 -1 0 1 2 -2 -1 0 1 2 i sα (A) i sβ (A) -2 -1 0 1 2 -2 -1 0 1 2 i sx (A) i sy (A) 1.3 1.35 1.4 1.45 1.5 1.55 1.6 -2 -1 0 1 2 Time (s) Current (A) i sa i sb i sc i sd i se -2 -1 0 1 2 -2 -1 0 1 2 i sα (A) i sβ (A) -2 -1 0 1 2 -2 -1 0 1 2 i sx (A) i sy (A) 1.3 1.35 1.4 1.45 1.5 1.55 1.6 -2 -1 0 1 2 Time (s) Current (A) i sa i sb i sc i sd i se -2 -1 0 1 2 -2 -1 0 1 2 i sα (A) i sβ (A) -2 -1 0 1 2 -2 -1 0 1 2 i sx (A) i sy (A)

Fig. 1 .

 1 Fig. 1. Schematic diagram of the five-phase induction machine modeled, with a fault in phase 'a'.

Fig. 2 .Fig. 3 .

 23 Fig. 2. (a) Available and (b) virtual voltage vectors in five-phase induction motor drives with the open-phase fault condition.

Fig. 4 .

 4 Fig. 4. RFOC control scheme based on proportional resonant (PR) regulators and PCC controllers.

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig.5. Speed response in the five-phase induction motor drive when the reference speed is changed in the system using a load torque of about 25% of the nominal one.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Steady state operation. Stator phase currents (left hand side plots) and evolution in the α-β (middle plots) and x-y (right hand side plots) planes, with a reference speed of 500 rpm and a load torque of about 25% of the nominal one, implementing (a) PR, (b) PCC and (c) DTC controllers, respectively.

TABLE I .

 I LOOK-UPTABLE FOR THE DTC CONTROLLER IN POST-FAULT SITUATION PROPOSED IN[START_REF] Bermúdez | Open-Phase Fault Operation of 5-Phase Induction Motor Drives using DTC Techniques[END_REF]

	dλs	dTe	1	2	Position of stator flux (Sector) 3 4 5 6	7	8
		+1
	+1

TABLE II

 II

	.	ELECTRICAL AND MECHANICAL PARAMETERS OF THE
	ANALYZED FIVE-PHASE INDUCTION MOTOR DRIVE
	Parameter	Value	Units
	Stator resistance, Rs	12.85	Ω
	Rotor resistance, Rr	4.80	Ω
	Stator leakage inductance, Lls	79.93	mH
	Rotor leakage inductance, Llr	79.93	mH
	Mutual inductance, M	681.7	mH
	Moment of inertia, J	0.02	kg-m 2
	Number of pole pairs, P	3	--
	Rated torque,

ACKNOWLEDGMENT

The authors would like to thank the Junta de Andalucía and the Ministerio de Economía y Competitividad of the Spanish Government for their funding of this research under references P11-TEP-7555, DPI2013-44278-R and ENE2014-52536-C2-1-R.


Sébastien Dubois
email: sebastien.dubois@insa-strasbourg.fr

Philippe Lutz
email: philippe.lutz@ens2m.fr

François Rousselot
email: francois.rousselot@insa-strasbourg.fr

Gérard Vieux
email: gerard.vieux@trixell-thalesgroup.com

A model for problems' representation at various generic levels to assist inventive design

Keywords: inventive design, TRIZ, UML model

Inventive design requires specific competences. Designing involves creating new concepts out of acquired knowledge and requires cognitive competences. TRIZ, a theory for inventive problem-solving, is based on the abstraction of knowledge to be able to make analogies with any technical domain. This principle of abstraction is of great interest, but it also requires the ability to shift from a high level of abstraction to a more specific level. The links between abstract models of problems and more specific ones are missing in TRIZ. This paper proposes a UML model to make this link to enable the construction of abstract formulation of problems from a functional description of the systems. A case study illustrates the different descriptions of the problems and the link between them.

