DEVICE AND METHOD FOR CONTROLLING A SYNCHRONOUS MACHINE AND FOR ESTIMATING ROTOR POSITION, FROM START-UP TO A PREDETERMINED LOW SPEED

Abstract

One aspect of the invention relates to a control device (2) for starting up a synchronous electric motor (1) up to a predetermined threshold speed, comprising: a current regulator (4) that delivers a voltage setpoint (V #dq) in accordance with a regulation current setpoint (l #dq), a computing unit (5) for computing a current feedback. (Idq) in accordance with measurements of the phase currents (lu, Iv, Iw), an estimator (6) for estimating an angular position of the rotor (elec), in accordance with a difference between a reference stator flux vector (q) that depends on the feedback currents (Iq) and an adaptive stator flux vector (qv) that depends on the voltage setpoint (V.sup.#dq), on the feedback currents (Iq, Id), and on an estimated electrical speed (elec), a setpoint current modifier (7) that computes, when the estimated electrical speed (elec) is lower than the predetermined threshold speed, a regulator setpoint DC current (l.sup.#d) having a non-zero value.

Claims

1. A control device for controlling an inverter converter for starting a multiphase synchronous electric motor of an electric machine up to a predetermined threshold speed, the control device comprising: a regulation loop, comprising: a current regulator for delivering a voltage setpoint comprising a quadratic and direct voltage with an angle, from a regulation current setpoint, a calculation unit for calculating a direct and indirect Park transformation, the calculation unit comprising a current return output in a Park reference frame, from measurement values of the phase currents received, transformed in a Park reference frame, into a return quadratic current and into a return direct current, taking account of a value of estimated rotor angular position received, characterised in that the control device further includes: a closed loop adaptive angle estimator, for estimating the value of the estimated rotor angular position, based on a difference between at least one piece of data of a reference stator flux vector calculated as a function of the return currents, and a piece of data of the adaptive stator flux vector, calculated from the voltage setpoint, the return currents, and an estimated electrical speed calculated as a function of this difference, and a modifier of the setpoint current, wherein, when an absolute value of the estimated electrical speed received by the adaptive angle estimator is less than the predetermined threshold speed, the modifier calculates a regulator setpoint direct current having a non-zero value, thus modifying a setpoint direct current of a setpoint current received.

2. The control device for controlling an inverter converter for starting an electric motor according to claim 2, wherein the adaptive angle estimator comprises: a first stator flux calculator comprising: 1. a first block for calculating the reference stator quadratic flux, 2. a second block for calculating the adaptive quadratic stator flux, a second calculator for an estimated electrical speed as a function of a comparison between the adaptive quadratic stator flux and the reference quadratic stator flux, a third calculator for estimating a value for the estimated rotor angular position as a function of the estimated electrical speed calculated.

3. The control device for controlling an inverter converter for starting an electric motor according to claim 2, the first calculation block calculates the reference quadratic flux according to the formula: L.sub.ql.sub.q wherein L.sub.q is the stator inductance on the axis q.

4. The control device for controlling an inverter converter for starting an electric motor according to claim 2, wherein the second calculation block calculates the adaptive quadratic stator flux according to the integral of the following formula: v.sub.qR.sub.s{dot over (.Math.)}.sub.q{circumflex over ()}.sub.elec{circumflex over ()}.sub.d.sub.v+k{tilde over (.Math.)}.sub.q wherein R.sub.s is the stator resistance, .sub.d.sub.v is the adaptive direct stator flux equal to the integral of the following formula: v.sub.dR.sub.s{dot over (.Math.)}.sub.d+{circumflex over ()}.sub.elec{circumflex over ()}.sub.q.sub.v+k{tilde over (.Math.)}.sub.d and K is a positive gain matrix, {tilde over (l)}.sub.d and {tilde over (l)}.sub.q are the direct and quadratic components of the error in currents with: ${\tilde{i}}_d=i_d-{\hat{i}}_d$ ${\tilde{i}}_q=i_q-{\hat{i}}_q$ and wherein the estimated direct current {tilde over (l)}.sub.d and the estimated quadratic current {tilde over (l)}.sub.q are calculated as a function of: ${\hat{i}}_d=\frac{{\hat{}}_{q_v}-{}_{\mathrm{PM}}}{L_d}$ ${\hat{i}}_q=\frac{{\hat{}}_{q_v}}{L_q}.$

5. The control device for controlling an inverter converter for starting an electric motor according to claim 1, wherein the modifier of the setpoint direct current calculates a regulator setpoint direct current equal to the square root of the sum of a value of the squared maximum quadratic current with the value of the setpoint quadratic current, received in the setpoint current: $I_{d^{}}^{\#}=\sqrt{\mathrm{Iq}{\max }^2-I_q^{\mathrm{\#2}}}.$

6. The control device for controlling an inverter converter for starting an electric motor according to claim 5, wherein calculating the modified setpoint direct current is imposed with the same sign as the estimated electrical speed received.

