A Fault Tolerant Control Method for a Dual-Winding Steer-by-Wire System Based on a Prediction Model

Abstract

The present invention discloses a fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model, including: designing a single-phase open fault diagnosis method to perform fault diagnosis on a dual-winding motor to obtain a fault diagnosis result; judging the health state of the dual-winding motor according to the fault diagnosis result, establishing a prediction model of the dual-winding motor in a healthy state, and reconstructing the prediction model of the dual-winding motor in a single-phase open fault state; applying the control input voltage in the nominal state and the auxiliary control input together to act on the dual-winding motor to achieve stability control of the dual-winding motor in the healthy state and the single-phase open fault state. The control method of the present invention can ensure that the dual-winding steering motor has fault tolerance when local failure faults occur, enabling the steer-by-wire system to effectively isolate and actively reconstruct the fault point according to the stability conditions, and improving the accuracy, stability and high safety of the control in the case of local failure of the steering motor.

Description

Technical Field

[0001] The present invention belongs to the technical field of automotive steering systems, and specifically refers to a fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model. Background Art

[0002] The steer-by-wire system cancels the mechanical connection components between the steering wheel and the steering wheels, completely getting rid of the limitations of mechanical firmware, and realizing steering entirely by electric energy. It not only has all the advantages of traditional mechanical steering systems, but also can optimize the angular transmission characteristics that are difficult to achieve by mechanical systems.

[0003] In the existing steer-by-wire system, the actuator motor part uses a dual-winding motor, which is composed of two sets of three-phase windings. The two windings are electrically independent of each other and do not affect each other during normal operation. When a fault occurs, it can improve the stability and good fault-tolerant performance of the system.

[0004] However, when a phase loss fault occurs in the dual-winding motor, it is necessary to diagnose and perform fault-tolerant control on the faulty phase. There are few existing research methods for active fault-tolerant control of dual-winding motors. Chinese Patent Application No. CN202111646267.4 discloses a dual-motor steer-by-wire system and its convolutional neural network fault-tolerant control method, which uses the convolutional neural network method for real-time fault detection of the dual-motor steer-by-wire system, but it does not consider the change of the dual-winding motor model under the phase loss fault state. Chinese Patent Application No. CN202211481201.9 discloses a dual-motor steer-by-wire system and its active fault-tolerant control method, which calculates the fault coefficient by comparing the control torque output by the dual-motor torque sensor and the front wheel angle tracking controller, and optimizes the steering actuator model into a variable parameter nonlinear structure containing motor fault parameters, but it does not consider the influence law of time-varying parameters on the tracking control after the fault occurs. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned existing technologies, the purpose of the present invention is to provide a fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model to solve the problems of inaccurate fault motor models and low accuracy of fault-tolerant control strategies in the existing dual-winding steer-by-wire system technologies. The control method of the present invention can ensure that the dual-winding steering motor has fault-tolerant capabilities when local failure faults occur, enabling the steer-by-wire system to effectively isolate and actively reconstruct the fault points according to stability conditions, and improving the accuracy, stability, and high safety of control in the case of local failure of the steering motor.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0007] A fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model of the present invention comprises the following steps:

[0008] Step 1): Design a single-phase fault diagnosis method to diagnose the faults of the dual-winding motor and obtain the fault diagnosis result;

[0009] Step 2): Judge the health state of the dual-winding motor according to the fault diagnosis result in Step 1). If the dual-winding motor is in a healthy state, establish a prediction model of the dual-winding motor under the healthy state. If the dual-winding motor is in a single-phase fault state, reconstruct the prediction model of the dual-winding motor under the single-phase fault state;

[0010] Step 3): According to the prediction model of the dual-winding motor in Step 2), solve the objective function to obtain the control input voltage of the nominal state; use the actual state of the dual-winding motor and the updated Tube invariant set to update the objective function and solve to obtain the control input voltage of the nominal state at the k + i moment, and generate the auxiliary control input at the k + i moment; superimpose the control input voltage of the nominal state at the k + i moment and the auxiliary control input at the k + i moment and jointly act on the dual-winding motor to realize the stability control of the dual-winding motor under the healthy state and the single-phase fault state.