Introduction

A lot of competences are required to design new technical systems [START_REF] Visser | Dynamic Aspects of Design Cognition: Elements for a Cognitive Model of Design[END_REF][START_REF] Adams | Educating effective engineering designers: the role of reflective practice[END_REF][START_REF] Dörner | Approaching design thinking research[END_REF][START_REF] Greeno | Natures of problem solving abilities[END_REF]. Designing is being able to synthesize new concepts. Two kind of design can be distinguished implying different kind of competences: routine design and inventive design. Inventive design is particular in the sense that new ideas have to emerge. However these new ideas have to be built out of known things. This is a real paradox: engineers have to build new things in order to be able to design inventively but engineers do not have to build new things as they only have the existing knowledge. Regarding how inventive products are designed, one of the main principles is the application, in a new domain, of things known in another domain [START_REF] Bonnardel | Creative Design Activities: the Evocation and its Evolution with Regard to Expertise[END_REF]. This principle has brought interesting results. How to be able to make bridges between different domains? It means how to be able to identify and recognize that one principle used in one domain could be useful and applicable in another domain. Moreover, engineers are specialized in the one domain in which that have got to solve problems, and looking for solutions from other domains are out of their competences. Even more, lot of psychological barriers disable human being to seek for solutions in a non mastered domain.

One theory for inventive problem solving in design of technical systems is TRIZ [START_REF] Altshuller | Creativity as an Exact Science[END_REF]. It is based on the building of analogies between different domains. To enable these analogies, TRIZ proposes to define the problem that has to be solved at a high level of abstraction. It means that TRIZ proposes both models to formulate the problems and principles of solution linked to these models. The basis of this theory is the analysis of millions of patents and the description of the problems solved by these patents in abstract shape. This analysis lead to the conclusion that, regarding problems and solutions at a high level of abstraction, there are not infinite numbers of generic problems as there is no infinite ways to solve these generic problems.

One of the main advantages of the use of TRIZ methods is to oblige engineers to think at different levels of abstraction. One of the main drawbacks of the use of TRIZ methods is to enable engineers to shift from their traditional models to the ones proposed by TRIZ methods.

The synthesis of a general model enabling a good understanding of the knowledge that has to be represented throughout the TRIZ problem formulation models and to explicit the links between these different models is a key stake. The analysis of the different software ( [START_REF] Ideation | Innovation WorkBench[END_REF][START_REF] Ideation | Improver[END_REF][START_REF] Ideation | Knowledge Wizard[END_REF][START_REF] Invention Machine | [END_REF][START_REF] Trisolver | [END_REF]) to support TRIZ application (see [START_REF] Dubois | Contribution à la formulation des problèmes en conception de systèmes techniques[END_REF]) shows that the software are complementary as each of it brings a partial support for the problem resolution steps. For example, none of the software consider the systemic description of the problem, which is though one of the core benefits of TRIZ models.

To overcome this drawback a model is proposed in this article to elicit the links between the different models of TRIZ for problem formulation and the functional description of systems.

Inventive design is specific in that it concerns open-ended, but ill-defined, problems [START_REF] Bonnardel | Towards understanding and supporting creativity in design: analogies in a constrained cognitive environment[END_REF]. The design problems are considered ill-defined since initially, designers only have an incomplete and imprecise mental representation of the design objectives. Designers' mental representations develop as the problem-solving process progresses [START_REF] Simon | The structure of ill-structured problems[END_REF]. This specificity in terms of design problems has been described as being based on an iterative dialectic between positioning the problem and finding a solution to the problem [START_REF] Simon | Problem Forming, Problem Finding, and Problem Solving[END_REF]. To summarize this approach, during the positioning of the problem, the designers refine the design objectives and its specifications and therefore refine their mental representation of the problem. During the problem-solving phase, designers work out solutions and assess these solutions in relation to a variety of criteria and constraints. Furthermore, the design problems are also defined in infinite space as no single correct solution can exist for a given problem, but rather a range of potential solutions is proposed. For this reason, inventive design problems are defined as open-ended problems.

These are the very characteristics of design problems that make them hard to solve and requiring high level competencies of analysis. Indeed, the problem is inadequately defined at the beginning and reformulation processes are therefore required to give a precise definition of the problem to be solved.

The reformulation processes mean that it is possible to move on from a description of the problem situation to a definition of the problem itself. The problem situation, which is a description of the objective to be reached without specifying the situation's mode of evolution can be distinguished from the problem, which defines a mode of evolution which will meet the objective; also the reason why it is impossible to achieve this evolution with known solutions will be explicit. This elicitation is the definition of the core of problem.

The formulation space is an open areathe formulation of the problem may differ for the same description of the problem situation. The path leading from the problem situation to the formulated problem depends on several factors.

 The constraints integrated during the reformulation processthese constraints are specific to the problem situation.

