Youssouf Mini
email: youssouf.mini@ensam.eu

Ngac Ky Nguyen
email: ngacky.nguyen@ensam.eu

Eric Semail
email: eric.semail@ensam.eu

Duc Tan Vu

Enhancement of Sensorless Control for Non-Sinusoidal Multiphase Drives -Part I: Operation in Medium and High-Speed Range

Keywords: Sensorless control, back-EMF observer, sliding mode observer, integrated motor drive, multiphase machine, seven-phase permanent magnet synchronous machine

This two-part study proposes a new sensorless control strategy for non-sinusoidal multiphase permanent magnet synchronous machines (PMSMs), especially in integrated motor drives (IMDs). Based on the Sliding Mode Observer (SMO), the proposed sensorless control strategy uses the signals (currents and voltages) of all fictitious machines of the multiphase PMSMs. It can estimate the high-accuracy rotor position that is required in the vector control. This proposed strategy is compared to the conventional sensorless control strategy applying only current and voltage signals of the main fictitious machine, including the fundamental component of back electromotive force (back-EMF) of the non-sinusoidal multiphase PMSMs. Therefore, in order to choose an appropriate sensorless control strategy for the non-sinusoidal multiphase PMSMs, these two sensorless control strategies will be highlighted in terms of precision in the rotor position and speed estimations. Simulation and experimental results of a non-sinusoidal seven-phase PMSM will be shown to verify and compare the two sensorless control strategies. In this part of the study (part I), only the sensorless control in medium and high-speed range is considered. The sensorless control at zero and low-speed range will be treated in the second part of this study (part II).

Introduction

With the huge development of electrified automotive vehicles, low-cost electrical drives but with high performances are sought. At first, for a good torque quality in terms of low ripples and high dynamics, vector control with precise knowledge of rotor position is a requirement. With three-phase PMSM, it is then necessary to consider machines with sinusoidal electromotive forces. This requirement impacts their cost and torque density in comparison with three-phase machine with trapezoidal electromotive forces. With nphase multiphase PMSM, it is possible to obtain simultaneously the torque quality of a three-phase sinusoidal PM machines and the torque density [START_REF] Wang | Harmonic current effect on torque density of a multiphase permanent magnet machine[END_REF][START_REF] Wang | Torque Improvement of Five-Phase Surface-Mounted Permanent Magnet Machine Using Third-Order Harmonic[END_REF] of non-sinusoidal trapezoidal three-phase PM machines thanks to their specific harmonic properties. More precisely, for a machine with (2k+1) phases, a generalized vector control with k dq rotating frames using k rotation angles has been proposed [START_REF] Kestelyn | Vectorial Modeling and Control of Multiphase Machines with Non-salient Poles Supplied by an Inverter[END_REF][START_REF] Slunjski | General Torque Enhancement Approach for a Nine-Phase Surface PMSM With Built-In Fault Tolerance[END_REF] in case of electromotive force spectrum with (k+1) harmonics. These multiphase machines not only place less stress on design and manufacturing, they also exhibit tolerance to power failures. Moreover, the usual drawback of numerous (2k+1) AC cables to connect between the machine and an external Voltage Source Inverter is disappearing with the development of integrated motor drives (IMDs) in which the power inverter is integrated into the electrical machine [START_REF] Burkhardt | Design and analysis of a highly integrated 9-phase drivetrain for EV applications[END_REF][START_REF] Deng | Design Consideration of a High-Speed Integrated Permanent Magnet Machine and its Drive System[END_REF][START_REF] Abebe | Integrated motor drives: state of the art and future trends[END_REF].

In this context, the mechanical position encoder appears to be the weak point with its constraints of size, cost and reliability leading to the development of a "soft" position sensor, i. e., applying only electrical sensors (of currents and voltages) or integrated magnetic sensors (Hall effect sensors). As sensorless controls have been extensively studied for three-phase machines the first approach is to consider the methods already developed to estimate the position keeping in mind nevertheless that for a non-sinusoidal machine with (2k+1) phases it is necessary to consider not only one rotation angle but k in order to work in k (d-q) rotating frames. Each rotating angle is chosen in relation to the most important harmonic component of the electromotive force at the origin of torque in the corresponding fictitious machine [START_REF] Kestelyn | Vectorial Modeling and Control of Multiphase Machines with Non-salient Poles Supplied by an Inverter[END_REF][START_REF] Slunjski | General Torque Enhancement Approach for a Nine-Phase Surface PMSM With Built-In Fault Tolerance[END_REF][START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF]. As example for a five-phase machine  (resp 3

) for the first (resp. the second) fictitious machine associated to the first (resp. the third) harmonic.

For three-phase machines, there have been several methods which have proposed the sensorless control strategies of PMSM [START_REF] Vas | Sensorless Vector and Direct Torque Control[END_REF][START_REF] Rind | Electric Motors and Speed Sensorless Control for Electric and Hybrid Electric Vehicles: A Review[END_REF]. All methods are based on the measurement of currents and voltages of the machines to compute (estimate) the rotor position and speed information. As back-EMFs are functions of the rotor position, they can be used to provide the rotor position and speed information [START_REF] Ribeiro | Dynamic Properties of Back-emf Based Sensorless Drives[END_REF]. Based on the machine model, the quality of the back-EMF estimation essentially depends on their amplitude. It means that when the machine operates at low speed, the estimation will be not precise because of the low amplitude of back-EMFs [START_REF] Ribeiro | Dynamic Properties of Back-emf Based Sensorless Drives[END_REF]. Indeed, in the sensorless control, back-EMFs are estimated from current and voltage signals, and the voltage amplitude is very tiny at low speed, especially for low-voltage machines. In addition, the voltage signal is affected by the voltage drop in inverter legs and disturbed by the non-linearities of the inverter and PWM harmonics [START_REF] Hejny | Evaluating the Practical Low-Speed Limits for Back-EMF Tracking-Based Sensorless Speed Control Using Drive Stiffness as a Key Metric[END_REF]. When the rotating speed decreases, the signal-to-noise ratio is reduced, leading to a noisier estimation of rotor position and speed. When the machine runs at a significant speed, the back-EMF estimation becomes more precise, allowing an accurate estimation of the rotor position [START_REF] Hejny | Evaluating the Practical Low-Speed Limits for Back-EMF Tracking-Based Sensorless Speed Control Using Drive Stiffness as a Key Metric[END_REF]. In fact, for the sensorless control of PMSM, two speed range have been defined in the literature review [START_REF] Hejny | Evaluating the Practical Low-Speed Limits for Back-EMF Tracking-Based Sensorless Speed Control Using Drive Stiffness as a Key Metric[END_REF][START_REF] Bo | The position-sensorless control of low voltage high power permanent magnet synchronous motors in zero/low-speed regions[END_REF] according to the rotor speed. The "medium and high-speed range" refers to speeds greater than 10% of the base speed while the "zero and low-speed range" includes speeds less than 10% of the base speed.

In zero and low-speed range, the sensorless control of PMSM is based on High Frequency (HF) signal injection methods [START_REF] Liu | Sensorless Control for Five-Phase IPMSM Drives by Injecting HF Square-Wave Voltage Signal into Third Harmonic Space[END_REF][START_REF] Zine | Optimisation of HF signal injection parameters for EV applications based on sensorless IPMSM drives[END_REF]. The basic theory of these methods is based on the tracking of machine saliency (inductance variations due to geometrical effects and saturation) that is modulated by the rotor position [START_REF] Ramezani | The Modeling and Position-Sensorless Estimation Technique for A Nine-Phase Interior Permanent-Magnet Machine Using High-Frequency Injections[END_REF]. Meanwhile, the sensorless control in medium and high-speed range, which will be treated in this paper, is essentially based on back-EMF observers to estimate the rotor position information [START_REF] Vas | Sensorless Vector and Direct Torque Control[END_REF][START_REF] Benjak | Review of position estimation methods for IPMSM drives without a position sensor part II: Adaptive methods[END_REF]. These observers are almost based on techniques such as Luenberger Observer (LO) [START_REF] Andersson | Motion Sensorless IPMSM Control Using Linear Moving Horizon Estimation With Luenberger Observer State Feedback[END_REF], Model Reference Adaptive System (MRAS) [START_REF] Ouvang | Speed Sensorless Control of PMSM Based on MRAS Parameter Identification[END_REF], Extended Kalman Filter (EKF) [START_REF] Shi | Online Identification of Permanent Magnet Flux Based on Extended Kalman Filter for IPMSM Drive With Position Sensorless Control[END_REF], and SMO [START_REF] Qiao | New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor[END_REF]. However, all these techniques are not feasible at standstill and low speed with the very low amplitude of back-EMF. Among these techniques, the SMO has been widely used for the sensorless control of PMSM since the chattering phenomenon (main disadvantage of SMO) can be reduced by using the sigmoid function as non-linear element [START_REF] Qiao | New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor[END_REF][START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF] or the novel hybrid reaching law with disturbance observer as proposed in [START_REF] Sun | A Composite Sliding Mode Control for SPMSM Drives Based on a New Hybrid Reaching Law With Disturbance Compensation[END_REF]. The sigmoid function is used by SMO to correct the error between the estimated variables and the measured ones. This structure can maintain a good robustness of the entire observer to perturbations [START_REF] Qiao | New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor[END_REF]. Therefore, to perform the accurate sensorless control of non-sinusoidal multiphase PMSMs, SMO is preferable due to its simple implementation compared to EKF. Indeed, EKF requires a long calculation time especially in the case of multiphase machines [START_REF] Michalski | Sensorless control of five phase PMSM based on extended Kalman filter[END_REF]. Moreover, compared to the LO [START_REF] Olivieri | Sensorless control of five-phase brushless DC motors[END_REF] and MRAS [START_REF] Saad | Investigation on SVM-Backstepping sensorless control of five-phase open-end winding induction motor based on model reference adaptive system and parameter estimation[END_REF], SMO [START_REF] Zhang | Fault-Tolerant Sensorless Control of a Five-Phase FTFSCW-IPM Motor Based on a Wide-Speed Strong-Robustness Sliding Mode Observer[END_REF] presents a robust structure dealing with variations of machine parameters and noises.