[0011] Further, the specific content of Step 1) includes:

[0012] Step 11): Design the single-phase fault d-q axis current determination condition: If the d-q axis current i d = 0, i q = I m , then the dual-winding motor is in a healthy state; if the d-q axis current i′ d ≠ 0, i q ′≠ I m , then the dual-winding motor is in a single-phase fault state, i d , i q are the direct-axis current and quadrature-axis current in the synchronous rotating coordinate system under the healthy state respectively, i′ d , i q ′ are the direct-axis current and quadrature-axis current in the synchronous rotating coordinate system under the single-phase fault state respectively, and I m is the amplitude of the stator current;

[0013] Step 12): Design the single-phase fault cost function determination condition: If the cost function does not generate a DC component and a second harmonic component, then the dual-winding motor is in a healthy state; if the cost function generates a DC component and a second harmonic component, then the dual-winding motor is in a single-phase fault state, and extract the fault index as the amplitude of the DC component and the second harmonic component generated by the cost function;

[0014] Step 13): Design the fault phase location judgment condition: Detect the initial phase angle deviation. If the initial phase angle deviations of all windings are equal to 120°, the dual-winding motor is in a healthy state; if the initial phase angle deviations of all windings show a large change, the dual-winding motor is in a single-phase fault state, and extract the initial phase angle deviation index as the initial phase angle deviation.

[0015] Step 14): Design the fault diagnosis algorithm: If the detected fault detection flag is 0, the dual-winding motor is in a healthy state, and the six-phase fault location flag is 0; if the detected fault detection flag is 1, the dual-winding motor is in a single-phase fault state, perform fault location. If the detected fault location flag of a certain phase is 1 and the fault location flags of the other five phases are 0, then this phase is the fault phase.

[0016] Further, when the dual-winding motor is in a healthy state in step 11), the d-q axis currents i d and i q have the following expressions:

[0017]

[0018] In the formula, i a , i b , i c , i u , i v , i w are the six-phase stator currents of the dual-winding motor; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor.

[0019] Further, when a certain phase fails in step 11) and the dual-winding motor is in a single-phase fault state, the d-q axis currents i' d and i q ' have the following expressions:

[0020]

[0021] In the formula, ζ is the amplitude coefficient; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor; θ cf is the angle offset.

[0022] Further, the discretized expressions of the d-q axis currents i' d and i' q of the faulty winding in step 12) are as follows:

[0023]

[0024] In the formula, i' d(k + 2) and i' q (k + 2) is the d-q axis current detected at the (k + 2)-th moment under the fault state; i d (k + 2) and i q (k + 2) is the d-q axis current detected at the (k + 2)-th moment under the healthy state; θ e is the electrical angle of the rotor; θ cf is the angle offset.

[0025] Furthermore, the expression of the cost function J in step 12) is as follows:

[0026]

[0027] In the formula, Q and R are the weight coefficient matrices of the output quantity and the control increment respectively; ζ is the amplitude coefficient; θ e is the electrical angle of the rotor; θ cf is the angle offset; I m is the amplitude of the stator current; Δu is the difference between the voltage inputs at the k-th sampling moment and the (k - 1)-th sampling moment.

[0028] Furthermore, the deviation d of the initial phase angle of the winding in step 13) mn is expressed as follows:

[0029]

[0030] In the formula, θ j is the initial phase angle of the fundamental component of the stator current, j = a, b, c; under the healthy state, d mn is equal to 120°; it is assumed that a fault occurs in phase c, then d ab is equal to 180°, d ac and d bc are variables.

[0031] Furthermore, the fault diagnosis algorithm in step 14) is expressed as follows:

[0032]

[0033] In the formula, when the Boolean variable is zero, the value of the counter counter1 is reset to zero. If the value of the counter counter1 is greater than the constant COUNT1, Flag is set from low to high; Flag and Flag mn are the fault detection flag and the fault location flag respectively; counter1 is the count value from the detection start of the Boolean variable ε = 1 to reaching the constant COUNT1; counter2 is the count value from the detection start of the Boolean variable ε mn = 1 to reaching the constant COUNT2.

[0034] Further, in the step 14), the Boolean variables ε and ε mn and the count value expressions are as follows:

[0035]

[0036] In the formula, I dc and I2 are the amplitudes of the DC component and the second harmonic component respectively; and are the set thresholds; ε and ε mn are the Boolean type variables of the generated fault indication and the phase deviation angle indication respectively;

[0037]

[0038] In the formula, T s is the sampling period; T is the stator current period; m is the sensitivity factor, COUNT1 = m1 * T / T s , COUNT2 = m2 * T / T s .