 The strategic choices made by the designerthese choices are directed by the strategic policy at the time the problem is to be solved.

The knowledge of the designer solving the problem also guides the reformulation process. This knowledge is related to the problem and the field in which it occurs.

Gero, [START_REF] Gero | Conceptual designing as a sequence of situated acts[END_REF], defines conceptual design, the creative phase in the design process, as being characteristic of the fact that "all knowledge required to achieve the design is not known in theory, i.e. part of the design process consists in determining what is required." As specific knowledge are no sufficient to solve the problems, it is required to use more generic, more abstract, descriptions to be able to imagine new concepts and also to better understand and define the core of problems.

3 Models of TRIZ TRIZ, a Russian acronym which means the Theory of Inventive Problem Solving [START_REF] Altshuller | Creativity as an Exact Science[END_REF], is a design theory centered on formulating and solving problems. In TRIZ several models for formulation of problems are proposed. Each of these models corresponds to a different level of abstraction. Some of the models are used to enable resolution by the use of shaped databases of generic solutions; some of the models are only intermediary steps in the problem formulation process. At the lowest level of abstraction, the more specific level, there is what is called, in TRIZ terminology, the technical contradiction. This level of problem formulation is an intermediary step in the resolution process, as this frame of problem formulation is dedicated to a better understanding of the problem without aiming at an inventive resolution of the problem. The technical contradiction is the expression of the opposition between two states of a system that seems impossible to satisfy at the same time. In TRIZ terminology, the two states are defined as being two parameters of the same system. Khomenko [START_REF] Khomenko | Materials for Seminars: OTSM-TRIZ: Main Technologies of Problem Solving[END_REF] has proposed a more precise definition of this level of definition of the problem, describing these parameters as evaluation parameters. Evaluation parameters are used to check if the problem is solved or not, but not used as parameters on which we can proceed to solve the problem. The simplest way proposed in TRIZ to formulate the problem through this shape is to explain why a known solution, a typical solution, can not be applied in the considered case.

A technical contradiction exists when a solution is known to reach the satisfaction of the evaluation parameter 1, but the application of this solution disables the satisfaction of the evaluation parameter 2.

For example a technical contradiction exists in belt-pinion systems when the rigidification of the belt enables a better transmission, but then disables the ability of the belt to turn around the pinion.

The next frame of problem definition, at a higher generic level, is the Vepole model, also known as Substance-Field Model. This frame is the representation of the interactions existing between the resources present in the problem. The resources are classified according to the fact they are a substance or a field. This model represents the nature of the interaction and the role (useful or harmful) it plays in the problem. The main objective of this model is to focus on the few elements directly implied in the problem. For this model of the problem, 76 rules to modify the interactions between the resources as required to solve the problem are proposed [START_REF] Altshuller | System of Standard Solutions for Inventive Problems[END_REF]. These generic rules are called the inventive standards.

A Vepole model is defined when some interactions between resources (which can be either substance or field) have to be modified.

For example, the interaction between the belt and the pinions is insufficient, as we need to rigidify the belt to provide a better transmission. The resources are two substances, the belt and at least one pinion, and also a mechanical field.

A last model is proposed in TRIZ and is called the physical contradiction. This model is the more abstract one. This model focuses the problem on one single element of the system, which is the core of problem. According to TRIZ a problem can always be formulated as a physical contradiction. Such a contradiction is defined as the requirement for one element to be in two contradictory states. The two benefits of such a formulation are:

 The focus on one single element, which is the core of problem  The formulation that is totally not specific to a domain A physical contradiction exists when one element of a system has to be in two contradictory states.

For example a physical contradiction exists in belt-pinion systems as the belt as to be both rigid to transmit energy efficiently and flexible to turn around the pinions.

Another interest of this level of formulation is that few principles exist to satisfy both contradictory states, in TRIZ a list of 11 principles is proposed. One of these principles is designing a system having globally one property but made of elements having the contradictory property. This principle is applied by the chain to solve the problem of the belt. The chain is globally flexible and made of rigid elements.

Presentation of the UML model

The built model [START_REF] Dubois | Contribution à la formulation des problèmes en conception de systèmes techniques[END_REF] is the object-oriented representation of the TRIZ problem formulation frames. It does not include all the concepts of the theory; especially TRIZ proposes laws of evolution for technical systems, which are not available. The objectives are both to propose a clear description of TRIZ problem formulation frames that are proposed at different levels of abstraction, and to make the link between these frames and a functional description of systems.