Non-sinusoidal multiphase PMSMs presents non-sinusoidal back-EMF signals. It means that the torque of the multiphase PMSMs is produced not only by the fundamental of back-EMFs and currents, but also by the other harmonics contained in the back-EMF signal. According to the decomposition theory [START_REF] Semail | Right harmonic spectrum for the back-electromotive force of an n-phase synchronous motor[END_REF], a real multiphase machine can be decomposed into several fictitious machines (reference frames), including the main fictitious machine (which generates most of the torque) and other fictitious machines. A given family of harmonics is associated with each fictitious machine. Moreover, the sensorless control based on SMO estimates back-EMFs through current and voltage signals, and then deduces the rotor position and speed. Sensorless control strategies for the non-sinusoidal multiphase PMSMs, based on only the fundamental component of back-EMFs (associated with the main fictitious machine), have been found in [START_REF] Zhang | Fault-Tolerant Sensorless Control of a Five-Phase FTFSCW-IPM Motor Based on a Wide-Speed Strong-Robustness Sliding Mode Observer[END_REF][START_REF] Chen | Speed control for two series-connected five-phase permanent-magnet synchronous motors without position sensor[END_REF][START_REF] Stiscia | Sensorless Control of a Nine-phase Surface Mounted Permanent Magnet Synchronous Machine with Highly Non-Sinusoidal Back-EMF[END_REF]. In this case, only currents and voltages of the main fictitious machine are used to estimate the rotor position.

In this part of the study, an original sensorless strategy using several harmonics of back-EMFs to estimate an accurate rotor position of non-sinusoidal multiphase machines is proposed. Signals from all fictitious machines (currents and voltages) are required to perform the sensorless control strategy. This is in order to improve the quality of currents regulation of equivalent fictitious machines, that can lead therefore to a good torque response specially in transient states. This proposed strategy is compared with the classical strategy which utilizes only the fundamental component of back-EMF. Both strategies are tested, through simulations, on a non-sinusoidal seven-phase PMSM and a non-sinusoidal five-phase PMSM. The torque of the seven-phase PMSM is mainly produced by the 1 st harmonic of back-EMF and current. Meanwhile, the torque of the five-phase PMSM used in this study is mainly generated by the 3rd harmonic of back-EMF and current. The use of different harmonics in this study to generate torque aims at highlighting the generality of the proposed sensorless control strategy to all non-sinusoidal multiphase PMSMs. For advanced verification, both sensorless control strategies will be experimentally verified on a non-sinusoidal seven-phase PMSM. This study is an extension of [START_REF] Mini | A novel Sensorless Control Strategy Based on Sliding Mode Observer for Non-Sinusoidal Seven-phase PMSM[END_REF] which has presented only numerical results of seven-phase machines. Compared to [START_REF] Mini | A novel Sensorless Control Strategy Based on Sliding Mode Observer for Non-Sinusoidal Seven-phase PMSM[END_REF], more comparisons and experimental results are provided in this present paper. In addition, artificial intelligence is added to solve the multi-harmonic problem of back-EMF.

Part I of this study is organized as follows. The seven-phase PMSM modeling is presented in section 2. The sliding mode observer design and the two sensorless control strategies will be explained and detailed in section 3. Simulation and experimental results will be respectively shown in sections 4 and 5 to analyze and highlight each sensorless control strategy.

Seven-phase PMSM Modelling

The design of the non-sinusoidal seven-phase PMSM is proposed in [START_REF] Locment | Control of a Seven-phase Axial Flux Machine Designed for Fault Operation[END_REF] with axial flux machine with one stator and two rotors as shown in Figure 1. It is assumed that there is no magnetic saturation and saliency. The model of the machine in the natural frame can be described in [START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF] as:

  di v Ri e dt = + + L (1)
where v , e , and i are the 7-dimension vectors of phase voltages, back-EMFs, and phase currents, respectively;   L and R are the stator inductance matrix and the stator winding resistance of one phase, respectively. By using the Concordia matrix [START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF], a seven-phase PMSM can be decomposed into four fictitious machines. In other words, a real seven-phase PMSM is equivalent to three fictitious two-phase machines and one homopolar machine associated with the different groups of harmonics as shown in Figure 2. Due to a wye connection of stator windings, the homopolar machine is not considered [START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF]. Four fictitious machines and associated harmonic groups of seven-phase PMSM [START_REF] Semail | Vectorial formalism for analysis and design of polyphase synchronous machines[END_REF].

The measured back-EMF of one phase of the non-sinusoidal seven-phase PMSM and the harmonic spectrum are described in Figure 3. It can be seen that the amplitudes of 1 st , 9 th and 3 rd harmonics are highest in the back-EMF. By decomposing the seven-phase PMSM into several fictitious machines (see Figures 2 and3), the 1 st , 13 th , 15 th , and 27 th harmonics are associated with in the Main Machine (MM), the 9 th , 19 th and 23 rd harmonics present in the Secondary Machine (SM), the 3 rd , 11 th , and 17 th harmonics with the Third Machine (TM). By the same way, the 7 th and 21 st are associated with the Homopolar Machine (HM) (homopolar currents are equal to zero with the wye connection). Therefore, the model of a seven-phase PMSM, considering the 1 st harmonic in MM, the 9 th harmonic in SM and the 3 rd harmonic in TM, can be expressed in the stationary reference frames ( )  -by: By considering the main harmonics (1 st , 3 rd , and 9 th ) of the back-EMF, the electromagnetic torque of the non-sinusoidal seven-phase PMSM can be obtained by the sum of torques from the three fictitious machines as follows:

1 1 1 1 9 9 9 9 3 3 3 3 m s t di L Ri e v dt di L Ri e v dt di L Ri e v dt              = - - +     = - - +     = - - +   (2)
1 9 3  =  +  +  (3)
                      =              =              =     where 1
 is the torque of MM; 9  is the torque of SM; 3  is the torque of TM ;  is the rotating speed.

When only the 1 st , 3 rd and 9 th harmonics are considered, the back-EMFs in ( )  - frames can be expressed as [START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF]: dq -. In this context, from (4), the back-EMF signal contains the rotor position information. Thus, to implement the sensorless control of the seven-phase PMSM, an algorithm based on the SMO will be designed to estimate the back-EMF signals which are necessary to extract the rotor position and speed information with high accuracy. This machine, with 32% for the third harmonic and 12% for the ninth harmonic, is interesting to compare the two approaches that will be presented in this article. These approaches are to estimate the three rotation angles which are used for the determination of the three rotating frames in a seven-phase machine.

                  =   = -   =   = -   =  = -   (4)

Sliding Mode Observer -based Sensorless Control Strategies

The SMO algorithm can be designed in ( )  - frames. Measured currents and reference voltages are used as inputs of the numerical algorithm [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF] as shown in Figure 4.

From the reference voltages and the outputs of the non-linear element (sigmoid function), the currents are estimated in ( )  - frame. Then, the estimated currents are compared to the measured currents. The error between these currents is put in the sigmoid function in order to minimize the error. The back-EMF estimation unit is fed by the outputs of the sigmoid function, which contain the back-EMF signal disturbed by a high-frequency component from the chattering phenomenon. The objective is to eliminate the high-frequency component to extract the estimated back-EMF signal for the estimation of the rotor position and speed. The estimation process by SMO is described in Figure 4 for each fictitious machine. The speed ˆr  and rotor position  are extracted from the estimated back-EMF

( )

ˆ, ee  [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF][START_REF] Zhang | Fault-Tolerant Sensorless Control of a Five-Phase FTFSCW-IPM Motor Based on a Wide-Speed Strong-Robustness Sliding Mode Observer[END_REF]. The sigmoid function, used to reduce the chattering phenomenon (in- ducing a high frequency component) in SMO, is a continuous function [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF].

For the seven-phase PMSM, the estimated currents of each fictitious machine by SMO can be expressed as [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF]: ˆˆ(

) i i i i i i i di L Ri v k F i i dt        = - + - -   (5)
with () Fx is the sigmoid function [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF] and:

()

() i i i i i i i i z k F i i z k F i i        =-    =-  (6)
where i= {1, 9 , 3}, and ( )

Back-EMF estimation

Current

Observer (SMO)

Sigmoid Function

Rotor position and speed estimation

By comparing equations ( 2) and ( 5), it can be considered that (6) represents respectively the back-EMF signals of MM, SM and TM. However, it should be noted that the signals contain a high-frequency component caused by the sigmoid function "chattering phenomenon". Thus, to extract only the useful back-EMF signals for the rotor position estimation, a back-EMF observer will be constructed. Therefore, based on ( 6) and ( 4), the back-EMF observer of each fictitious machine of the seven-phase PMSM is built as [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF][START_REF] Zhang | Fault-Tolerant Sensorless Control of a Five-Phase FTFSCW-IPM Motor Based on a Wide-Speed Strong-Robustness Sliding Mode Observer[END_REF]:

ˆˆˆ() ˆˆˆ() i r i i i i i r i i i i de i e l e z dt de i e l e z dt            = - - -     = - -   (7)
where ˆˆˆ

T i i i e e e     =  is the estimated back-EMF in ( )
 - frames of the fictitious machines; ( )

1 9 3 ,, l l l
represent the SMO gains. The suitable gains ( )

1 9 3 ,, k k k
and ( )

1 9 3
,, l l l , are defined by considering the SMO stability [START_REF] Yang | Iterative sliding mode observer for sensorless control of five-phase permanent magnet synchronous motor[END_REF]- [START_REF] Zhang | Fault-Tolerant Sensorless Control of a Five-Phase FTFSCW-IPM Motor Based on a Wide-Speed Strong-Robustness Sliding Mode Observer[END_REF].