[0039] Further, in the step 2), establishing a prediction model for the dual-winding motor in the healthy state specifically includes:

[0040] Step 211): Establishing the electrical equation in the rotating coordinate system in the healthy state, and the expression is as follows:

[0041]

[0042] In the formula, u d , u q are the stator voltages in the d-q plane; u x , u y are the stator voltages in the x-y plane; i d , i q are the stator currents in the d-q plane; i x , i y are the stator currents in the x-y plane; L d , L q are the inductances in the d-q coordinate system; L ls is the stator leakage inductance; ψ f is the magnetic flux amplitude; R s is the stator resistance; ω e is the electrical angular velocity; ψ d , ψ q are the magnetic flux values in the d-q plane; ψ x , ψ y are the magnetic flux values in the x-y plane;

[0043] Step 212): Establishing a prediction model for the dual-winding motor in the healthy state, and the expression is as follows:

[0044]

[0045] wherein, i(k) and i(k + 1) are the current value at the k sampling moment and the predicted current value at the (k + 1) sampling moment respectively; i d , i q , i x , i y are state variables and output variables of the dual-winding steer-by-wire system; y(k) is the current input at the k sampling moment; is the voltage input at the k sampling moment; ω e (k) is the electrical angular velocity at the k moment; ψ f is the magnetic flux amplitude; the expressions of the state update coefficient matrices A, B, and C are as follows:

[0046]

[0047] wherein, L d , L q are the inductances in the d-q coordinate system; T s is the sampling period; L z is the inductance in the x-y coordinate system; R s is the stator resistance.

[0048] Furthermore, reconstructing the prediction model of the dual-winding motor in the open-phase fault state in step 2) specifically includes:

[0049] Step 221): Reconstructing the voltage equation and magnetic flux equation in the natural coordinate system in the open-phase fault state;

[0050] After one phase of the dual-winding motor is open-circuited, reconstruct the voltage equation and magnetic flux equation of the other phases in the natural coordinate system. The expressions are as follows:

[0051]

[0052] ψ s = L s ·i s + ψ f ·F(θ e )

[0053]

[0054]

[0055] wherein, u s = [u A u B u C u U u V T is the stator voltage matrix; i​s = [i A i B i C i U i V T is the stator current matrix; R n = RI5 is the winding resistance matrix; F(θ e ) is the flux linkage coefficient matrix; ψ s = [ψ A ψ B ψ C ψ U ψ V T is the flux linkage matrix of each phase; ψ f is the flux linkage amplitude; I5 is the five-dimensional identity matrix; L1 is the leakage inductance of the stator winding; L m is the main self-inductance; L s is the stator inductance matrix; θ e is the electrical angle of the rotor;

[0056] Step 222): Reconstruct the prediction model of the dual-winding motor under the open-phase fault state;

[0057] Reconstruct the electrical equations in the synchronous rotating coordinate system and the harmonic subspace, and the expression is as follows:

[0058]

[0059] In the formula, u d , u q represent the d-q axis voltages; i d , i q represent the d-q axis currents; u z1 , u z2 , u z3 represent the harmonic subspace voltages; i z1 , i z2 , i z3 represent the currents in the z1, z2, z3 subspaces; L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; V1(θ e ) and W1(θ e ) are the coefficient matrices when one phase is open-circuited, and the expressions are as follows:

[0060]

[0061] In the formula, θ e is the electrical angle of the rotor;

[0062] Reconstruct the prediction model of the dual-winding motor under the open-phase fault state, and the expression is as follows: ​​

[0063]

[0064]

[0065] Wherein, u' d is the d-axis voltage under the open-phase fault state, and u' q is the q-axis voltage under the open-phase fault state. L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; ψ f is the magnetic flux amplitude; ω e is the electrical angular velocity, is the inverse matrix of the coefficient matrix during single-phase open circuit; υ(θ e ) represents the rotor flux offset vector generated due to current imbalance in the d-q axis coordinate system.