The model is represented on figure 1, in UML (Unified Modeling Language), and is described below. The next description of the model is the description of the TRIZ frames to represent the real elements and the problems. In this model some peculiarities appear in regard of classical TRIZ frames. First of all, the technical contradiction model is not present; it has been replaced by a functional description of the systems. This proposal is based on the fact that the evaluation parameters of systems are a representation some functionalities of a specific system. Considering the example of the bicycle chain, ability to transfer energy was defined as an evaluation parameter, but it can also be described as a function. Thus the functions in the presented models are on the same level, and provide the same role of intermediary problem statement, as technical contradiction in classical TRIZ.

A resource is the basic element representing a real object characterized by its localization and described by a whole of parameters. A resource could be localized inside the system implied in the study, in an adjacent system or, more globally, in the environment. A resource could be a field, a geographical zone (a space), a temporal period (a time) or a material resource. The nature of the field could be magnetic, mechanic, electric, chemical or thermal. A material resource could be a system or a substance in regard of its decomposability. A system is composed of, at least, four material resources, enabling its functionality. These four main elements assume the roles of motor, transmission, tool and control to provide the function.

A function is the modification of the value of a parameter of a resource. The realization of the function modifies the parameter from an initial value into a final value. The function operates during an operational time and within an operational zone. The importance of the function could be principal, if it is the function for which the system has been designed, or technical, if it is a sub-function enabling the realization of the principal one. The type of the function could be useful or harmful. It is harmful if it is a non desired function to be eliminated, resulting of the realization of other useful functions. A function could participate to the realization of a super-function and could be decomposed into sub-functions.

Figure 1. UML model of TRIZ frames

A contradiction arises if one or several functions require that the parameter of a resource has one value, when another, or several others, functions require this parameter to have another value.

An interaction is the representation of the action of a material resource on another material resource. This action is produced by a field. The interaction could be satisfying, excessive, insufficient or harmful. It is harmful if it is a non desired interaction, which is to eliminate (for example the Joule effect of a component inside an electric circuit). If the interaction is useful, it could be excessive, if it is realized more than necessary and then occurs disturbances (the sun radiations on the skin in summer, for example). A useful interaction could also be insufficient if its action has to be increased (the oxygen inflow in high altitude, for example). At last, if the interaction is to be kept as is, it is a satisfying one.

A Vepole model is made of interactions and of resources. This model is characterized by the additivity constrains and by the contact necessity. The possibilities to add a field, an additive or a substance are thus defined, as the possibility to break the contact between two substances of the Vepole model.

Illustration

TRIXELL develops and produces a complete family of X-ray flat panel digital detectors for the entire radiological imaging industry. TRIXELL has developed a real competitive strategy based on cost reduction. To reach this objective they are producing flat scanners made of assembled TFT plates. Using smaller TFT plates enable dramatic cost reductions, but imply developing algorithms to calibrate the scanners. To pursue their cot reduction strategy, TRIXELL was looking for a new principle of flat scanner production keeping their today's quality and reliability but requiring less calibration. One of the main difficulties for TRIXELL is to be able to imagine new solutions after ten years of development.

To solve their problems TRIXELL asked for TRIZ experts to help them in the description of their problematic situation and in the proposal of new concepts. As inventive concepts have been defined for which patents are in validation process, the results of this study won't be presented in this article. But the main objective of the article is to present the link between the different levels of problem formulation.

General description of the problematic situation

The studied system is a flat numeric scanner (cf. figure 2) used to scan human bodies to detect irregularities of 140µm. It is made of several layers and at least 2 butted TFT plates.

G la s s -s u b s tra te C e s iu m Io d id e s c in tilla to r c o n ve rts X -R a ys in to lig h t A m o rp h o u s s ilic o n p h o to d io d e c o n ve rts lig h t in to

e le c tric a l s ig n a ls

X -R a y s

L ig h t

Figure 3. Main working principle of the flat numeric scanner

The use of several TFT plates enables the reduction of costs, as small TFT plates are less expensive to produce but in the same time it generates non homogeneous artefacts on the image, from one scanner to another. Thus specific algorithms have to be defined to calibrate each scanner.

The case study aim at designing a new flat numeric scanner made of several TFT plates, but taking off the need of calibration algorithms.