As mentioned in section 1, two SMO -based sensorless control strategies for the nonsinusoidal seven-phase PMSM will be detailed and then compared in the next subsections. From the back-EMF estimation in [START_REF] Abebe | Integrated motor drives: state of the art and future trends[END_REF], the two strategies can be defined. Specifically, the first strategy (conventional strategy), denoted by S1, uses only the estimated back-EMF signals of fictitious MM (1st harmonic). The second strategy (proposed strategy), denoted by S2, is based on all estimated back-EMF signals (1 st , 3 rd , and 9 th harmonics).

3.1.Conventionnal Sensorless Control of Seven-phase PMSM using only Main Fictitious Machine (S1)

For this sensorless control strategy, SMO algorithm uses only the fictitious MM signals. By considering only the 1st harmonic in MM, the rotation angle m  is assumed as  . Similarly, with only the 9th and 3rd harmonics in SM and TM, the rotation angles s  and t

 can be obtained directly by multiplying angle  by 9 (to form 9 ) and 3 (to have 3 ). Because there is no initial phase shift angles in the back-EMF harmonics for this seven-phase PMSM. In fact, the rotor position  is estimated from MM. After that, angles 3 and 9 are calculated from the multiplications of  with 3 and 9, respectively. As aforementioned, these angular values are necessary to perform the vector control of SM and TM.

Based on (4) and the relationship between the rotor position and the back-EMF, the estimated values of the rotating speed and rotor position can be written by:

2 2 1 1 1 ˆr ee     + = (8) 1 1 ârctan ê e     =-    (9)
From (9) and Figure 5, angles 9 and 3 can be expressed as:

( )

ˆ9 9 9 9 9 err err       = -  = - (10)
( )

ˆ3 3 3 3 3 err err       = -  = - (11)
It can be seen from ( 10) and ( 11) that the multiplications of  with 3 and 9 to respectively construct 3 and 9 significantly increase the estimation error. Indeed, the estimated angle to control fictitious TM will contain an error 3 times bigger than err  (the error of the estimation process of  with MM signals). Similarly, the estimation error with 9 to control SM will be 9 times bigger than err  . Thus, the current regulation of TM and SM will be affected by the estimation error values during the calculations to find the rotor position. It should be noted that such calculations lead to inaccurate and inefficient sensorless control, especially when err  is high.

3.2.Proposed Sensorless Control of Seven-phase PMSM using all Fictitious Machines (S2)

The proposed SMO -based sensorless control strategy is described in Figure 6. The voltage and current signals (of all fictitious machines) are used for the SMO algorithm as inputs. This is to separately estimate ˆm Based on (4), the estimations of rotor position  and speed ˆr  are given by ( 8) and [START_REF] Vas | Sensorless Vector and Direct Torque Control[END_REF]. For the other angles 9 and 3 , the estimation can be expressed as:

 from MM
In the following section, these two SMO -based sensorless control strategies S1 and S2 will be tested on a non-sinusoidal seven-phase PMSM and a highly non-sinusoidal five-phase PMSM through numerical simulations in MATLAB/Simulink. In section 5, strategies S1 and S2 will be experimentally tested on the non-sinusoidal seven-phase PMSM. The performance of the machine using an encoder (to provide the rotor position) for the control will be used to validate sensorless control strategies S1 and S2. Thus, the effectiveness of each strategy is highlighted in terms of rotor position estimation accuracy.

  err    d q d q ˆerr    = - r  ˆr 

Verification of Sensorless Control Strategies by Simulation Results

Simulations are implemented to verify the effectiveness of the proposed sensorless control strategy S2 in comparison with the conventional sensorless control strategy S1. These two SMO -based sensorless control strategies are implemented in MATLAB/Simulink, and the PWM frequency is set at 10kHz. A torque control is considered for the seven-phase PMSM as described in Figure 6, with a reference torque of 5Nm. The 0 d i = control strategy is carried out. The machine parameters are provided in Table 2 For torque control using the sensorless strategies, the rotating speed is not required but it is still estimated to verify the feasibility of the proposed sensorless control strategy in response to variations of the speed. The zero and low-speed range is not considered in this part of the study but it is going to be studied in the second part of this study. In the sensorless control simulations, SMO parameters are provided in Table 1.

In Figure 3, the back-EMF signal is measured at 20 rad/s. In fact, the simulations will be examined for a rotor speed around 20 rad/s (~200 rpm). It should be noted that the base speed of this machine is around 400 rpm, because the DC power supply limit is 200 V. The estimated back-EMF, and then the estimated rotor position and speed will be compared to real results supposed obtained by the "encoder".

Sensorless Control by Strategy S1

As aforementioned in section 3.1, this sensorless control strategy is based only on the estimated back-EMF of the 1 st harmonic. It should be noted that the estimated values of the back-EMF components in ( )  - frame are obtained from SMO, and then used to estimate the rotor position and speed, as described in section 3. This means that an accurate estimation of the back-EMF signals is necessary for a precise rotor position and speed estimation. In fact, the actual back-EMF and estimated one from SMO for the fictitious MM are shown and compared in Figure 7. From Figure 7, the estimated back-EMF in α-axis of the 1 st harmonic converges to the actual one. It means that the estimated back-EMF signals of MM are quite similar in terms of amplitude and phase to the actual ones. Based on this precise estimation by SMO, the rotor position is estimated directly from [START_REF] Vas | Sensorless Vector and Direct Torque Control[END_REF].and compared to actual one in Figure 8.

In fact, it can be noticed in Figure 8 (a) that the rotation angle  is estimated accurately by the strategy S1. The estimation of rotation angles ( 3 and 9 ), which estimated by multiplying respectively  by 3 and 9 as shown in ( 11) and [START_REF] Rind | Electric Motors and Speed Sensorless Control for Electric and Hybrid Electric Vehicles: A Review[END_REF], is not precise compared to the actual ones as can be seen in Figures 8 (b) et (c). This can be potentially due to the multiplying by 3 and 9 the estimation error err  resulting in the estimation of angle  . To highlight this significant inaccuracy, the error estimation of different rotation angles will be evaluated for strategy S1 in the section 4.3.

Sensorless Control by Strategy S2

Unlike the strategy S1, this sensorless control strategy guarantees a separation in the rotation angles estimation. Therefore, the back-EMF estimation of 1 st , 9 th , and 3 rd harmonic are required to perform the sensorless control of the seven-phase PMSM. Accurate estimation of different back-EMF signals is primordial for the feasibility of the strategy S2. Thus, the estimated back-EMF of MM, SM, and TM will be compared to measured ones in Figure 9. The back-EMF estimation of 1 st harmonic in Figure 9 (a) is the same to the estimated one for strategy S1. As the SMO algorithm used for MM is the same regardless the sensorless control strategy, this back-EMF estimation still accurate compared to the actual one. However, it can be seen in Figures 9 (b) and 9 (c) that the estimated back-EMF of the 9 th and 3 rd harmonic are disturbed and not accurate compared to actual back-EMF. This is potentially due to the impact of 19 th and 11 th harmonics, which are present respectively in SM and TM as shown in Figure 2. It should be noted that the impact of 23 rd harmonic in SM and the 17 th harmonic in TM does not significant, because of their low amplitudes compared respectively to 9 th and 3 rd harmonics. In the same way, it can be noticed that the estimated back-EMF signal in TM is more disturbed than the one in SM. This is due to the amplitude of the 11 th harmonic which is more important than the 19 th harmonic as shown in Figure 3. The impact of such disturbance in the back-EMF estimation signals on the rotor position estimation is evaluated in Figure 10.

Figure 10 shows the actual rotor position and estimated one through the estimated back-EMF of the 3 rd harmonic. The estimated rotor position is not precise, impacted by the disturbance on the estimated back-EMF through TM. Therefore, the 9 th and 19 th harmonics contained in the estimated back-EMF of SM should be separate, in order to extracted only the back-EMF signal of the 9 th harmonic. In the same way, the 3 rd and 11 th harmonics contained in TM should be also separate, in order to extracted only the back-EMF signal of the 3 rd harmonic. From the extracted signals, the 9 and 3 are directly estimated as shown in ( 12) and ( 13), making possible the sensorless control strategy S2.