7. The control device for controlling an inverter converter for starting an electric motor according to claim 1, wherein the modifier of the setpoint direct current comprises a comparator for comparing the absolute value of the estimated electrical speed with the predetermined threshold speed.

8. The control device for controlling an inverter converter for starting an electric motor according to claim 1, wherein the control device is able to control the converter for a rotation speed beyond the predetermined threshold speed, wherein if the absolute value of the estimated electrical speed is greater than the predetermined threshold speed, the setpoint direct current modifier transmits the regulation setpoint current according to only the setpoint current.

9. The control device according to claim 8, wherein when the absolute value of the estimated electrical speed is greater than the predetermined threshold speed, the modifier of the setpoint direct current transmits the setpoint current with a setpoint direct current equal to zero, unless a defluxing setpoint is sent.

10. The control device according to claim 8, wherein, if the absolute value of the estimated electrical speed is greater than the predetermined threshold speed, the angular position estimator estimates the position and angular speed from an electromotive force EMF measured.

11. A synchronous electric machine comprising: an electric motor comprising a rotor and a stator, a current measurement sensor, an inverter converter comprising power switches and the control device according to claim 1, wherein the calculation unit transmits a command to the converter from the voltage setpoint to drive the electronic power switches to a specific chopping frequency and thus drive the fundamental frequency of the stator voltage input to the electric machine for driving the electric motor.

12. A method for driving a synchronous machine in a closed loop without a position sensor, from start-up to maximum rotation speed, comprising: modifying a received current setpoint by imposing a non-zero modified setpoint direct current as long as an estimated speed is less than a predetermined threshold speed value, calculating a voltage setpoint comprising a quadratic and direct voltage with an angle, from a regulation current setpoint comprising a modified setpoint direct current, calculating a command for driving the electronic power switches of the inverter converter at a specific chopping frequency and thus driving the fundamental frequency of the stator voltage input to the electric machine, by an inverse Park transformation of the voltage setpoint and of a rotor estimated angular position, measuring the phase currents and transforming the phase currents in a Park reference frame, into a return quadratic current and a return direct current, taking account of the estimated rotor angular position, calculating a reference stator quadratic flux as a function of the return quadratic current, the return direct current, the current return output and a calculated electrical frequency, calculating adaptive quadratic stator flux, from the voltage setpoint, the return quadratic current, the return direct current, and the estimated electrical speed calculated, calculating an electrical speed of the rotor from a comparison of the adaptive quadratic stator flux with the reference quadratic stator flux, and calculating the value of the estimated rotor angular position as a function of the estimated electrical speed calculated.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0078] The figures are set forth by way of indicating and in no way limiting purposes of the invention.

[0079] FIG. 1 shows a representation of a schematic diagram with functional blocks of an electric machine comprising a control device according to one embodiment of the invention.

[0080] FIG. 2 shows a schematic representation of an adaptive angle estimator of the control device according to one example of one embodiment of the invention.

[0081] FIG. 3 shows a schematic representation of a modifier of a setpoint direct current of a setpoint current of the control device according to one example of a first embodiment of the invention.

[0082] FIG. 4a shows a schematic representation of different graphs representing different measurements of a motor having a decreasing rotation speed.

[0083] FIG. 4b shows a schematic representation of a magnification of one of the graphs of FIG. 4a, representing the actual and estimated position measurement of a motor.

DETAILED DESCRIPTION

[0084] The figures are set forth by way of indicating and in no way limiting purposes of the invention.

[0085] FIG. 1 represents a schematic diagram with functional blocks of an electric machine M comprising a synchronous electric motor 1, an inverter converter C supplying phases of the synchronous electric motor 1, a battery B and a control device according to one embodiment of the invention controlling the inverter converter C.

