Method and system for estimating the electromagnetic torque of a synchronous machine.

Abstract

- Method and system for estimating the electromagnetic torque of a synchronous machine. - The method comprises a measurement step (E1) of the rotor voltage and the stator and rotor currents, a determination step (E2) of a flux-current model of the machine in which the dynamic magnetic uncertainties have a non-zero constant second derivative, a determination step (E3) of a polytopic linear variable-parameter system from the flux-current model, a determination step (E4) of a state observer for the linear variable-parameter system, an estimation step (E5) of the state variables by the state observer, and an estimation step (E6) of the electromagnetic torque from the estimated state variables. Figure for the abstract: Fig. 1

Description

Title of the invention: Method and system for estimating the electromagnetic torque of a synchronous machine. technical field

[0001] The present invention relates to a method and a system for estimating an electromagnetic torque of a synchronous machine, in particular in an electric or hybrid motor vehicle. State of the art

[0002] Wound rotor synchronous machines (WRSMs) are frequently used in the field of electric or hybrid vehicles. In particular, they can be used as pivoting drive motors for motor vehicles.

[0003] Estimating motor torque is important for ensuring the safe operation of an electric drive system, optimizing its performance, and improving its energy efficiency. It allows for real-time monitoring of motor performance to detect abnormal operation and react quickly to it. By precisely adjusting control algorithms, accurately estimated motor torque optimizes speed, acceleration, and overall vehicle performance, thereby extending battery life and the vehicle's operating range. Furthermore, accurate torque prediction minimizes power losses, thus reducing energy consumption and operating costs. Its adaptability to different motor types and configurations ensures compatibility across various applications, making it an important component of electric drive technology.

[0004] Several methods exist for estimating electromagnetic motor torque. In particular, a torque estimation method based on current measurements is known. This method involves training a predictive neural network model with current data to deduce flux information. The torque is then calculated using the derived current and flux data. However, this method has significant drawbacks. In particular, it can neglect important details about the motor's transient performance and requires extensive training of the neural network model, which can lead to discrepancies between the estimated and actual torque values.

[0005] There is also another method for estimating electromagnetic torque for permanent magnet synchronous machines (PMSMs) and MSRBs. This method is Based on a state-space model of the machine, this method adapts to fluctuations in the machine's magnetic parameters, taking into account the uncertainties of these parameters, which can manifest as constant dynamics or slow variation. The system model adopted for this estimation method treats the dynamics as a linear variation over time, to design a time-varying Kalman observer. Despite its usefulness, this method has some limitations. First, the method requires proving the existence of solutions for the time-varying Riccati equation to determine the observation gain. This proof can be difficult to provide, even under certain observability conditions. Second, the calculation of the observation gain is performed in real time, which can generate a significant amount of computation.

[0006] Current methods for estimating electromagnetic torque are therefore not fully satisfactory. Description of the invention

[0007] The present invention aims to provide a method and system for estimating electromagnetic torque, enabling the estimation of electromagnetic torque to be obtained with high accuracy, requiring little computing power.

[0008] For this purpose, it relates to a method for estimating an electromagnetic torque of a synchronous machine comprising a stator having phases and a rotor having a winding.

[0009] According to the invention, the estimation method comprises the following steps: - a measurement step, implemented by a set of sensors, to measure a voltage across the rotor winding and to measure in a rotating frame of the rotor the stator currents and a current through the rotor winding; - a first determination step, implemented by a computer, to determine a flux-current model of the machine at least as a function of the measured voltages, the measured currents, the stator inductances, a rotor inductance, a mutual inductance between the stator and the rotor, a rotor angular velocity and state variables including dynamic magnetic uncertainties, the dynamic magnetic uncertainties having a non-zero constant second derivative corresponding to disturbances; - a second determination step, implemented by the computer, to determine a linear system with a polytopic varying parameter from the flow-current model; - a third determination step, implemented by the computer, to determine a state observer allowing the estimation of the state variables of the linear system with varying parameters; - a first estimation step, implemented by the computer, to estimate the state variables by the state observer; - a second estimation step, implemented by the computer, to estimate the electromagnetic torque from the estimated state variables.