Back-EMF Harmonics Separation

As discussed above, the harmonics contained in the estimated back-EMF of fictitious machines should be separate in order to perform the sensorless control by the strategy S2. The separation of 3 rd and 11 th harmonics contained in the back-EMF of TM will be detailed in the following section, and the same concept will be applied to separate the 9 th and 19 th contained in the back-EMF of the SM. To extract the 3 rd harmonic signals from the estimated back-EMF through TM, a neural synchronous method can be used as a relevant solution [START_REF] Flieller | A Self-Learning Solution for Torque Ripple Reduction for Nonsinusoidal Permanent-Magnet Motor Drives Based on Artificial Neural Networks[END_REF]. The principle of this method is to learn the decomposition of the estimated back-EMF signals in ( ) ê frame with an Adaline (ADAptive LInear NEuron) [START_REF] Nguyen | Artificial neural networks for harmonic currents identification in active power filtering schemes[END_REF]. The Adaline neural network represents an intelligent self-learning system that can adapt to achieve a given linear modeling task. In this case, one Adaline per axis is used to learn on-line and estimate each component contained in the estimated back-EMF as shown in Figure 11. The decomposition is therefore learned and it allows to extract the fundamental component (3 rd harmonic of the estimated back-EMF through TM) as well as the 11 th harmonic. More information about the principle of this neural network (Figure 11) are given in [START_REF] Vu | Eliminations of Low-frequency Current Harmonics for Five-phase Open-end Winding Non-sinusoidal Machine Drives applying Neural Networks[END_REF].

 -  Weight updating 1  4  ( ) ĉos 3θ ( ) ŝin 3θ ( ) ĉos 1 1 θ ( ) ŝin 1 1 θ e error ( ) ( ) ( ) ( ) 1
The Neural Synchronous Method (NSM) will be compared to a traditional method using only a second order Low Pass Filter (LPF). This is in order to separate the 3 rd and 11 th harmonic by removing, in the estimated back-EMF signals through TM, the 11 th harmonic component. Therefore, it can be considered that the signal at the output of the LPF contains only the estimated back-EMF of 3 rd harmonic, and that the impact of 11 th harmonic is eliminated (filtered). The extracted signal, which contains the 3 rd harmonic of estimated back-EMF, will be used to estimate the rotor position 3 . From Figure 12 (a), it can be seen that the estimated back-EMF signal through TM contains the 3 rd harmonic at 30 Hz and the 11 th harmonic at 110 Hz. As the rotor speed is at 200 rpm, the fundamental of the back-EMF is at 10 Hz. Therefore, the cut off frequency of the second order LPF is set to 50 Hz and then to 80 Hz as shown in Figure . 12 (b), in order to keep the 3 rd harmonic (at 30 Hz) and to eliminate the 11 th harmonic (at 110 Hz). In Figure 13, it can be noticed that the method using a LPF induces an important delay on the estimated back-EMF. For the two cut-off frequency, the resulting signal is out of phase with the actual back-EMF of 3 rd harmonic. However, the resulting signal from the neural synchronous method converge with high accuracy to actual back-EMF signal of 3 rd harmonic as shown in Figure 13. Therefore, as the harmonics separation method using the NSM is the more accurate, it will be selected to enhance the estimated back-EMF by SMO for the sensorless control strategy S2.

In fact, the estimated back-EMF of 3 rd harmonic (Figure 14. (b)) is extracted to the estimated one through TM (which contains initially the 3 rd and 11 th harmonics). In the same way, and applying the neural synchronous method, the estimated back-EMF of 9 th harmonic is extracted to the estimated one through SM (which contains initially 9 th and 19 th harmonics) as shown in Figure 14. (a).

Rotor Position Estimation

We aim by the improvement of the back-EMF estimation process to ensure an accurate estimation of the rotor position and speed by the strategy S2. In fact, as described in the section 3.2, the rotation angles used to control each fictitious machine are  , 9 , and 3 . Therefore, all estimated angles are compared to the actual angles assumed obtained by "encoder" in Figure 15. From Figure 15, it can be seen that the estimated rotation angles  , 9 , and 3 converge to the actual ones with accuracy compared to obtained results in Figure 8 with strategy S1. In Figure 15 Therefore, based on the obtained results for the two sensorless control strategies, it can be already noted that the strategy S2 is more performant than S1 in terms of precision especially for the estimated angles required to control the fictitious machines SM and TM. To highlight the performance of strategy S2, the estimation error of different rotation angles will be evaluated for strategy S2, and then compared to the resulting ones from strategy S1.

Estimation Error Resulting from Strategies S1 and S2

To quantify the estimation errors of the two sensorless control strategies, the errors resulting on the estimated angles will be computed between the actual rotor position and the estimated one. The resulting errors will be compared (Figure 16) for the two strategies, in order to verify the performance of the strategy S2 observed on Figures 8 and15. From Figure 16 (a), it can be seen that the position error resulting of strategies S1 and S2 is the same (~ 2.3°). In Figure 16 (b), the position error resulting of the strategy S1 is around 20° (electrical angle), and the one resulting of the strategy S2 is around 2.5° (electrical angle). This important position error (20°) is a consequence of the multiplication by 9 the position error err  as described in section 3.1. In the same way, it can be seen in Figure 16 (c) that the position error resulting of strategy S1 is around 7.2°, due to the multiplication by 3 the position error err  . However, the error resulting of strategy S2 is around 2.3° (electrical angle). These results are summarized in Table 3, with



are respectively the position error of rotation angles 9 and 3 . Based on the esti- mation error results, it can be concluded that the sensorless control strategy S2 is more performant in terms of accuracy than strategy S1. In the other hand, the pulses present in the position error (Figure 16), caused by the computation of the estimation error, do not have any impacts on the control loop thanks to the cos and sin functions used in the rotating matrix.

The rotor speed is estimated through the estimated back-EMF in ( ) described in [START_REF] Locment | Vectorial Approach-Based Control of a Seven-Phase Axial Flux Machine Designed for Fault Operation[END_REF]. It can be noticed that the rotor speed is estimated in the same way (using MM signals) for strategies S1 and S2. As shown in Figure 17 (a), SMO allows an accurate estimation of the rotating speed. In Figure 17 (b), the torque of the seven-phase PMSM resulting of the control with sensor (encoder) and the torque resulting of the sensorless control by strategies S1 and S2 are shown. The two sensorless control strategies guarantee the same quality of torque as the one obtained when the machine is controlled by encoder.

It can be noticed that the precision in the estimation of position is higher with S2 strategy (see Table 3). But as the position error around 20° and the one around 7.2° resulting from strategy S1 induces respectively a torque ripples around 13% and 2% of the torques produced by SM and TM, therefore the impact of the position error becomes not significant on the global torque of the seven-phase PMSM. This is due to the small amount of torque produced by SM and TM, compared to the amount of torque produced by the MM. With the machine considered in the next paragraph the impact will significant.

Sensorless Control of a Non-sinusoidal Five-phase PMSM

To examine the improvement in terms of torque ripples that can guarantee the proposed sensorless control strategy S2, a highly non-sinusoidal five phase PMSM [START_REF] Aslan | New 5-phase concentrated winding machine with bi-harmonic rotor for automotive application[END_REF] will be used as mentioned above in section 1. The back-EMF of this machine contains the 1 st and 3 rd harmonic as shown in Figure 19. The 3 rd harmonic represents roughly 120% of the fundamental (1 st harmonic). It can be noticed that this high ratio is not classical, but it corresponds to recent studied machines [START_REF] Aslan | New 5-phase concentrated winding machine with bi-harmonic rotor for automotive application[END_REF][START_REF] Zahr | Comparison of Optimized Control Strategies of a High-Speed Traction Machine with Five Phases and Bi-Harmonic Electromotive Force[END_REF][START_REF] Gong | Design Considerations of Five-Phase Machine With Double p/3p Polarity[END_REF] which are characterized by a double polarity (p and 3p). In machine for traction this double polarity gives a two-speed gearbox functionality which is interesting when the flux-weakening controls are not satisfying with only one polarity. This concept of multi-polarity with gearbox functionality can be found also in [START_REF] Dajaku | Low costs and high efficiency asynchronous machine with stator cage winding[END_REF][START_REF] Runde | ISCAD -Design, control and car integration of a 48 volt high performance drive[END_REF] in ISCAD concept for low voltage multiphase induction machines. This is in order to highlight the sensorless control when the principal amount of torque is not produced by only the fundamental (1 st harmonic) of current and back-EMF, as it is by the non-sinusoidal seven-phase PMSM studied above. The modelling of the nonsinusoidal five-phase PMSM and corresponding SMO design are detailed in [START_REF] Mini | Sensorless Control for Non-Sinusoidal Five-phase IPMSM Based on Sliding Mode Observer[END_REF]. The decomposition of the five-phase PMSM to several fictitious machines and the associated harmonics is given by Figure 18. As shown in Figure 18, the five-phase PMSM is decomposed to 3 fictitious machines (MM, SM an HM). The torque produced by MM is created by the 1 st harmonic, and the torque produced by SM is created by the 3 rd harmonic. The fictitious machine HM is not considered with a star connection. For this five-phase machine, the base speed is around 750 rpm for DC power supply limit set at 48 V To perform the sensorless control of the five-phase PMSM, two rotation angles are required for the vector control: m  to control MM, and s  to control the SM. Assuming no initial phase shift in the back-EMF harmon- ics, the rotation angle of 1 st harmonic m  is considered as  . In the same way, the rota- tion angle of the 3 rd harmonic s  is considered as 3 . Therefore, the accuracy of the an- gles estimation by the two sensorless control strategies will be highlight in the following section. From the simulation waveforms of Figure 20 (a), the estimated rotor position  through strategies S1 and S2 converges to the actual one. In this case, the two strategies show the same level of accuracy. This can be verified in Figure 21 (a) which shows that the estimation error resulting from the two strategies is around 1.5° (electrical angle). However, the estimated angle 3 through the strategy S2 is more accurate than the one estimated through S1 as can be seen in Figure 21 (b). The estimation error resulting from the strategy S1 is around 5° (verifying the theory (11) mentioned above), and the resulting one from S2 is around 0.5°. These results are summarized in Table 4. The impact of the estimation errors on the torque of the highly non-sinusoidal five phase PMSM will be examine in Figure 22. To highlight the performance of the two sensorless control strategies, the quality of the electromagnetic torque is evaluated when the five phase PMSM operates in steady and transient states. In fact, it can be seen in Figure 22 (a) that the estimated rotor speed converges to the measured one with accuracy in both transient and steady states. For the measured torque in Figure 22 (b), it can be noticed that the two sensorless control strategies guarantee the same quality of torque in the steady states. This can be verified in Figure 22 (c), which shows that the torque error is around 0% of the mean torque for the two strategies at steady states. However, in Figure 22 (b), at transient states (when the rotor speed changes), the torque ripple is more significant when the machine operates under the sensorless control by strategy S1. From Figure 22 (c), the torque error can reach 98% of the mean torque for strategy S1. When the machine operates with the strategy S2, it can be seen that the quality of the torque is much better in the transient states, and the torque error is less than 45% of the mean torque. Thus, the sensorless control strategy S2 is more performant in terms of accuracy and torque ripple than the strategy S1. Therefore, it can be concluded that for non-sinusoidal multiphase PMSMs, producing an important part of torque through SM and TM, the sensorless control should be performed by strategy S2 to avoid a significant torque ripple.