[0066] Furthermore, the specific steps of step 3) include:

[0067] Step 31): Solve the model predictive control objective function to obtain the control input voltage of the nominal state

[0068] Define the model predictive control objective function J as the sum of the absolute value of the current error and the control increment, and the expression is as follows:

[0069]

[0070] Wherein, y p (k+i|k) is the predicted value of the control output, N c is the control step, i = 0, 1,..., N c -1; G and R are the weight coefficient matrices of the output quantity and the control increment respectively; y ref (k+i|k) is the reference value of the control output; N p is the prediction step;

[0071] Set the constraint conditions as:

[0072] u min ≤u(k+i)≤u max , i = 0, 1,..., N c -1

[0073] Wherein, u min is the minimum value of the output voltage, and u max is the maximum value of the output voltage;

[0074] According to the above model predictive control objective function and constraint conditions, transform the model predictive control into an optimization problem that minimizes the model predictive control objective function under the premise of meeting the constraint conditions, and the expression is as follows:

[0075]

[0076] The linear matrix inequality method is used to solve the model predictive control objective function, and the voltage control signal at time k is obtained. The expression is as follows:

[0077]

[0078] In the formula, u d (k) and u q (k) are the stator voltages in the d-q plane at time k; u x (k) and u y (k) are the stator voltages in the x-y plane at time k; the control input voltage of the nominal state at time k is obtained

[0079] Step 32): Obtain the rotor electrical angle θ e (k) of the open-phase fault dual-winding motor at time k, and update the Tube invariant set;

[0080] Design the compensation control gain K so that the trajectory of the actual dual-winding motor system is within the Tube sequence. This Tube sequence X is centered on the optimal trajectory of the nominal model without disturbance terms, so as to ensure that the dual-winding motor can asymptotically and stably converge within the Tube invariant set Z. The expression of the Tube sequence X is as follows:

[0081] X := {X1, X2, ···, X N}

[0082] In the formula, is the nominal model state;

[0083] From time k, the expression of the Tube invariant set Z at the i-th step is as follows:

[0084]

[0085] Among them, Z(i|k) is the Tube invariant set containing the origin; N c is the control step size; w(i - 1|k) is the disturbance suffered by the system at time k + i - 1; Z(i - 1|k) is the Tube invariant set of the system at time k + i - 1; A K is the parameter matrix of the system at time k + i - 1, and the expression is as follows:

[0086] A K = A 0 + QK

[0087] In the formula, A 0is the nominal state matrix without considering the change of electrical rotation angle, and Q is the control matrix, and the expressions are as follows:

[0088]

[0089] In the formula, θ e (k) is the rotor electrical angle at time k; L d 、L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; T s is the sampling period; R s is the stator resistance;

[0090] Step 33): Update the objective function and constraints using the Tube invariant set Z at the i-th step starting from time k obtained in Step 32), and solve the model predictive control objective function using the linear matrix inequality method to obtain the control input voltage at time k+i;

[0091] The updated objective function and constraints are as follows:

[0092]

[0093] Among them, x ref (i|k) is the reference current, G and R are the weight coefficient matrices of the reference current and the nominal state respectively, P is the weight coefficient matrix of the control input voltage, X m is the terminal constraint and X m ∈X;

[0094] Step 34): Obtain the actual state x(i|k) of the system, calculate the error between the actual state of the system and the center trajectory of the Tube invariant set Generate the auxiliary control input Superimpose it with the control input voltage of the nominal state at time k+i obtained in Step 31), and jointly act on the dual-winding motor to achieve the stability control of the dual-winding motor in the healthy state and the open-phase fault state;

[0095] The expression of the input u(i|k) actually acting on the dual-winding steer-by-wire system is as follows:

[0096]

[0097] Advantages of the present invention:

[0098] The present invention can ensure the fault tolerance ability when the steering motor has local failure faults, so that the steer-by-wire system can effectively isolate and actively reconstruct the fault point according to the stability conditions. At the same time, the accuracy, stability and safety control performance are better in the case of local failure of the steering motor. Description of the Drawings

[0099] Figure 1 is a schematic flow chart of the method of the present invention;

[0100] Figure 2 is a flow chart for diagnosing the open-phase fault of a dual-winding motor. Specific embodiments

[0101] For the convenience of those skilled in the art to understand, the present invention will be further described below in conjunction with embodiments and drawings. The content mentioned in the embodiments does not limit the present invention.