[0086] The electric machine M may be a machine of a turbomachine, wherein the electric motor 1 comprises a stator comprising X phases, a rotor surrounded by the stator. The electric motor 1 may operate in a motor mode and/or in a generator mode. The electric machine M is, for example, a multiphase synchronous electric machine of an aircraft propulsion unit. The rotor comprises a shaft and an active part mounted to the shaft. The active part of the rotor comprises magnets forming P pairs of poles. The number X in this example is three, but could be greater, for example five or six. The stator therefore comprises in this example three windings forming three phase outputs U, V, W of three phases which are represented in FIG. 1, as star-coupled but could for example be delta-coupled.

[0087] The inverter converter C is in this example of an inverter with a DC voltage input source either a DC/AC converter or a reversible inverter converter i.e. AC/DC and DC/AC converter in the case where the electric machine M also allows generator mode. The inverter converter C comprises N outputs, herein three outputs each connected to one of the corresponding phase outputs U, V, W. The inverter converter C further comprises power inputs, herein two DC voltage potentials connected to the terminals of a DC voltage bus B. The inverter converter C comprises electronic power switches and a control setpoint input, herein a pulse width modulation control which makes it possible to drive the electronic power switches at a specific chopping frequency and thus drive the fundamental frequency of the stator voltage input to the electric machine for driving the electric motor 1 of the electric machine.

[0088] The electric machine M further comprises a measurement means 3 for measuring phase currents Iu, Iv, Iw circulating on the phase outputs U, V, W. The measurement means 3 comprises, for example, a current sensor per phase for measuring the current in the corresponding phase.

[0089] The control device 2 comprises a regulation loop R schematically represented according to one example of a current regulator 4 comprising a current setpoint input of a regulation current setpoint I.sup.#.sub.dq comprising a modified setpoint direct current I.sup.#.sub.d, explained in the following. The regulation current setpoint I.sup.#.sub.dq further comprises a quadratic current and an angle a.

[0090] The current regulator 4 comprises an output of voltage setpoint V.sup.#.sub.dq comprising a forward setpoint voltage and a quadratic setpoint voltage.

[0091] The regulation loop R further comprises a calculation unit 5 using a known mathematical method, namely the so-called direct Park transform to shift from a three-phase reference frame U; V; W linked to the stator to a two-phase rotating reference frame d; q, also knowing the angular position of the rotor of the electric motor 1 with respect to its stator, as well as the inverse Park transform to shift from the Park reference frame d; q to the three-phase reference frame U; V; W, also using an angular position of the rotor. The angular position of the rotor that is the position of the axis d in the reference frame dq, of the rotor with respect to the reference magnetic axis (which is the horizontal axis in (abc) which is fixed). The reference frame dq is rotational. Thus, between the two reference frames, there is an angle which varies from 0 to 360. This is the position of the rotor in space.

[0092] The calculation unit 5 comprises a voltage setpoint input connected to the output of the regulator 4 for transforming the voltage setpoint V.sup.#.sub.dq, with an inverse transformation and control calculator, and a control output connected to the control input of the inverter converter C, to transmit a PWM command calculated by the direct transformation calculator, herein in pulse width modulation. The inverse Park transformation and control calculator is therefore configured to transform vectors of the direct and quadratic setpoint voltages in a Park plane from an estimated position value of the rotor angular ({circumflex over ()}.sub.elec) explained below, into a pulse width modulation PWM command. The pulse width modulation PWM command comprises electrical voltage signals, to control each phase in pulse width modulation and thus generate a balanced three-phase AC voltage system.

[0093] The calculation unit 5 further comprises measured current inputs receiving the phase currents i.sub.u, i.sub.v, i.sub.w measured, the current inputs measured are connected to the measurement means 3, and a quadratic current I.sub.q (sometimes noted I.sub.q here) and direct current Id (sometimes noted I.sub.d) return output connected to the return input of the current regulator 4.

[0094] The calculation unit 5 also comprises an estimated angular position input receiving the estimated value of the rotor angular position {circumflex over ()}.sub.elec explained below, and a Park transformer calculator configured to transform the currents Iu, Iv, Iw measured according to the estimated value of the rotor angular position {circumflex over ()}.sub.elec received as a component on the quadratic axis of the current vector referred to hereinafter as the quadratic current Iq, and the component on the direct axis of the direct current vector Id in a Park plane, also referred to hereinafter as the return direct current Id.