Experimental Results

The simulation results showed that the two sensorless control strategies based on the SMO allow an estimation of rotor position, with a significant level of accuracy in the estimation process by the proposed strategy S2. Thus, to further verify the feasibility and the effectiveness of the sensorless control strategies, a test bench constructed by a non-sinusoidal seven-phase PMSM is used.

Mechanical coupling

As shown in Figure 23, the seven-phase PMSM is mechanically coupled to a threephase PMSM (used as a load drive) which is controlled to tune the speed of the sevenphase machine. We consider a torque control as shown in Figure 6, and the 0 d i = con- trol strategy is carried out. A dSPACE1005 controller is used to drive the seven legs (IGBT) of the inverter supplying the seven-phase PMSM, and to collect the measured data of rotor position and currents. The inverter is supplied by a DC-bus voltage of 200 V. The PWM switching frequency is set to 10 kHz, and the sampling time of the control system is set as 350 µs. For the measure of the actual rotor position and speed, an incremental encoder is used as shown in Figure 23. Therefore, the control scheme in Figure 6 is implemented experimentally to verify the sensorless control strategies. position 9 through strategy S2 is more precise than the estimated one across strategy S1. In Figure 25 (b), the position error, resulting through strategy S1, is around 31° (verifying the theory in ( 10)) due to multiplication by 9 the position error given in Figure 25 (a). However, the position error resulting from strategy S2 is around 5.7° as shown in Figure 25 (b). Therefore, an error around 31° induces a torque ripples around 32% and the one around 5.7° induces a torque ripples around 0.9% of the produced torque by the SM.

Rotor Position Estimation

In the same way, it can be seen in Figure 24 (c) that the estimated rotor position 3 is more precise through strategy S2. The position error resulting from strategy S1 is around 11° (inducing a torque ripples around 3.7% of the produced torque by TM), and the one resulting from strategy S2 is around 2° (inducing a torque ripples around 0.1%) as shown in Figure 25

Rotor Speed and Electromagnetic Torque

The impact of the estimation errors resulting from the two sensorless control strategies will be highlight when the seven phase PMSM operates at steady and transient states. Therefore, the estimated rotor speed and the measured electromagnetic torque for diffent strategies are given in Figures 26 and27 From the experimental waveforms of Figure 26 (a), the estimated rotor speed by SMO converge to the measured one. When the machine operates at variable speed, SMO ensures this convergence as shown in Figure 27 (a). The estimated rotor speed is computed through the estimated back-EMF signals of MM. In another hand, it can be noticed from Figure 26 (b) and Figure 27 (b) that for the sensorless control by strategy S1 or S2, the measured torque in transient and steady states is similar to the obtained one when the machine is controlled by encoder. This is due, as aforementioned in section 4.3, to the small amount of torque produced by SM and TM of the seven-phase PMSM. Therefore, the estimation errors resulting from the estimation of angles 9 and 3 by strategy S1 does not a significant impact on the global torque in this case.

Conclusions

In the first part of this study, two sensorless control strategies have been compared through simulation and experimental results. From the results, it can be concluded that SMO can estimate the rotor position with high accuracy (error less than 3°), ensuring a precise sensorless control for non-sinusoidal multiphase PMSMs. For a non-sinusoidal multiphase PMSM in which the torque is mainly produced by the main fictitious machine (MM), strategies S1 (classical) and S2 (proposed) present the same level of accuracy in terms of torque ripples for the sensorless control. However, when the torque is generated by not only MM but also the others fictitious machines (e.g., SM and TM), the proposed sensorless control strategy S2 is more precise to compute the angles for the control of fictitious machines (SM and TM). This allows to perform a more accurate sensorless control in terms of torque ripples compared to the classical strategy S1. This improvement of electromagnetic torque quality (observed for strategy S2) is very significant when the machine operates in transient states. However, for steady states, the two sensorless control strategies present a similar performance. In addition, it can be noted that for a non-sinusoidal multiphase PMSM with more than two important harmonics in the same fictious machine, the sensorless control cannot be performed directly. The separation of harmonics presenting in the fictitious machine is required to estimate accurate back-EMF signals, which are essential to compute the rotor position. Furthermore, the proposed sensorless control strategy S2 does not require additional hardware to be implemented in the real time since this algorithm is quite similar to the classical strategy S1, but the number of observers is multiplied by three.

Figure 1 .

 1 Figure 1. Design of one sixth of the axial flux non-sinusoidal seven-phase PMSM [32].

Figure 2 .

 2 Figure 2. Four fictitious machines and associated harmonic groups of seven-phase PMSM [33].

L

  with i= {1, 9, 3}, represent respectively the currents, the back-EMF, and the voltages of the fictitious machines; represent respectively the inductances of MM, SM, and TM. In the following sections, it is assumed

where 1  , 3  , and 9 

 139 are the 1 st , 3 rd , and 9 th harmonics of the flux linkage of the perma- nent magnets, respectively; r  is the electrical angular velocity; electrical rotation angles of the fictitious MM, SM, and TM. To perform an accurate vector control, the rotor position information is required to compute the Park transformation in the rotor reference frames ( )

Figure 3 .

 3 Figure 3. Waveform and harmonic spectrum of the experimental back-EMF of phase "a" at 20 rad/s [34].

Figure 4 .

 4 Figure 4. Block diagram of SMO for the sensorless control. where ( ) , vv  and ( ) , ii  are respectively voltages and currents in stationary refer-

  represent the current observer gains.

Figure 5 .

 5 Figure 5. Relationship between the actual () dqframe and the estimated ˆ() dqframe.

Figure 6 .

 6 Figure 6. Block diagram of two sensorless control strategies S1 and S2 for the non-sinusoidal seven-phase PMSMs.

Figure 7 .Figure 8 .

 78 Figure 7. Simulated waveforms of actual and estimated α-axis back-EMF of the 1 st harmonic in MM.

Figure 9 .

 9 Figure 9. Simulation waveforms of actual and estimated back-EMF in α-axis: (a) the 1 st harmonic in MM, (b) the 9 th harmonic in SM, (c) the 3 rd harmonic in TM.

Figure 10 .

 10 Figure 10. Simulation waveforms: actual rotor position and estimated one through the estimated back-EMF of 3 rd harmonic (TM).

Figure 11 :

 11 Figure 11:Structure of the ADALINE used by the neural synchronous method[START_REF] Nguyen | Artificial neural networks for harmonic currents identification in active power filtering schemes[END_REF].

Figure 12 .

 12 Figure 12. Simulation waveforms: (a) Harmonic spectrum of the estimated back-EMF of 3rd harmonic TM, (b) Bode diagram of the second order Low Pass Filter.

Figure 13 .

 13 Figure[START_REF] Bo | The position-sensorless control of low voltage high power permanent magnet synchronous motors in zero/low-speed regions[END_REF]. Simulation waveforms of the actual back-EMF of 3 rd harmonic and the estimated back-EMF through TM in α-axis using the methods of harmonics separation.

Figure 14 .

 14 Figure 14. Simulated waveforms of actual and estimated α-axis back-EMF using the neural synchronous method: (a) the 9 th harmonic in SM, (b) the 3 rd harmonic in TM.

Figure 15 .

 15 Figure 15. Simulation waveforms of actual and estimated rotor position through (S1) and (S2): (a) angle required to control MM, (b) angle required to control SM, (c) angle required to control TM.

9

  (b), the estimated angle 9 by strategy S2 is more precise than obtained with strategy S1 in Figure 8 (b). In the same way, Figure 15 (c) shows that the estimated angles 3 is more precise than the 3 obtained by the strategy S1 in Figure 8 (c).

Figure 16 .

 16 Figure 16. Simulation waveforms of resulting position error (electrical angle) through (S1) and (S2): (a) error on the angle required to control MM, (b) error on the angle required to control SM, (c) error on the angle required to control TM.

Figure 17 .

 17 Figure 17. Simulated waveforms: (a) actual and estimated rotor speed, (b) torque when the sevenphase PMSM is controlled by encoder, sensorless control (S1) and sensorless control (S2).