[0010] Thus, thanks to the determination of a linear system with a polytopic varying parameter, the determination of the formulation of a robust state observer is simplified, which reduces the computational resources required.

[0011] Furthermore, the polytopic linear variable parameter system has the following form: x = A (ouch) x + Bu + Ed y-Cx in which, x is a state vector x = id, iq, if, g# ggCd, Cq, Cf}, id, iq, if correspond to the measured currents, Sq' Sf correspond to the dynamic magnetic uncertainties, ctb cf correspond to the second derivatives of the dynamic uncertainties, u is a control and measurement vector U = ( Vd, Vq, Vf ) , vd' vf correspond to the calculated and measured voltages, d is a disturbance vector d = ( dd, dq, df}, dd, dq, df correspond to the disturbances, A( (¼) corresponds to a state matrix that is a function at least of the angular speed of the rotor, the inductances of the stator, the inductance of the rotor, the mutual inductance between the stator and the rotor, the state matrix being in the form of a convex combination of constant matrices, B corresponds to a control matrix that is a function of at least the stator inductance, the rotor inductance, and the mutual inductance between the stator and the rotor.

[0012] C corresponds to a predetermined constant observation matrix, E corresponds to a predetermined constant perturbation matrix.

[0013] Furthermore, the convex combination of the state matrix has the following form: A (we) = a (oee) A! + ( 1 -a ( (¾ ) ) A2, in which: The angular velocity We is bounded between œy = min ( we ) and oy = max ( oy ), =~' A] = A(œy) and A2 = A ( we ).

[0014] Furthermore, the state observer, determined in the third determination step, has the following form: x = A(a) e}x+Bu + K(a) e (y-Cx) ,y-Cx in which: x corresponds to an estimated state vector $ = iq, if correspond to the estimated currents, Sq > g} correspond to the estimated dynamic magnetic uncertainties, q, fy, Cf correspond to the second derivatives of the estimated dynamic uncertainties, C corresponds to the estimated predetermined constant observation matrix, K ( œe ) corresponds to a gain parameter that is a function of the angular speed of the rotor.

[0015] Furthermore, the gain parameter as a function of the angular speed of the rotor has the following form: K(we) = a(uje)+ ( 1-a ( toe))K2, in which corresponds to a first observer gain and K2 corresponds to a second observer gain.

[0016] Furthermore, the third determination step comprises: - a minimization substep, implemented by the computer, to minimize a positive performance parameter using linear matrix inequalities to determine a positive definite matrix, a first matrix relating to the first observer gain and a second matrix relating to the second observer gain; - a first sub-step of determination, implemented by the computer, to determine the first observer gain from the first matrix and the positive definite matrix; - a second sub-step of determination, implemented by the computer, to determine the second observer gain from the second matrix and the positive definite matrix.

[0017] Furthermore, the dynamic magnetic uncertainties of the state variables estimated in the first estimation step are estimated from the state observer, the first observer gain and the second observer gain.

[0018] In addition, the second estimation step includes: - an estimation substep, implemented by the computer, to estimate the stator fluxes from the estimated dynamic magnetic uncertainties, the inductances of the stator, mutual inductance and measured currents; - a calculation substep, implemented by the computer, to calculate the estimated electromagnetic torque from the rotor fluxes estimated in the estimation substep, the measured currents and a number of pole pairs of the machine.

[0019] The invention also relates to a system for estimating the electromagnetic torque of a synchronous machine comprising a stator having phases and a rotor having a winding.

[0020] According to the invention, the estimation system comprises: - a set of sensors configured to measure a voltage across the rotor winding and to measure in the rotating frame of the rotor the currents of the stator phases and a current through the rotor winding; - a calculator configured for: To determine a flux-current model of the machine at least as a function of the measured voltages, the measured currents, the stator inductances, a rotor inductance, a mutual inductance between the stator and the rotor, a rotor angular velocity and state variables with magnetic uncertainties, the magnetic uncertainties having a non-zero constant second derivative corresponding to disturbances; To determine a linear system with a varying polytopic parameter from the flow-current model; To determine a state observer for the linear system with varying parameters; To estimate the state variables using the state observer; To estimate the electromagnetic torque from the estimated state variables.