[0095] In the application, each reference in the following with {circumflex over ()} is an estimated value.

[0096] The return direct current Id is therefore in the following the direct component of the stator current in the Park plane calculated from the stator currents measured.

[0097] The return quadratic current Iq is therefore hereinafter the quadratic component of the stator current in the Park plane calculated from the stator currents measured.

[0098] The current regulator 4 comprises summers 41 (represented by a single summer in FIG. 1), receiving as non-inverting input the setpoint quadratic current vector I.sup.#.sub.q and the setpoint direct current vector I.sup.#.sub.d modified and as inverting input the return quadratic current vector Iq as well as the return direct current vector Id.

[0099] At the output of the summers 41, the regulator 4 includes a line on which the difference between the quadratic setpoint current I.sup.#.sub.q and the return quadratic current Iq circulates, as well as the setpoint direct current I.sup.#.sub.d and the return direct current Id on another line. Both lines are represented by a single line. The current regulator 4 comprises a block of PI (proportional-integral) current regulators 42 connected to the difference lines and delivering the voltage setpoint V.sup.#.sub.dq comprising quadratic voltages and direct voltages.

[0100] The control device 2 comprises, in addition to the regulation loop R, a closed loop adaptive angle estimator 6, for estimating an estimated value of the rotor angular position {circumflex over ()}.sub.elec, in particular from start-up of the electric machine (rotor rotation speed=0) to the predetermined threshold speed. The regulation loop R may comprise an angle estimator, not represented, according to the electromotive force which is then used beyond the predetermined speed.

[0101] In this example of this embodiment, the speed is the electrical speed (volts/s) but could be the rotor rotation speed. The predetermined threshold speed is, for example, the speed required for operation of the angle estimator according to the electromotive force. For example of the predetermined threshold speed is an electrical speed corresponding to a value of rotor rotation speed at 500 rpm. An electrical angle=mechanical angle of the rotor multiplied by the number of pole pairs.

[0102] The closed loop adaptive angle estimator 6, represented in detail in FIG. 2, comprises a first stator flux calculator 61. The first stator flux calculator 61 comprises two calculation blocks for calculating a reference stator quadratic flux q calculated from measured value and predetermined constant and an adaptive stator quadratic flux qv different from the reference stator quadratic flux q in that it is further dependent on the voltage setpoint V #dq calculated.

[0103] The first stator flux calculator 61 therefore comprises a first calculation block 611 for calculating the reference stator quadratic flux q as a function of the return quadratic current I.sub.q. In particular, in this example of this embodiment, the reference stator quadratic flux q is calculated according to the formula: L.sub.qI.sub.q in which L.sub.q is the stator inductance on the axis q. In this example, the stator inductance L.sub.q is a predetermined value, here it is assumed that the variation in the inductances as a function of the current is negligible, i.e. the stator does not exhibit magnetic saturation (inductance which sharply falls when the stator current increases in amplitude). The inductances are considered as apparent inductances (i.e. almost constant for a given current point) or the link between the flux and the current remains linear via this inductance: L=flux/current.fwdarw.an increasing straight line.

[0104] The first stator flux calculator 61 therefore also comprises a second block 612 for calculating the adaptive quadratic stator flux qv, which may also be called an adaptive flux observer, from the voltage setpoint V #dq, the return quadratic current I.sub.q, the return direct current I.sub.d, and the estimated electrical speed {circumflex over ()}.sub.elec calculated.

[0105] In particular, in this example of this embodiment, the adaptive quadratic stator flux qv is calculated by the integral of the following formula:

[00008]$\begin{array}{cc}{v}_q-R_s{i}_q-{\hat{}}_{\mathrm{elec}}{\hat{}}_{d_v}+k{\tilde{i}}_q& \left[\mathrm{Math}8\right]\end{array}$ [0106] wherein R.sub.s is the stator resistance, {circumflex over ()}.sub.d.sub.v is the adaptive direct stator flux equal to the integral of the following formula:

[00009]$\begin{array}{cc}{v}_d-R_s{i}_d-{\hat{}}_{\mathrm{elec}}{\hat{}}_{q_v}+k{\tilde{i}}_d& \left[\mathrm{Math}9\right]\end{array}$ [0107] and in that K is a positive gain matrix. [0108] {circumflex over (.Math.)}.sub.d and {circumflex over (.Math.)}.sub.q are the direct and quadratic components of the error in currents with