Figure 18 .

 18 Figure 18. Three fictitious machines and associated groups of harmonics of a five-phase PMSM.

Figure 19 .

 19 Figure 19. Waveform and harmonic spectrum of the back-EMF of phase "a" of the highly nonsinusoidal five-phase PMSM at 78 rad/s.

Figure 20 .

 20 Figure 20. Simulation waveforms at 78 rad/s of actual and estimated rotor position through (S1) and (S2): (a) angle required to control MM, (b) angle required to control SM.

Table 4 .Figure 21 .

 421 Figure 21. Simulation waveforms at 78 rad/s of resulting position error through (S1) and (S2): (a) error on the angle required to control MM, (b) error on the angle required to control SM.

Figure 22 .

 22 Figure 22. Simulation waveforms for variable rotor speed: torque when the five-phase PMSM is controlled by encoder, sensorless control (S1), and sensorless control (S2).

Figure 23 .

 23 Figure 23. Experimental test bench of the seven-phase PMSM

From

  the estimated back-EMF signals, the rotor position is estimated through strategies S1 and S2. For the sensorless control by strategy S1, only the estimated back-EMF signals of MM are used to compute the angles  , 9 and 3 . And for the sensorless control by Strategy S2, all estimated back-EMF signals are used to compute the angles , 9 and 3 required to control respectively the fictitious machines MM, SM and TM. In Figure24, the measured rotor position "by encoder" is compared to the estimated one, and the resulting estimation errors from strategies S1 and S2 are given in Figure25.

Figure 24 .

 24 Figure 24. Experimental waveforms: measured and estimated rotor position through (S1) and (S2): (a) angle required to control MM, (b) angle required to control SM, (c) angle required to control TM.The experimental waveforms of Figure24(a) show that the estimated rotor position  with strategies S1 and S2 converge to the measured one. The position error, resulting to the estimation through the two strategies S1 and S2, is quite similar and around 3.5° as shown in Figure25 (a). Such error can induce a torque ripples around 0.37% of the produced torque by MM. From Figure24(b), it can be noticed that the estimated rotor

  (c). The position errors results are summarized in Table5

Figure 25 .Table 5 .

 255 Figure 25. Experimental waveforms: resulting position error through (S1) and (S2): (a) error on the angle required to control MM, (b) error on the angle required to control SM, (c) error on the angle required to control TM.Table 5. Resulting position error (electrical angle) from strategies (S1) and (S2)

  .

Figure 26 .Figure 27 .

 2627 Figure 26. Experimental waveforms: (a) measured and estimated rotor speed, (b) measured torque when the seven-phase PMSM is controlled by encoder, sensorless control (S1) and sensorless control (S2)

Table 1 .

 1 . Sliding mode observer parameters

	SMO gains

Table 2 .

 2 Seven-phase PMSMs characteristics

	Seven-phase PMSM parameters	Values
	Stator Resistance of one phase [Ω]	1.4
	Self-inductance of one phase [mH]	14.7
	Number of pole pairs	3
	Speed-normalized amplitude of 1st harmonic of back-EMF [V/rad/s]	1.2650
	Speed-normalized amplitude of 9th har-monic of back-EMF [V/rad/s]	0.1569
	Speed-normalized amplitude of 3rd har-monic of back-EMF [V/rad/s]	0.4073
	Maximum DC bus voltage [V]	200

Table 3 .

 3 Resulting position error (electrical angle) from strategies (

S1) and (S2)

			err		err	9		err	3
	Strategy (S1)	2.3°	20°	7.2°
	Strategy (S2)	2.3°	2.5°	2.3°

Funding: This work has been achieved within the framework of CE2I project. CE2I is co-financed by European Union with the financial support of European Regional Development Fund (ERDF), French State and the French Region of Hauts-de-France.

Author Contributions: Methodology, Software, Validation, Writing-original draft preparation, Y.M.; Writing-review and editing, N.K.N., D.T.V. and E.S; Supervision, N.K.N. and E.S.

Conflicts of Interest:

The authors declare no conflict of interest.


Dr François Chasset
email: francois.chasset@gmail.com

Alexis Mathian

Karim Dorgham

Camillo Ribi

Marten Trendelenburg

Uyen Huynh-Do

Pascale Roux-Lombard

Delphine Sophie Courvoisier

Zahir Amoura

Guy Gorochov

Carlo Chizzolini

Serum interferon-α levels and IFN type I-stimulated genes score perform equally to assess systemic lupus erythematosus disease activity

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

(83%) were women, 98 (74%) were Caucasians and 75 patients (56%) had an active disease using clinical Systemic Lupus Erythematosus Disease Activity Index (cSLEDAI), the contribution of low serum complement and elevated anti-dsDNA autoantibodies with a cut-off>0 to define active disease was excluded. [START_REF] Pescarmona | Comparison of RT-qPCR and Nanostring in the measurement of blood interferon response for the diagnosis of type I interferonopathies[END_REF] Using the predefined cut-offs,3 4 the prevalence of high IFN-I gene scores, elevated IFN-α and IFN-γ serum levels were 44% (58/133), 45% (60/133) and 14% (18/133), respectively (figure 1A). Serum IFN-α levels showed a highly positive correlation with the IFN-I gene scores (Spearman's correlation coefficient: rho=0.82), as well as with the expression level of individual ISGs except for CXCL10 (figure 1B,C). In contrast, IFN-γ levels showed a weak positive correlation with IFN-I gene scores (rho=0.32) (figure 1D) and IFN-α levels (rho=0.35), as well as with the expression level of individual ISG, except for CXCL10 which showed a stronger positive correlation (rho=0.60) in accordance with a preferential induction of CXCL10 by IFN-γ (figure 1C). Using Cohen's kappa coefficient, serum IFN-α levels showed substantial agreement to classify SLE with high or low IFN-I gene scores κ=0.72 (95% CI: 0.60 to 0.84), whereas the agreement was low for IFN-γ (figure 1B,D). The sensitivity, specificity, negative and positive predictive values of serum IFN-α levels to classify SLE with high or low IFN-I gene score were 86%, 87%, 89% and 83%, respectively. Moreover, elevated serum IFN-α levels and IFN-I gene scores were associated with active SLE, as defined by cSLEDAI>0 or SLEDAI≥4 (online supplemental figure s1-s3) and were both associated with active skin lesions, arthritis and positive anti-dsDNA Abs in multivariable analysis (online supplemental table s2). In contrast, IFN-γ was neither associated with active SLE (online supplemental figure s1) nor with active SLE characteristics (online supplemental figure s2). Finally, IFN-I gene score AUC=0.63 (95% CI: 0.53 to 0.72) and serum IFN-α AUC=0.63 (95% CI: 0.53 to 0.72) performed similarly and significantly better than C3 levels AUC=0.42 (95% CI: 0.32 to 0.52) to discriminate inactive versus active SLE adjusted p value=0.03 and 0.03, respectively (online supplemental figure s3 and table s3). In this study, for the first time, we show that IFN-α assessed by digital ELISA and IFN-I gene score perform equally for identifying the association of IFN-I with SLE disease activity and clinical manifestations. Remarkably, this was specific to IFN-α, since no such association was observed with serum IFN-γ levels. Of importance, we observed no association of IFN-γ serum levels with active SLE clinical features and SLEDAI. This may suggest that IFN-γ serum levels may not perform optimally as SLE biomarkers and may not support the choice of IFN-γ as therapeutic target. However, further studies are needed to explore this issue. The limitations of our study are the cross-sectional design and the relatively low number of highly active patients with SLE, which reflects real-life practice in Switzerland. IFN-α levels measured by digital ELISA could be easier to standardise than IFN-I gene scores to characterise IFN-I overexpression in clinical practice. Thirty-five age-and sex-matched healthy controls (HCs) were selected from the Geneva Blood donation bank following classical guidelines on assessing donor suitability for blood donation. In particular, fever or viral symptoms the week before blood sampling were exclusion criteria. HCs could not be matched based on ethnicity and ancestry.

Patient and public involvement.

No patients nor public were involved in the conception or realization of the present study.

Data collection and definitions

We collected demographic data, SLE clinical characteristics, the Safety of Estrogens in Lupus Erythematosus National Assessment-Systemic Lupus Erythematosus Disease Activity Index (SELENA-SLEDAI) [START_REF] Petri | Combined oral contraceptives in women with systemic lupus erythematosus[END_REF]. The therapeutic regimen was recorded on the day of sample collection. Biological data collected were complete blood count, serum creatinine level, proteinuria, and complement C3 and C4 levels. Testing for anti-dsDNA (Q'Flash dsDNA Kit, Ruwag Life Science, Switzerland), anti-U1RNP, anti-SSA, anti-C1q antibodies (ELISA, Ruwag Life Science, Switzerland) was performed according to manufacturer protocols in a central laboratory in Geneva (Switzerland). Medication with disease-modifying drugs was classified in four groups: 1) no treatment versus active treatment, 2) antimalarial (AM) therapy only, 3) systemic glucocorticoids (GC) and 4) immunosuppressant agents (IS). Active clinical features were based on SELENA-SLEDAI and active skin disease included at least one active SELENA-BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s)

Ann

Quantitative assessment of mRNA levels and gene normalization

Gene expression was assessed by mRNA expression profiling by using a NanoString nCounter gene expression system (NanoString Technologies, Seattle, WA) as previously described [START_REF] Pescarmona | Comparison of RT-qPCR and Nanostring in the measurement of blood interferon response for the diagnosis of type I interferonopathies[END_REF].