[0021] The invention also relates to an electric or hybrid vehicle comprising a synchronous machine having a stator having phases and a rotor having a winding,

[0022] the vehicle comprising an estimation system as specified above. Brief description of the figures

[0023] The accompanying figures will clearly illustrate how the invention can be implemented. In these figures, identical reference numerals designate similar elements.

[0024] Fig. 1 schematically represents the estimation process.

[0025] Figure 2 schematically represents the estimation system embedded in a electric or hybrid motor vehicle.

[0026] Fig. 3 represents results of an experimental implementation of the estimation method.

[0027] Fig. 4 represents results from another experimental implementation of the estimation method. Detailed description

[0028] The estimation method 1 shown in [Fig. 1] can be used for different types of electrical machines in different applications. For example, the estimation method 1 can be used to estimate the electromagnetic torque of a MSRB.

[0029] This estimation method 1 can be used to estimate the electromagnetic torque of a MSRB of an electric or hybrid motor vehicle ([Fig. 2]). It can also be used: - for industrial robotics for tasks such as assembly or handling of materials, - for wind turbines, to monitor and control the turbine torque for optimal energy capture and good reliability, - for motor drives and control systems to provide real-time torque estimation in pumps, fans, and compressors, to simplify motor design and reduce costs, - for renewable energy systems to optimize the torque of hydroelectric generators, and for solar tracking systems to improve their efficiency, - for electric powertrains to improve the operation and efficiency of motor vehicles, trains and boats by improving the accuracy of torque estimation, - for aerospace and aviation in order to estimate the torque of control surfaces and propulsion systems and by improving reliability and reducing mass.

[0030] In order to estimate the electromagnetic torque, the estimation method 1 is based on a modified current model configured to capture the dynamic fluctuations of magnetic variables in the electric machine.

[0031] A synchronous machine (M) comprises a stator including phases and a rotor including a winding.

[0032] The estimation method 1 includes a measurement step El, implemented by a set of sensors, to measure stator voltages and a voltage across the rotor winding and to measure, for example in a rotating frame of the rotor, stator currents and a current through the rotor winding.

[0033] For example, sensors can measure the stator phase voltages and stator phase currents. These phase voltages and stator phase currents can be transformed by a Park transformation to express said voltages and stator currents in a Park frame. A Park frame corresponds to a rotating frame attached to the rotor.

[0034] The quantities in the Park frame are written using the index d along the direct Park axis and the index q along the quadrature Park axis.

[0035] The voltage, current and flux of the rotor are written using the subscript f.

[0036] The dynamics of the magnetic flux as a function of currents and voltages is expressed according to the following system of equations:

[0037] [Math.l] ^d ~ Vd " ^d + ù ' - Vq “ R^q ” t-'I^-d Tot^rRfif

[0038] in which: vd, V(i are the stator voltages calculated in the rotating Park frame, vf is the measured rotor voltage, Jj, iq are the measured stator currents in the rotating Park frame, if is the measured rotor current, Rs is the stator resistance, Rf is the rotor resistance, a'e is the (electrical) angular velocity of the rotor, ki is the stator flux in the Park frame, if is the rotor flux.

[0039] The estimation method 1 further comprises a first determination step E2, implemented by a computer 3, to determine a flux-current model of the machine at least as a function of the measured voltages, the measured currents, the stator inductances, a rotor inductance, a mutual inductance between the stator and the rotor, a rotor angular velocity, and state variables having dynamic magnetic uncertainties. Each of the dynamic magnetic uncertainties has a non-zero constant second derivative corresponding to perturbations.

[0040] This takes into account the uncertainties of the flux-current model which are caused, among other things, by a non-linear magnetic saturation.