[0102] Referring to Figure 1 as shown, a fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model of the present invention comprises the following steps:

[0103] Step 1): Design an open-phase fault diagnosis method to diagnose the faults of the dual-winding motor and obtain the fault diagnosis result; specifically including:

[0104] Step 11): Design the determination conditions for the d-q axis current of the open-phase fault: If the d-q axis current i d = 0, i q = I m , then the dual-winding motor is in a healthy state; if the d-q axis current i′ d ≠ 0, i q ′≠ I m , then the dual-winding motor is in an open-phase fault state, where i d , i q are the direct-axis current and quadrature-axis current in the synchronous rotating coordinate system under the healthy state respectively, i′ d , i q ′ are the direct-axis current and quadrature-axis current in the synchronous rotating coordinate system under the open-phase fault state respectively, and I m is the amplitude of the stator current;

[0105] Step 12): Design the determination conditions for the open-phase fault cost function: If the cost function does not generate a DC component and a second harmonic component, then the dual-winding motor is in a healthy state; if the cost function generates a DC component and a second harmonic component, then the dual-winding motor is in an open-phase fault state, and the fault index is extracted as the amplitude of the DC component and the second harmonic component generated by the cost function;

[0106] Step 13): Design the determination conditions for fault phase location: Detect the initial phase angle deviation. If the initial phase angle deviation of each winding is equal to 120°, then the dual-winding motor is in a healthy state; if there is a large change in the initial phase angle deviation of each winding, then the dual-winding motor is in an open-phase fault state, and the initial phase angle deviation index is extracted as the initial phase angle deviation;

[0107] Step 14): Design a fault diagnosis algorithm: If the detected fault detection flag is 0, the dual-winding motor is in a healthy state and the six-phase fault location flag is 0; if the detected fault detection flag is 1, the dual-winding motor is in a single-phase open fault state, perform fault location. If the detected fault location flag of a certain phase is 1 and the fault location flags of the other five phases are 0, then this phase is the faulty phase.

[0108] Among them, when the dual-winding motor is in a healthy state in the said step 11), the d-q axis currents i d and i q are expressed as follows:

[0109]

[0110] In the formula, i a , i b , i c , i u , i v , i w are the six-phase stator currents of the dual-winding motor; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor.

[0111] In the said step 11), assume that a certain phase fails and the dual-winding motor is in a single-phase open fault state. The d-q axis currents i′ d and i q ′ are expressed as follows:

[0112]

[0113] In the formula, ζ is the amplitude coefficient; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor; θ cf is the angle offset.

[0114] Among them, the discretized expressions of the d-q axis currents i d ′ and i q ′ of the faulty winding in the said step 12) are as follows:

[0115]

[0116] In the formula, i′ d (k + 2) and i′ q (k + 2) are the d-q axis currents detected at the (k + 2)-th moment in the fault state; i d (k + 2) and i q (k + 2) are the d-q axis currents detected at the (k + 2)-th moment in the healthy state; θ e is the electrical angle of the rotor; θ cf is the angle offset.

[0117] In the step 12), the expression of the cost function J is as follows:

[0118]

[0119] In the formula, Q and R are the weight coefficient matrices of the output quantity and the control increment respectively; ζ is the amplitude coefficient; θ e is the electrical angle of the rotor; θ cf is the angle offset; I m is the amplitude of the stator current; Δu is the difference between the voltage inputs at the k-th sampling moment and the (k - 1)-th sampling moment.

[0120] Among them, in the step 13), the deviation d of the initial phase angle of the winding mn has the following expression:

[0121]

[0122] In the formula, θ j is the initial phase angle of the fundamental component of the stator current, j = a, b, c; in the healthy state, d mn is equal to 120°; it is assumed that a fault occurs in phase c, then d ab is equal to 180°, and d ac and d bc are variables.

[0123] Among them, in the step 14), the expression of the fault diagnosis algorithm is as follows:

[0124]

[0125] In the formula, when the Boolean variable is zero, the value of the counter counter1 is reset to zero. If the value of the counter counter1 is greater than the constant COUNT1, Flag is set from low to high; Flag and Flag mn are the fault detection flag and the fault location flag respectively; counter1 is the count value from the detection start of the Boolean variable ε = 1 to reaching the constant COUNT1; counter2 is the count value from the detection start of the Boolean variable ε mn = 1 to reaching the constant COUNT2.

[0126] In the step 14), the Boolean variables ε, ε mn and the count value have the following expressions:

[0127]

[0128] In the formula, I dc and I2 are the amplitudes of the DC component and the second harmonic component respectively; and is the set threshold; ε and ε mn are respectively Boolean type variables of the generated fault indication and phase deviation angle indication;

[0129]

[0130] In the formula, T s is the sampling period; T is the stator current period; m is the sensitivity factor, COUNT1 = m1 * T / T s , COUNT2 = m2 * T / T s .