On figure 4 is presented a part of the modeled problem, which includes the definition of the main elements of the scanner and some of the underlined functions and problems identified throughout the analysis of the problematic situation. The building of the model has been guided by the use of two methods of TRIZ:

 The multi-screen scheme, which is based on a systemic analysis of problem, describing the implication of the problems on different systemic levels and according to its evolution in time.

 ARIZ, which is a method guiding the formulation of physical contradiction and the identification of the preferable resources to solve it.

Description of the problem at different generic levels

After an initial phase of general description of the system, of its components and of the objectives of the problem resolution, the first step in the process of problem clarification is the description of the specific required functions on which the problem focus.

A list of 6 functions has been listed as being main functions of the problem: A first peculiarity of this description is shown with the last listed function, as it is not a desirable function, but in reality it is performed and it has to be overcome. This function is identified as a harmful one.

 produce cheap
For example, the functions "guide visible light rays" and "create artefacts" are described as shown on figure 5. A Vepole model could then be built and enables a clarification of the problem (cf. figure 6). In fact, the reason why artefacts appear is the necessity to assemble the plates. Each step of the problem formulation brings better understanding of the reasons why problem appears, and thus enables to define potential direction of resolution and elimination of the non relevant ones.

Figure 6. Vepole model of problem formulation

The last step in the problem formulation process is the formulation of the physical contradiction. This formulation point out that the core of problem is the homogeneity of the space around the scintillator and the TFT plates, which is called here the environment, as illustrated on figure 7. As previously said these concepts won't be presented in the article but the objective was to explicit the different levels of problem formulation and the way it is used to shift from one level to another one. The three models of problem presented in figure 5 to 7 are all linked to the function "guide visible light rays".

Conclusion

The proposed model enables a clarification of the models of TRIZ for problem formulation. It also enables an easier transition from one model to another. This second point is of great interest as inventiveness requires the ability to shift from a high level of abstraction to a more specific level; thus it enables engineers to look for multi-domain analogies and then to apply generated inventive concepts to their specific situation. Moreover, this elicitation of the links between the models aims at facilitating the use of TRIZ models starting from a functional description of the systems.

As extension of this work, we are now studying how to link this model with a database to be able to build case-based reasoning for inventive problem-solving, storing cases at different levels of abstraction. Also another direction of application is making the link between contradictions for problems of high complexity, and looking for rules to establish and manage such networks of contradictions.

Figure 2 .

 2 Figure 2. Main components of a flat numeric scannerThe main working principle is the transformation of the X-ray flow into an electric signal, and it is provided by a scintillator made of CsI which transforms the x-ray flow into a visible light flow and of the TFT plates which transform the visible light signal into an electric signal, as illustrated on figure3.

Figure 4 .

 4 Figure 4. Global overview of the elements of the scanner

  scanners  transform X-rays into visible light rays  transform visible light into electric signal  assemble plates  guide visible light rays  create artefacts

Figure 5 .

 5 Figure 5. Functional level of problem formulation

L o ca lisa

  tio n = b e tw e e n th e T F T p la te s B u ttin g se ctio n : S p a ce In itia l va lu e = se p a ra te d F in a l va lu e = a sse m b le d typ e = u se fu l im p o rta n ce A sse m b le p la te s : F u n ctio n In itia l va lu e = in scin tilla to r F in a l va lu e = to p h o to d io d e s typ e = u se fu l im p o rta n ce G u id e visib le lig h t ra ys : F u n ctio n L o ca lisa tio n N a tu re V isib le lig h t ra ys : F ie ld L o ca lisa tio n P la te s : S u b sta n ce A d d a d d itive s : B o o le a n = T R U E A d d su b sta n ce : B o o le a n = T R U E A d d fie ld : B o o le a n = T R U E N e ce ssity o f co n ta ct : B o o le a n = F A L S E V e p o le 1 : V e p o le C h a ra cte r = H a rm fu l M a in ta in : In te ra ctio n C h a ra cte r = S a tisfyin g G u id e : In te ra ctio n L o ca lisa tio n N a tu re M e ch a n ica l a sse m b lin g : F ie ld L o ca lisa tio n N a tu re E le ctro -m a g n e tic p ro p a g a tio n :

Figure 7 .

 7 Figure 7. Contradiction model of problem formulationThe formulations of the previous Vepole model and of the physical contradiction enable a clarification of the role of each element of the system, and thus lead engineers from TRIXELL to a new understanding of