[0041] The flux-current model can thus be expressed by the following system of equations:

[0042] [Math.2] ^d ~ Ldh + Mfif + ^d^d + fif iq — Lqîq + ÀLqiq if — M fij + Lfi f + fij + AL fif

[0043] in which: il, ki are the stator fluxes in the Park frame, if is the rotor flux in the Park frame, Lj, Lq are the stator inductances in the Park frame, Lf is the rotor inductance, Mf is the mutual inductance between the stator and the rotor. ALj, are the uncertainties of the stator inductance in the Park frame. ALf is the uncertainty of the rotor inductance, AMf is the uncertainty of the mutual inductance between the stator and the rotor Sd, ëq are the magnetic uncertainties representing deviations between the actual and estimated flux of the stator in the Park frame, Sf is the magnetic uncertainty representing the deviation between the actual flux and the estimated flux of the rotor.

[0044] The magnetic uncertainties £d, Sq and Sj are thus expressed as a function of the uncertainties of the inductances of the stator and rotor ALd, and ALf as well as the uncertainties of the mutual inductance A Mf.

[0045] The flow-current model can be rewritten in matrix form as follows:

[0046] [Math.3] 'h îq

[0047] in which T- 'q

[0048] Substituting the system of equations [Math 1] into relation [Math 3], we obtain:

[0049] [Math.4] ld h -1 eq = T1 Vq- R^q - ( Ldid + Mfif+gd )

[0050] As stated previously, it is assumed that the second derivatives of the magnetic uncertainties 8d, Sq, and Sf are non-zero and bounded perturbations dd, dq, and dj. This assumption allows us to take into account both rapidly varying and slowly varying uncertainties.

[0051] Thus:

[0052] [Math.5] W [^1

[0053] The estimation method 1 further includes a second determination step E3, implemented by the computer 3, to determine a linear system with a polytopic varying parameter from the flow-current model.

[0054] By combining equations [Math 4] and [Math 5] and considering that the currents id, iq and if are measurable, it is possible to form the mathematical model for an MSRB as a polytopic linear variable parameter system (or LPV system for "linear parameter varying" in English) with the electric angular velocity of the rotor as the variable parameter.

[0055] Said mathematical model has the following form:

[0056] [Math.6] x = A ( ) x + Bu + Ed y = Cx

[0057] in which: A(tue) corresponds to a state matrix that is a function of at least the angular speed of the rotor, the stator inductances Ld, Lq, the rotor inductance Lf, and the mutual inductance My between the stator and the rotor. X = gxgli>grcd,cq, Q) e P9 corresponds to a state vector, Zj, iq, if correspond to the measured currents, Sg$ gf correspond to the dynamic magnetic uncertainties, cd' CQ> cf correspond to the second derivatives of the dynamic uncertainties, U — Ç Vq. Vf) E P3 corresponds to a vector of commands and measurements, vd> vf correspond to the calculated and measured voltages, d = dd, dq, df )E: P3 corresponds to a vector of disturbances, dd, dq, df correspond to the disturbances, ye P3 corresponds to a vector of measurable outputs, B corresponds to a control matrix that is a function of at least the rotor inductances, the stator inductance, and the mutual inductance between the stator and the rotor,

[0058] C corresponds to a predetermined constant observation matrix, E corresponds to a predetermined constant perturbation matrix.

[0059] Matrices A, B, C and E can be expressed as follows: Lg Lô - / ? pW y 0 -Lf'^ Lg 0 Lg 0 -Mf1 -Rs Lg 0 0 0 -1 Lit 0 -RsMf ~ï~ MfLqÜ>e Le Rf^ ^8 0 Mf^'e La 0 h, 0 Lg 21 ( ü)e ) — 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[0060] n 0 to 0 ror ^8 B = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 I

[0061] [1 0 0 0 0 0 0 0 0' C = 0 1 0 0 0 0 0 0 0 .0 0 1 0 0 0 0 0 0.

[0062] ro o o1 0 0 0 0 0 0 0 0 0 E = 0 0 0 0 0 0 100 0 1 0 .0 0 11

[0063] We assume that Mf-LdLf

[0064] It is assumed that the electrical angular velocity (°e) of the rotor is bounded, that is to say that the electrical angular velocity is within the interval [ (.¾ ] in which tee = min ( Me ) and = max ( we ).