[00010]$\begin{array}{cc}{\tilde{i}}_d=i_d-{\hat{i}}_d& \left[\mathrm{Math}10\right]\end{array}$${\tilde{i}}_q=i_q-{\hat{i}}_q$ [0109] and wherein the estimated direct current {circumflex over (.Math.)}.sub.d and the quadratic estimated current {circumflex over (.Math.)}.sub.q are calculated as a function of:

[00011]$\begin{array}{cc}{\hat{i}}_d=\frac{{\hat{}}_{q_v}-{}_{\mathrm{PM}}}{L_d}& \left[\mathrm{Math}11\right]\end{array}$${\hat{i}}_q=\frac{{\hat{}}_{q_v}}{L_q}$

[0110] The role of the first stator flux calculator 61 is to make it possible to obtain values of the reference quadratic flux q which has as a variable return currents which is a function of measured current and an estimated angular position, and the adaptive quadratic stator flux qv which also has as a variable the voltage setpoint V.sup.#.sub.dq and the calculated electrical speed in order to differentiate them to thus make it possible to identify a positioning estimation error.

[0111] The adaptive angle estimator 6 therefore comprises a second calculator 62 for an estimated electrical speed {circumflex over ()}.sub.elec as a function of the comparison of the adaptive quadratic stator flux q with the reference quadratic stator flux q. The second calculator 62 therefore comprises a comparator 620 comprising, herein as a negative input, the reference quadratic stator flux q and, as a positive input, the adaptive quadratic stator flux q and, as an output, a comparison value representing the difference between both fluxes calculated. The second calculator 62 also includes a phase-locked loop (PLL) 621 for calculating an estimated value of electrical speed {circumflex over ()}.sub.elec from the comparison value between the reference quadratic stator flux and the adaptive quadratic stator flux.

[0112] The adaptive angle estimator 6 further comprises a third calculator for calculating the electrical position of an estimated value of the rotor angular position {circumflex over ()}.sub.elec from the estimated values of electrical speed {circumflex over ()}.sub.elec. The estimated value of the rotor angular position {circumflex over ()}.sub.elec is transmitted to the calculation unit 5. The estimated value of the rotor angular position {circumflex over ()}.sub.elec is estimated at each instant t as a function of the integral of the estimated values of electrical speed {circumflex over ()}.sub.elec.

[0113] The control device 2 further comprises a modifier 7 for a setpoint direct current I.sup.#.sub.d of a setpoint current I.sup.#.sub.dq received by an input. The modifier 7 thus allows from start-up to the predetermined threshold speed modification of the setpoint direct current I.sup.#.sub.d into a non-zero direct regulator setpoint current I.sup.#.sub.d transmitted into the current regulator. In particular, modifier 7 comprises a comparator 70 for the absolute value of the estimated electrical speed {circumflex over ()}.sub.elec received by the adaptive angle estimator 6 with the predetermined threshold speed. If the estimated electrical speed {circumflex over ()}.sub.elec is less than the predetermined threshold speed, the modifier 7 comprises a calculation block 71 which calculates the regulator setpoint direct current I.sup.#.sub.d with a non-zero value and transmits it to the current regulator 4. Herein, in this example, the calculation block 71 calculates the regulator setpoint direct current I.sup.#.sub.d equal to the sign of the estimated electrical speed {circumflex over ()}.sub.elec (to determine the direction of rotation of the rotor) multiplied by a maximum of two terms which are as follows:

[0114] The first term, denoted i.sub.q.sup.# constitutes a proportion of the quadratic component of the current setpoint.

[0115] The second term is the square root of the difference between the squared value of the maximum amplitude of the stator currents that the voltage inverter can withstand (denoted Ipeak) and the squared value of the quadratic component of the current setpoint:

[00012]$\begin{array}{cc}\left(\sqrt{I_{\mathrm{peak}}^2-i_q^{\mathrm{\#2}}}\right)& \left[\mathrm{Math}12\right]\end{array}$

[0116] According to another example of, the regulator setpoint direct current I.sup.#.sub.d is a predetermined direct current.