[0131] Step 2): Determine the health state of the dual-winding motor according to the fault diagnosis result of Step 1). If the dual-winding motor is in a healthy state, establish a prediction model of the dual-winding motor under the healthy state. If the dual-winding motor is in a single-phase fault state, reconstruct the prediction model of the dual-winding motor under the single-phase fault state;

[0132] Among them, establishing the prediction model of the dual-winding motor under the healthy state in Step 2) specifically includes:

[0133] Step 211): Establish the electrical equation of the rotating coordinate system under the healthy state, and the expression is as follows:

[0134]

[0135] In the formula, u d , u q are the stator voltages in the d-q plane; u x , u y are the stator voltages in the x-y plane; i d , i q are the stator currents in the d-q plane; i x , i y are the stator currents in the x-y plane; L d , L q are the inductances in the d-q coordinate system; L ls is the stator leakage inductance; ψ f is the magnetic flux amplitude; R s is the stator resistance; ω e is the electrical angular velocity; ψ d , ψ q are the magnetic flux values in the d-q plane; ψ x , ψ y are the magnetic flux values in the x-y plane;

[0136] Step 212): Establish the prediction model of the dual-winding motor under the healthy state, and the expression is as follows:

[0137]

[0138] where \(i(k)\) and \(i(k + 1)\) are the current value at the \(k\) sampling moment and the predicted current value at the \((k + 1)\) sampling moment respectively; \(i\) d , \(i\) q , \(i\) x , \(i\) y are state variables and output variables of the dual - winding steer - by - wire system; \(y(k)\) is the current input at the \(k\) sampling moment; is the voltage input at the \(k\) sampling moment; \(\omega\) e (k) is the electrical angular velocity at the \(k\) moment; \(\psi\) f is the magnetic flux amplitude; the expressions of the state update coefficient matrices \(A\), \(B\), and \(C\) are as follows:

[0139]

[0140] where \(L\) d , \(L\) q are the inductances in the \(d - q\) coordinate system; \(T\) s is the sampling period; \(L\) z is the inductance in the \(x - y\) coordinate system; \(R\) s is the stator resistance.

[0141] In step 2), reconstructing the prediction model of the dual - winding motor under the open - phase fault state specifically includes:

[0142] Step 221): Reconstructing the voltage equation and magnetic flux equation in the natural coordinate system under the open - phase fault state;

[0143] After one phase of the dual - winding motor is open - circuited, reconstruct the voltage equation and magnetic flux equation of the other phases in the natural coordinate system, and the expressions are as follows:

[0144]

[0145] \(\psi\) s = \(L\) s ·\(i\) s +\(\psi\) f ·\(F(\theta\) e )

[0146]

[0147] where \(u\) s = [\(u\) A \(u\) B \(u\) C \(u\) U \(u\) V T is the stator voltage matrix; \(i\) s = [\(i\) A \(i\) B \(i\) C \(i\) U \(i\) V ​T is the stator current matrix; R n = RI5 is the winding resistance matrix; F(θ e ) is the flux linkage coefficient matrix; ψ s = [ψ A ψ B ψ C ψ U ψ V T is the flux linkage matrix of each phase; ψ f is the flux linkage amplitude; I5 is the five-dimensional identity matrix; L1 is the leakage inductance of the stator winding; L m is the main self-inductance; L s is the stator inductance matrix; θ e is the electrical angle of the rotor;

[0148] Step 222): Reconstruct the prediction model of the dual-winding motor under the open-phase fault state;

[0149] Reconstruct the electrical equation in the synchronous rotating coordinate system and the harmonic subspace, and the expression is as follows:

[0150]

[0151] In the formula, u d , u q represent the d-q axis voltages; i d , i q represent the d-q axis currents; u z1 , u z2 , u z3 represent the harmonic subspace voltages; i z1 , i z2 , i z3 represent the currents in the z1, z2, z3 subspaces; L d 、L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; V1(θ e ) and W1(θ e ) are the coefficient matrices when one phase is open-circuited, and the expressions are as follows:

[0152]

[0153] In the formula, θ e is the electrical angle of the rotor;

[0154] Reconstruct the prediction model of the dual-winding motor under the open-phase fault state, and the expression is as follows:

[0155]

[0156] In the formula, u′ d is the d-axis voltage under the open-phase fault state, u′​q is the q-axis voltage in the open-phase fault state, L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; ψ f is the magnetic flux amplitude; ω e is the electrical angular velocity, is the inverse matrix of the coefficient matrix during single-phase open circuit; υ(θ e ) represents the rotor flux offset vector caused by current imbalance in the d-q axis coordinate system.