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] We can see that the matrix A( can be formulated as a convex combination of constant matrices A! and A2. The convex combination of the state matrix can have the following form: A( œe ) = a ( ) Aj + ( la ( we ) ) A2, in which: ™ \ _ fdfy., with 0 < « ( ) < 1, A] = A(û)c and A2 = A ( we ). The estimation process 1 further includes a third determination step E4, implemented by the computer 3, to determine a state observer configured for or enabling the estimation of the state variables of the linear system with varying parameters. The state observer can take the following form: [Math.7] x — A ( tt) e ) x + Bu + K ( ü) e ) (y-ci) y-Cx in which: x corresponds to an estimated state vector * = ( C g} Cf ) ' if correspond to the estimated currents, Sf corresponds to the estimated dynamic magnetic uncertainties, cd, Cq, Cf correspond to the second derivatives of the estimated dynamic uncertainties, ç corresponds to the estimated predetermined constant observation matrix, K(œe) corresponds to a gain parameter that is a function of the rotor's angular speed. The matrix £ has the following form: c= 0 0 0 1 0 0 0 0 .0 0 0 0 1 0 0 0 0'. 0. The gain parameter as a function of the angular speed of the rotor can have the following form: K(we) = a( )K + (la(œe))K2, in which Kx corresponds to a first observer gain and K2 corresponds to a second observer gain. The error e is defined as being equal to the difference between actual states x and estimated states x; g — xx- The dynamics of the error can therefore be expressed according to the following system of equations:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] è- {A(të e )-K{w e )C)e + Ed . y = Cx The state observer [Math 7] is called a robust linear variable-parameter observer Hx for the mathematical model [Math 6] with a positive performance parameter, if the error dynamics are asymptotically stable when d = 0 and when: sup suppf <y in which ||.|| denotes the L2 norm or Euclidean norm. The following theorem gives the sufficient conditions for the existence of robust linear variable parameter observers Hx for the mathematical model [Math 6]. The theorem states that there exist robust variable-parameter linear observers Hx for the mathematical model [Math 6] if there exists a positive-definite matrix P~PT> (), a first matrix relating to the first observer gain, a second matrix AL relating to the second observer gain K2, and a positive performance parameter y such that the following linear matrix inequalities be respected: AfP + PAï-XiC-CfxT P PE PQ 1 0 EtP 0 -yl C 0 0 in which: Q - qt > o corresponds to a predetermined weighting matrix, K[ = P^Xy I corresponds to the identity matrix. To obtain K and K2, we minimize the performance parameter V, which optimizes the state observer robustness performance. The third determination step E4 can therefore include a minimization substep E41, implemented by the computer 3, to minimize the positive performance parameter y using the linear matrix inequalities expressed above to determine the positive definite matrix P, the first matrix Xj relating to the first observer gain and the second matrix X2 relating to the second observer gain K2.

[0082] For example, the minimization substep E41 can be implemented by the computer 3 using numerical analysis software such as "Matlab" including the LMI toolbox.

[0083] The third determination step E4 may also include a first determination substep E42, implemented by the computer 3, to determine the first observer gain Ki from the first matrix Xi and the positive definite matrix P and a second determination substep E43, implemented by the computer 3, to determine the second observer gain K2 from the second matrix X2 and the positive definite matrix P.

[0084] The first observer gain Ki and the second observer gain K2 can be determined using the equations = PrlXl and K2 =

[0085] The estimation method 1 also includes a first estimation step E5, implemented by the computer 3, to estimate the state variables by the state observer.

[0086] The dynamic magnetic uncertainties g" g\ of the estimated state variables U *1 j in the first estimation step E5 can be estimated from the state observer, the first observer gain and the second observer gain K2.

[0087] The estimation method 1 further includes a second estimation step E6, implemented by the computer 3, to estimate the electromagnetic torque from the estimated state variables.