Briefly, 100 ng total RNA was hybridized to the probes (a reporter probe and a capture probe) at 67 °C for 16-21 h by using a thermocycler. Samples were then inserted into the nCounter Prep Station for removing excessive probes, purification and immobilization onto the internal surface of a sample cartridge for 2 to 3 h. Finally, the sample cartridge was transferred to the nCounter Digital Analyzer, where color codes were counted and tabulated for each target molecule. Background correction involved subtracting from the raw counts the mean+2 SD of counts obtained with negative controls (alien probes lacking spiked transcript for background calculation). Values <1 were fixed to 1 to avoid negative values after log transformation. Positive controls (alien sequences of RNA spiked at various concentrations to assess the overall assay performance) were used as quality assessment: the ratio between the highest and the lowest positive controls average among samples was < 3. IFN-I, PMN and PB gene counts were normalized to the geometric mean of 7 housekeeping gene counts selected as the most stable by using the geNorm algorithm [START_REF] Vandesompele | Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes[END_REF].

Gene selection and computation of the IFN-I gene scores

A literature review was performed to identify genes previously used to assess IFN-I signature as part of modules of genes [START_REF] Banchereau | Personalized Immunomonitoring Uncovers Molecular Networks that Stratify Lupus Patients[END_REF] or as quantitative scores [START_REF] Yao | Neutralization of interferon-alpha/beta-inducible genes and downstream effect in a phase I trial of an anti-interferon-alpha monoclonal antibody in systemic lupus erythematosus[END_REF]. A custom panel of 23 genes was BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s) then developed allowing the computation of six IFN-I gene scores [START_REF] Yao | Neutralization of interferon-alpha/beta-inducible genes and downstream effect in a phase I trial of an anti-interferon-alpha monoclonal antibody in systemic lupus erythematosus[END_REF][START_REF] Mcbride | Safety and pharmacodynamics of rontalizumab in patients with systemic lupus erythematosus: results of a phase I, placebo-controlled, double-blind, dose-escalation study[END_REF][START_REF] Kennedy | Association of the interferon signature metric with serological disease manifestations but not global activity scores in multiple cohorts of patients with SLE[END_REF][START_REF] Khamashta | Sifalimumab, an anti-interferon-α monoclonal antibody, in moderate to severe systemic lupus erythematosus: a randomised, doubleblind, placebo-controlled study[END_REF][START_REF] Petri | Longitudinal expression of type I interferon responsive genes in systemic lupus erythematosus[END_REF][START_REF] Rice | Assessment of interferon-related biomarkers in Aicardi-Goutières syndrome associated with mutations in TREX1, RNASEH2A, RNASEH2B, RNASEH2C, SAMHD1, and ADAR: a case-control study[END_REF] as well as CXCL10 which was used in the Module M1.2 of Banchereau et al [START_REF] Banchereau | Personalized Immunomonitoring Uncovers Molecular Networks that Stratify Lupus Patients[END_REF]. The detailed gene list used to generate each score, is the following IFI27, IFI6, RSAD2, IFI44, IFI44L, USP18, LY6E, OAS1,

IFIT3, IFITM3, LAMP3, LY6E, MX1, OAS1, OAS2, OAS3, OASL, OTOF, RSAD2, RTP4, SERPING1, TRIM6

The computation of the score was performed as previously described [START_REF] Yao | Neutralization of interferon-alpha/beta-inducible genes and downstream effect in a phase I trial of an anti-interferon-alpha monoclonal antibody in systemic lupus erythematosus[END_REF][START_REF] Rice | Assessment of interferon-related biomarkers in Aicardi-Goutières syndrome associated with mutations in TREX1, RNASEH2A, RNASEH2B, RNASEH2C, SAMHD1, and ADAR: a case-control study[END_REF]. Briefly, for each individual, the relative expression of each gene was computed by dividing its normalized value by the median of the normalized HC expression. Then IFN-I gene scores were calculated as the median of the relative expression of all genes contributing to the score. The mean plus 2 SD of HC values was used as a threshold to define high scores. Unless otherwise stated, the IFN-I gene score refers to the score of Khamastha et al. [START_REF] Khamashta | Sifalimumab, an anti-interferon-α monoclonal antibody, in moderate to severe systemic lupus erythematosus: a randomised, doubleblind, placebo-controlled study[END_REF] with a cut-off of high score of 17.5 UI as previously described [START_REF] Chasset | Identification of highly active systemic lupus erythematosus by combined type I interferon and neutrophil gene scores vs classical serologic markers[END_REF]. In individual gene expression analysis, TYK1 was excluded because it was not expressed (count of 0) in most patients.

Single-molecule array (Simoa) IFN-α and IFN-γ digital ELISA

BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s) The Simoa TM (single molecule array) HD-1 analyzer (Quanterix, Lexington, MA, USA) was used for ultrasensitive immunodetection (digital ELISA) [START_REF] Rissin | Single-molecule enzyme-linked immunosorbent assay detects serum proteins at subfemtomolar concentrations[END_REF] of IFN-α and IFN-γ, using singleplex bead-based assays and procedures obtained from Quanterix Corporation.

According to the manufacturer's instructions, the working dilutions were 1:2 for all sera. At low cytokine concentration, the percentage of bead-containing wells in the array that have a positive signal is proportional to the amount of cytokine present in the sample (digital measurement). At higher concentration, when most of the bead-containing wells have one or more labeled-cytokine molecules, the total fluorescence signal is proportional to the amount of cytokine present in the sample (analog measurement). Calibrators were run in duplicate and fit with a four-parameter logistic (4PL) regression, with 1/y2 weighting.

Cytokine concentrations in serum samples were interpolated from the standard curves. We used a serum-IFN-α level threshold value of 136 fg/mL to define high IFN-α levels based on 3 SD above the mean value from 68 HC as previously described [START_REF] Mathian | Monitoring disease activity in systemic lupus erythematosus with single-molecule array digital ELISA quantification of serum interferon-α[END_REF] and an IFN-γ threshold of 2558 fg/mL based on 3 SD above the mean value from 74 HC to define elevated IFN-γ levels.

Statistical analysis

Data are presented as median (interquartile (IQR) range) or counts (percentage). Chi-square test and Fisher's exact test were used to compare categorical variables; Mann-Whitney test was used to compare non-paired variables, and Spearman correlation analysis (rho) was used for correlations. Agreement for classifying SLE as having high IFN levels between IFN-I gene scores and IFN-α and IFN-γ serum levels measured by SIMOA was assessed using Kappa coefficient, with values defined as follows: 0 <κ <0.2 slight; 0.2≤ κ <0.4 fair agreement, 0.4≤ κ <0.6 moderate 0.60≤ κ <0.80 substantial agreement and κ ≥0.80 almost perfect agreement [START_REF] Landis | The measurement of observer agreement for categorical data[END_REF]. In order to assess features associated with high IFN-I gene score and IFN-α or IFN-γ serum levels, parameters with p <0.2 on univariable analysis were entered in multivariable logistic models. A 2-tailed p < 0.05 was considered statistically significant. The areas under (AUCs) the receiver operating characteristics (ROC) curves to differentiate active vs inactive SLE according to IFN-α and IFN-γ serum levels, IFN-I gene score, C3 levels and anti-dsDNA titers were compared [START_REF] Goksuluk | easyROC: An Interactive Webtool for ROC Curve Analysis Using R Language Environment[END_REF]. compared Analyses were performed with JMP v15 (SAS Institute Inc, Cary, NC).

BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s)

REFERENCES 1

 1 Bennett L, Palucka AK, Arce E, et al. Interferon and granulopoiesis signatures in systemic lupus erythematosus blood. J Exp Med 2003;197:711-23. 2 Khamashta M, Merrill JT, Werth VP, et al. Sifalimumab, an anti-interferon-α monoclonal antibody, in moderate to severe systemic lupus erythematosus: a randomised, doubleblind, placebo-controlled study. Ann Rheum Dis 2016;75:1909-16. 3 Chasset F, Ribi C, Trendelenburg M, et al. Identification of highly active systemic lupus erythematosus by combined type I interferon and neutrophil gene scores vs classical serologic markers. Rheumatology 2020;59:3468-78. 4 Mathian A, Mouries-Martin S, Dorgham K, et al. Monitoring disease activity in systemic lupus erythematosus with single-molecule array digital enzyme-linked immunosorbent assay quantification of serum interferon-α. Arthritis Rheumatol 2019;71:756-65. 5 Mathian A, Mouries-Martin S, Dorgham K, et al. Ultrasensitive serum interferon-α quantification during SLE remission identifies patients at risk for relapse. Ann Rheum Dis 2019;78:1669-76. 6 Hall JC, Casciola-Rosen L, Berger AE, et al. Precise probes of type II interferon activity define the origin of interferon signatures in target tissues in rheumatic diseases. Proc Natl Acad Sci U S A 2012;109:17609-14.