[0117] The setpoint current I.sup.#.sub.dq may originate from a control unit of the propulsion unit(s) transmitting the setpoint in setpoint direct current I.sup.#.sub.d and in quadratic setpoint current I.sup.#.sub.q, with an angle a to the modifier 7.

[0118] In this example, the modifier 7 also transmits the regulator quadratic setpoint current I.sup.#.sub.q which is equal to the quadratic setpoint current I.sup.#.sub.q, wherein the same can be directly transmitted to the current regulator 4.

[0119] In this embodiment, the control device is adapted to control the converter for a rotation speed beyond the predetermined threshold speed. The modifier 7 of setpoint current transmits the regulation setpoint current I.sup.#.sub.dq according to the setpoint current I.sup.#.sub.dq only if the absolute value of the estimated electrical speed {circumflex over ()}.sub.elec is greater than the predetermined threshold speed.

[0120] In this embodiment, the setpoint current I.sup.#.sub.dq comprises a setpoint direct current I.sup.#.sub.d equal to zero. According to another example, in the case where the setpoint direct current I.sup.#.sub.d is different from zero, for a rotation speed beyond the predetermined threshold speed, the modifier 7 of the setpoint current imposes the regulator setpoint direct current I.sup.#.sub.d to zero except in the case of defluxing control.

[0121] FIG. 4a represents various time graphs showing the performance of the control device according to the invention.

[0122] Column 1, row 2 represents the speed as a function of time wherein, the speed decreases from 0.15 (t) from 2000 rpm to 200 rpm stabilised from 0.2 to 0.35 (t), (t) being a time unit.

[0123] Column 1, row 1 represents a curve of the set torque Temc as a function of time and a curve of the measured torque Temmes, wherein the setpoint torque is 2500N.Math.m between 0(t) and 0.3(t) and a curve of the measured torque Temc equal to K I.sub.q which begins to deviate from the actual torque between 0.2(t) and 0.3(t) and then between 0.3(t). This deviation is linked to an angular position error in the control.

[0124] Column 2, row 1 represents the regulator setpoint direct current I.sup.#.sub.d wherein between 0.25(t) and 0.3 (t) the regulator setpoint direct current I.sup.#.sub.dq=50 Amp and then from 0.3 (t) to 0.35 (t)=200 Amp is modified.

[0125] Column 2, row 2 represents the regulator quadratic setpoint current I.sup.#.sub.q which is regular around 550 Amperes.

[0126] Column 2, row 2 represents the actual rotor angular position relative to the rotor angular position {circumflex over ()} calculated (a function of the electrical angular position .sub.elec and the number of poles in the rotor). FIG. 4b represents a magnification of this graph in zone Z, of the actual rotor angular position relative to calculated rotor angular position {circumflex over ()} between 0.25 (t) and 0.35 (t). In this figure, a significant difference in angular position at around 0.25 which slightly decreases at around 0.3 and then sharply decreases from 0.3 to 0.35 can be seen.

[0127] Thus, the fact that the direct current modifier 7 modifies the setpoint direct current I.sup.#.sub.d from 0 to 50 Amperes very slightly reduces the angular position error (angular position difference ) but by significantly modifying the setpoint direct current I.sup.#.sub.d from 0 to 200 Amperes, the position error is significantly reduced. As explained previously, the actual torque T.sub.em is equal to the sum of the estimated torque {circumflex over (T)}.sub.em=Klq and K.sub.t{circumflex over (.Math.)}.sub.d sin(), but as sin() tends towards 0 when there is no position error, the product K.sub.t{circumflex over (.Math.)}.sub.d sin(), tends towards zero and thus {circumflex over (T)}.sub.em=K.sub.t{circumflex over (.Math.)}.sub.q without angular position error as is visible on row 1 column 1 from 0.3(t) to 0.35(t).

[0128] Thus, the control device of the invention makes it possible to estimate an angular position of a rotor of a synchronous motor coupled to a load with a torque which may be significant, from standstill (start-up) up to a predetermined threshold speed, for example of 1000 rpm. Beyond the predetermined threshold speed, the control device can calculate the rotor angular position and the rotation speed according to the flux by the adaptive angle estimator 6, but with a regulator setpoint direct current equal to zero or by another angular position estimator calculating the position according to the electromotive force as in prior art.

[0129] Unless otherwise specified, a same element appearing in different figures has a single reference.