[0088] In particular, the second estimation step E6 may include an estimation substep E61, implemented by the computer 3, to estimate the stator fluxes 2, in the Park frame from the estimated dynamic magnetic uncertainties, the stator inductances Ld, Lq (in the Park frame), the mutual inductance Mf and the measured currents id, iq, if.

[0089] The stator fluxes estimated in the Park frame can be determined at starting from the following equations: K “ LJd + + Sd "y __ F ' A Ad~ L^ + Sq

[0090] The second estimation step E6 may further include a sub- Calculation step E62, implemented by computer 3, to calculate the estimated electromagnetic torque from the estimated stator fluxes in estimation substep E61, the measured stator currents id, 4 in the Park frame and a number of pole pairs p of the machine.

[0091] The estimated electromagnetic torque y can be determined from the following equation: A / 3 \ / / 'AA < \

[0092] The second estimation step E6 can be followed by a transmission step E7 to transmit a signal representative of the estimated electromagnetic torque j to a user device 4.

[0093] The user device may be an embedded computer configured to monitor engine performance in real time in order to detect abnormal operation and react quickly to this abnormal operation.

[0094] The invention also relates to an estimation system S of an electromagnetic torque of a synchronous machine M comprising a stator having phases and a rotor having a winding ([Fig.2]).

[0095] The estimation system S comprises: - the set of sensors 2 configured to measure the voltage across the rotor winding and to measure in the rotating frame of the rotor the currents of the stator phases and the current through the rotor winding; - Calculator 3 configured for: • determine the flux-current model of the machine at least as a function of the measured voltages, the measured currents, the stator inductances, the rotor inductance, a mutual inductance between the stator and the rotor, the angular speed of the rotor and the state variables including magnetic uncertainties, the magnetic uncertainties having a non-zero constant second derivative corresponding to disturbances; • determine the linear system with varying polytopic parameters from the flow-current model; • determine the state observer for the linear system with varying parameters; • estimate the state variables by the state observer; • estimate the electromagnetic torque from the estimated state variables.

[0096] To determine the state observer for the linear variable parameter system, the computer 3 can be configured to: - minimize the positive performance parameter F using linear matrix inequalities in order to determine the positive definite matrix P, the first matrix relating to the first observer gain and the second matrix AL relating to the second observer gain K2; - determine the first observer gain from the first matrix X] and the positive definite matrix P; - determine the second observer gain K2 from the second matrix X2 and the positive definite matrix P.

[0097] To estimate the electromagnetic torque from the estimated state variables, the calculator 3 can be configured to: - estimate the stator fluxes from the estimated dynamic magnetic uncertainties, stator inductances, mutual inductance and measured currents; - calculate the estimated electromagnetic torque from the estimated rotor fluxes, measured currents and a number of pole pairs of the machine.

[0098] The calculator 3 can also be configured to transmit a signal representative of the estimated electromagnetic torque to the user device 4.

[0099] Estimation method 1 and estimation system S implement a polytopic LPV linear variable parameter system for a MSRB, unlike the usual practice. Indeed, for an MSRB, a linear time-varying system (LTV) is typically used. However, the use of an LPV system simplifies the determination of a robust state observer (LPV observer) with pre-calculated and programmable gains, which considerably reduces computation time compared to the computation time resulting from a state observer (LTV observer) determined from an LTV system.

[0100] Furthermore, the existence of an LPV observer can be verified offline, whereas, in the case of an LTV observer, the existence of solutions for the time-varying Riccati equation can be difficult to prove. This can lead to a reduction in the reliability of LTV observers over long operating times.

[0101] Finally, the simple structure and direct gain control of the LPV observer facilitate its implementation in machine systems, offering a new approach to sensorless torque estimation.