Figure 1

 1 Figure 1 Prevalence, correlation and agreement between serum IFN-α and IFN-I gene score. (A) Prevalence of high serum IFN-α, serum IFN-γ and IFN-I gene score. A custom panel of 22 genes was developed and we calculated one IFN-I gene score (IFI27, IFI44, IFI44L, RSAD2)2 with a cut-off≥17.5 to define high score.3 Cut-off for high serum IFN-α was 136 fg/mL (blue line) as previously defined,4 cut-off for high IFN-gene score was 17.5 (red line) as previously defined3 and cut-off for high IFN-γ was 2558 fg/mL based on 3 SD above the mean from 74 HC to define elevated IFN-γ levels. (B) Spearman correlation coefficient (rho) between IFN-I gene scores and serum IFN-α values and Cohen's kappa to assess agreement between IFN-I gene score and serum IFN-α to classify patients with SLE. (C) Correlation matrix diagram of individual IFN genes with serum IFN-α and serum IFN-γ levels. Spearman correlation analysis (rho) was applied and values were condensed in a colour scale. (D) Spearman correlation (rs) between IFN-I gene score and serum IFN-γ and Cohen's kappa to assess agreement between IFN-I gene score and serum IFN-γ to classify patients with systemic lupus erythematosus (SLE). IFN, interferon.

  SLEDAI features among active lupus rash, mucosal ulcers and alopecia. Patients were classified in 2 groups active and inactive SLE according to a modified definition of active SLEDAI, named clinical SLEDAI, that excluded the contribution of low serum complement and elevated dsDNA autoantibodies with a cut-off > 0 to define active disease. mRNA collection extraction and quality Whole blood was collected in Tempus tubes (Thermo Fisher Scientific, Waltham, USA), and stored at -80°C until mRNA purification. Serum samples were collected concomitantly. Total RNA was extracted by using MagMA for the Stabilized Blood Tubes RNA Isolation Kit (Thermo Fisher Scientific) and RNA quality was assessed post-extraction in a subset of samples by bioanalyzer RNA chip (Agilent Technologies). RNA quality assessed by RNA Integrity Number (RIN) was good in representative samples, with values > 8.

  SIGLEC1, ISG15, IFIT1, OAS3, HERC5, MX1, LAMP3, EPSTI1, IFIT3, OAS2, RTP4, PLSCR1, DNAPTP6, TYK1, CXCL10 Moreover, our gene selection allowed the computation of the following IFN-I gene scores: -Yao Y 2009 [7]: IFI27, IFI6, RSAD2, IFI44, IFI44L, USP18, LY6E, OAS1, SIGLEC1, ISG15, IFIT1, OAS3, HERC5, MX1, LAMP3, EPSTI1, IFIT3, OAS2, RTP4, PLSCR1, DNAPTP6 -Petri M 2009 [11]: IFI27, OAS3, IFI44 -McBride 2012 [8]: IFI27, IFI44, IFIT1, MX1, OAS1, OAS2, OAS3 -Rice 2013 [12]: IFI27, IFI44L, IFIT1, ISG15, RSAD2, SIGLEC1 -Morimoto 2015 [9]: EPSTI1, HERC5, TYK1 -Khamashta 2016 [10]: IFI27, IFI44, IFI44L, RSAD2 -Banchereau 2016 [6] (Module M1.2) (gene included are highlighted in bold): BATF2, BIRC4BP, CXCL10, DNAPTP6, EPSTI1, FLJ20035, ISG15, HERC5, HES4, IFI44, IFI44L, IFIT1,

Supplementary table s1. Baseline characteristics and active features at the time of sampling in SLE patients (n=133)

  Flash or ELISA as described in the methods section in supplementary material. SLEDAI,Safety of Estrogens in Lupus Erythematosus National Assessment-Systemic LupusErythematosus Disease Activity Index (SELENA-SLEDAI).BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s)

	BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance
	Supplemental material	placed on this supplemental material which has been supplied by the author(s)	Ann Rheum Dis Ann Rheum Dis Ann Rheum Dis
	RESULTS Features Female Age, median (range), years Ethnicity Caucasian African Asian Others data: Antinuclear autoantibodies (ANA), Sm and aPL (antiphospholipid), C3 and C4. Double 111 (83) 45.6 (19-78.8) 98 (74) 16 (12) 12 (9) 7 (5) * historical stranded DNA (ds-DNA), U1 ribonucleoprotein (U1RNP), anti-C1q were determined by 4 (0-46) Current treatment No treatment Antimalarials Systemic glucocorticoids Immunosuppressant agents 14 (11) 97 (73) 53 (40) 64 (48) Q'SLEDAI, median (range) B cell targeted agents 9 (7)
	Active manifestations at the time of study
	Fever		5 (4)
	Arthritis		26 (20)
	Cutaneous		28 (21)
	Serositis		6 (5)
	Neurological disorder	9 (7)
	Leukopenia		6 (5)
	Thrombocytopenia	8 (6)
	Proteinuria > 0.5 g/24h	6 (5)
	Immunological features (presence)
	ANA*		125 (94)
	Anti-dsDNA		61 (46)
	Anti-SSA		55 (41)
	Anti-Sm*		34 (26)
	Anti-U1RNP		37 (28)
	Anti-C1q		34 (26)
	aPL*		53 (40)
	Low complement		28 (21)
	C3 (g/l) median, range*	0.90 (0.39-1.8)
	C4 (g/l) median, range*	0.16 (0.01-0.45)
	Activity
	Clinical SLEDAI > 0		75 (56)
	Clinical SLEDAI, median (range)	2 (0-42)
		, et al. Chasset F , et al. Chasset F , et al. Chasset F	Ann Rheum Dis Ann Rheum Dis Ann Rheum Dis	:1 0 2022; :1 0 2022; :1 0 2022;	-2. -2. -2.	doi: 10.1136/annrheumdis-2021-221835 doi: 10.1136/annrheumdis-2021-221835 doi: 10.1136/annrheumdis-2021-221835

Supplementary Figure s4. Association between serum IFN-γ levels with SLE activity and active phenotypes.

  Chi-square and Fisher's exact tests were used to compare categorical variables as appropriate. NS: Not significant

  BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s)

					Ann Rheum Dis
	, et al. Chasset F	Ann Rheum Dis	:1 0 2022;	-2.	doi: 10.1136/annrheumdis-2021-221835

Supplementary Table s2. Association of high IFN-I gene score and high serum IFN-α with active SLE features

Features N (%) ⱡ

Low IFN the Youden Index (the sum of sensitivity and specificity -1). By using an optimal cutoff computed using the Youden Index, only the specificity and the positive predictive value increased substantially, for both IFN-I gene scores and serum IFN-α levels.

BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s) BMJ Publishing Group Limited (BMJ) disclaims all liability and responsibility arising from any reliance Supplemental material placed on this supplemental material which has been supplied by the author(s)


Stéphanie Bellocchi

Andrea Huau

Marianne Jover

Florence Brun-Henin

Josette Mancini

Stéphanie Ducrot

Oculomotor control in DCD children with and without developmental dyslexia : what is the impact of co

Keywords: saccade computation, eye movements, developmental dyslexia, developmental coordination disorder, co-occurrence

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

Oculomotor control in DCD children with and without developmental dyslexia: What is the impact of co-occurrence between neurodevelopmental disorders? S. Bellocchi 1 , A. Huau 2 , M. Jover 2,4 , F. Brun-Hénin 3 , J. Mancini 3 & S. Ducrot 4

Abstract :

Introduction. In previous studies, we showed that the perceptual low-level pre-processing step that is responsible for landing position pattern in oculomotor control is not yet implemented in dyslexic children without developmental coordination disorder (DCD). This result has been interpreted with the idea that saccade computation (i.e. where and when the eyes land in a word) is not dysfunctional but rather a mirror of their less reading exposure (e.g. [START_REF] Bellocchi | Dyslexic readers and saccade computation: effects of reading exposure and visuo-perceptual constraints[END_REF]. In the same vain, some studies suggest a delay in the maturation of low-level oculomotor skills in children with DCD (e.g. pursuit system, Robert et al., 2014).

Aim: Considering that DCD and developmental dyslexia (DD) are often associated, the aim of the present study was to investigate the role of co-occurrence between these two disorders in saccade computation.

Method:

We assessed the eye movements of four groups of children (12 DCD children with DD, 11 DCD children without DD, 20 DD children without DCD and 29 typical developing children -mean age: 117,3 months; SD: 10,2 months) using an oculomotor bisection task (participants were asked to move their eyes to a position they thought to be the middle of the stimulus). The type of stimulus -linguistic factor (words vs non-linguistic stimuli) and discreteness (lines vs strings of hashes) -in combination with the stimulus presentation side (left vs. right) were manipulated.

Results: Main results showed differences between groups with regard to saccade latency: "DCD + DD" and "DCD only" groups were slower compared to typical developing children in programming their first saccade. Moreover, in the LVF those two groups made shorter saccade size, suggesting that they struggled to reach the preferred viewing location (PVL) in this visual side. Furthermore, those two groups seem to suffer more for the absence of discreteness of the stimuli in order to compute their saccades and move their eyes in the middle of the stimulus. Finally, results seem to suggest differences between children with DCD (with or without DD) and children with DD only.

Discussion: Overall, it seems that no differences emerged between "DCD+DD" and "DCD only" groups, suggesting that co-occurrence in itself does not sharpen difficulties in saccade computation. However, the presence of a motor disorder seems to generate a dysfunction in saccade computation. These results strengthen the importance to take into account oculomotor control involved in visual word recognition for clinical assessment and intervention in children with DCD.

1

  Epsylon Research Unit EA 4556, University of Montpellier & Paul Valéry University, Montpellier, 34000, France. stephanie.bellocchi@univ-montp3.fr 2 Centre PsyCLE EA 3273, 13621, Aix-Marseille University, Aix en Provence, 13100, France. 3 APHM, Salvator Hospital, CERTA (Centre of reference for learning disabilities), Marseille, 13000, France. 4 Laboratoire Parole et Langage, UMR 7309, CNRS & Aix-Marseille University, Aix en Provence, 13100, France.