[0102] To evaluate the effectiveness of the LPV observer, a mathematical model of a magnetic resonance sensor (MRS) incorporating real measured magnetic parameters and resistances is tested in a Matlab / Simulink environment. Figure 3 shows two graphs: a lower graph and an upper graph. The upper graph shows three curves representing the evolution of a torque T as a function of time t. A first curve, C1, shown as a solid line, represents the evolution of the actual torque over time. A second curve, C2, shown as a dashed line, represents the evolution of the torque estimated using the LPV observer. A third curve, C3, shown as a dashed line, represents the evolution of the torque estimated using the LPV observer. This evaluation is performed with static and dynamic time-dependent variations of the mutual inductance AMf, as represented in the lower graph of [Fig. 3] by the CM curve. Notably, during the dynamic changes introduced between 3 s and 6 s, the robust LPV observer accurately estimates the electromagnetic torque, while the LTV method struggles to compensate for the torque estimation errors at 0.2 s. This discrepancy can be attributed to the difficulties in solving the time-varying Riccati equation, highlighting the reliability of the LPV approach. Between 2 s and 3 s, the LPV observer consistently outperforms the LTV observer. Furthermore, the method with the LPV observer exhibits less overshoot than the method with the LTV observer during sudden changes, such as the step function at 6 s, in the mutual inductance. It is also worth noting that the Cl and C3 curves coincide in [Fig. 3].

[0103] As with [Fig. 3], [Fig. 4] shows two graphs: a lower graph and an upper graph. The upper graph shows three curves representing the evolution of a torque T as a function of time t. A first curve C4, shown as a solid line, represents the evolution of the actual torque over time. A second curve C5, shown as a dashed line, represents the evolution of the estimated torque using the LTV observer. A third curve C6, shown as a dashed line, represents the evolution of the estimated torque using the LPV observer. This evaluation is performed with static and dynamic variations over time of the inductance A Ld of the direct axis d of the stator, as represented in the lower graph of [Fig. 4] by the curve CL. This test aims to elucidate the impact of higher-order derivatives of the inductance variations. To simulate this effect, a sinusoidal function is used to vary the inductance of the direct axis d.During the initial simulation phase from 0 s to 4 s, the LTV observer exhibits pronounced oscillations. This behavior stems from the LTV observer's design assumption, which neglects the presence of high-order derivatives of the dynamic magnetic uncertainties. However, the nontrivial high-order time derivatives of the sinusoidal function contradict this assumption. Conversely, the LPV observer demonstrates robustness to such high-order derivatives, providing a relatively accurate torque estimate during this interval (the C6 curve is virtually identical to the C4 curve above 1 s). Furthermore, due to its simple structure and low computational cost for gain calculation, the method using the LPV observer offers faster tracking performance.

Claims

1.

2. Demands Method for estimating the electromagnetic torque fe of a synchronous machine (M) comprising a stator having phases and a rotor having a winding, characterized in that it comprises the following steps: - a measurement step (El), implemented by a set of sensors (2), to measure a voltage across the rotor winding and to measure in a rotating frame of the rotor currents of the stator and a current through the rotor winding; - a first determination step (E2), implemented by a computer (3), to determine a flux-current model of the machine at least as a function of the measured voltages, the measured currents, the stator inductances, the rotor inductance, the mutual inductance between the stator and the rotor, the angular velocity of the rotor and state variables including dynamic magnetic uncertainties, the dynamic magnetic uncertainties having a non-zero constant second derivative corresponding to disturbances; - a second determination step (E3), implemented by the computer (3), to determine a linear system with polytopic varying parameters from the flow-current model; - a third determination step (E4), implemented by the computer (3), to determine a state observer allowing estimation of the state variables of the linear system with varying parameters; - a first estimation step (E5), implemented by the computer (3), to estimate the state variables by the state observer; - a second estimation step (E6), implemented by the computer (3), to estimate the electromagnetic torque from the estimated state variables. A method according to claim 1, characterized in that the polytopic linear variable parameter system has the following form: ( x-AÇw^x + Bu + Ed ( j = Cx in which, x is a state vector X = (id, iq, if, g^ g^ gCd, Cq, Cf^, id, iq, if correspond to the measured currents, Sq > Sf correspond to the dynamic magnetic uncertainties, c & Cq, Cf correspond to the second derivatives of the dynamic uncertainties, “ is a control and measurement vector U = ( Vd. Vq, Vf), Vd, V#, Vf correspond to the calculated and measured voltages, d is a disturbance vector d — ( dd, dq, df), dd, dq, df correspond to the disturbances, A( œe) corresponds to a state matrix that is a function at least of the angular speed of the rotor, the inductances of the stator, the inductance of the rotor, the mutual inductance between the stator and the rotor, the state matrix being in the form of a convex combination of constant matrices, B corresponds to a control matrix based at least on the inductances of the stator, the inductance of the rotor, and the mutual inductance between the stator and the rotor; C corresponds to a predetermined constant observation matrix; E corresponds to a predetermined constant disturbance matrix.

3. A method according to claim 2, characterized in that the convex combination of the state matrix has the following form: A( œe) = a(we)A{ + ( ia( œe) )A2, where: the angular velocity We is bounded between we = Hlin( and we — max ( ), a ((Ce) = —' Aj = A(we) and A2 = A(Me).

4. A method according to any one of claims 1 to 3, characterized in that the state observer, determined in the third determination step (E4), has the following form: x = A(a) € )x + Bu + K(a) e ) (y-Cx) y = Cx in which: r corresponds to an estimated state vector * = (Ç, Ç, gp C* C^Cf)' y correspond to the estimated currents, g". g''.. correspond to the dynamic magnetic uncertainties estimated, Q, c^, Cf correspond to the second derivatives of the estimated dynamic uncertainties, £ corresponds to the estimated predetermined constant observation matrix, K(cûe) corresponds to a gain parameter that is a function of the angular speed of the rotor.

5. Method according to claim 4, characterized in that the gain parameter, a function of the angular speed of the rotor, has the following form: K(toe) ( l-aCœJ )X2, in which corresponds to a first observer gain and K2 corresponds to a second observer gain.

6. A method according to any one of claims 1 to 5, characterized in that the third determination step (E4) comprises: - a minimization substep (E41), implemented by the computer (3), to minimize a positive performance parameter (P) using linear matrix inequalities to determine a positive definite matrix (P), a first matrix (X9) relating to the first observer gain (Xj) and a second matrix (X2) relating to the second observer gain (X2); - a first sub-step of determination (E42), implemented by the computer (3), to determine the first observer gain (K^) from the first matrix (Xj) and the positive definite matrix (P); - a second determination sub-step (E43), implemented by the computer, to determine the second gain

7.

8.

9. observer (Æ2) from the second matrix (¾) and the positive definite matrix (P). Method according to any one of claims 1 to 6, characterized in that the dynamic magnetic uncertainties of the state variables estimated in the first estimation step (E5) are estimated from the state observer, the first observer gain (K^ and the second observer gain (^2). A method according to any one of claims 1 to 7, characterized in that the second estimation step (E6) comprises: - an estimation substep (E61), implemented by the calculator (3), to estimate the stator fluxes from the estimated dynamic magnetic uncertainties, the stator inductances, the mutual inductance and the measured currents; - a calculation substep (E62), implemented by the computer (3), to calculate the estimated electromagnetic torque from the rotor fluxes estimated in the estimation substep (E61), the measured currents and a number of pole pairs of the machine. System for estimating the electromagnetic torque of a synchronous machine (M) comprising a stator having phases and a rotor having a winding, characterized in that it comprises: - a set of sensors (2) configured to measure a voltage across the rotor winding and to measure in the rotating frame of the rotor currents of the stator phases and a current through the rotor winding; - a calculator (3) configured for: • determine a flux-current model of the machine at least as a function of the measured voltages, measured currents, stator inductances, rotor inductance, mutual inductance between the stator and rotor, rotor angular velocity and state variables with magnetic uncertainties, the magnetic uncertainties exhibiting a derivative second non-zero constant corresponding to perturbations; • determine a polytopic linear variable parameter system from the flux-current model; • determine a state observer for the linear variable parameter system; • estimate the state variables by the state observer; • estimate the electromagnetic torque from the estimated state variables.

10. Electric or hybrid vehicle comprising a synchronous machine (M) comprising a stator comprising phases and a rotor comprising a winding, characterized in that it comprises an estimation system as specified in claim 8.

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