[0157] Step 3): According to the dual-winding motor prediction model in Step 2), solve the objective function to obtain the control input voltage of the nominal state; use the actual state of the dual-winding motor and the updated Tube invariant set to update the objective function and solve to obtain the control input voltage of the nominal state at the k+i moment, and generate the auxiliary control input at the k+i moment; superimpose the control input voltage of the nominal state at the k+i moment and the auxiliary control input at the k+i moment and act on the dual-winding motor together to achieve the stability control of the dual-winding motor in the healthy state and open-phase fault state; specifically including:

[0158] Step 31): Solve the model predictive control objective function to obtain the control input voltage of the nominal state

[0159] Define the model predictive control objective function J as the sum of the absolute value of the current error and the control increment, and the expression is as follows:

[0160]

[0161] In the formula, y p (k+i|k) is the predicted value of the control output, N c is the control step, i = 0, 1,..., N c -1; G and R are the weight coefficient matrices of the output quantity and the control increment respectively; y ref (k+i|k) is the reference value of the control output; N p is the prediction step;

[0162] Set the constraint conditions as:

[0163] u min ≤u(k+i)≤u max , i = 0, 1,..., N c -1

[0164] In the formula, u min is the minimum value of the output voltage, u max is the maximum value of the output voltage;

[0165] According to the above model predictive control objective function and constraint conditions, the model predictive control is transformed into an optimization problem that minimizes the model predictive control objective function under the premise of satisfying the constraint conditions. The expression is as follows:

[0166]

[0167] The linear matrix inequality method is used to solve the model predictive control objective function, and the voltage control signal at time k is obtained. The expression is as follows:

[0168]

[0169] where u d (k) and u q (k) are the stator voltages in the d-q plane at time k; u x (k) and u y (k) are the stator voltages in the x-y plane at time k; the control input voltage of the nominal state at time k is obtained

[0170] Step 32): Obtain the rotor electrical angle θ e (k) of the dual-winding motor with open-phase fault, and update the Tube invariant set;

[0171] Design the compensation control gain K so that the trajectory of the actual dual-winding motor system is in the Tube sequence. This Tube sequence X is centered on the optimal trajectory of the nominal model without disturbance terms, so as to ensure that the dual-winding motor can asymptotically and stably converge within the Tube invariant set Z. The expression of the Tube sequence X is as follows:

[0172] X := {X1, X2, ···, X N}

[0173] where is the nominal model state;

[0174] From time k, the expression of the Tube invariant set Z at the i-th step is as follows:

[0175]

[0176] where Z(i|k) is the Tube invariant set containing the origin; N c is the control step size; w(i - 1|k) is the disturbance suffered by the system at time k + i - 1; Z(i - 1|k) is the Tube invariant set of the system at time k + i - 1; A K is the parameter matrix of the system at time k + i - 1, and the expression is as follows:

[0177] A K = A 0 + QK

[0178] Wherein, A 0 is the nominal state matrix without considering the change of electrical rotation angle, and Q is the control matrix, and the expressions are as follows:

[0179]

[0180] Wherein, θ e (k) is the rotor electrical angle at time k; L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; T s is the sampling period; R s is the stator resistance;

[0181] Step 33): Update the objective function and constraint conditions using the Tube invariant set Z at the i-th step starting from time k obtained in Step 32), and solve the model predictive control objective function using the linear matrix inequality method to obtain the control input voltage at time k+i;

[0182] The updated objective function and constraint conditions are as follows:

[0183]

[0184] Wherein, x ref (i|k) is the reference current, G and R are the weight coefficient matrices of the reference current and the nominal state respectively, P is the weight coefficient matrix of the control input voltage, X m is the terminal constraint and X m ∈X;

[0185] Step 34): Obtain the actual state x(i|k) of the system, calculate the error between the actual state of the system and the center trajectory of the Tube invariant set Generate the auxiliary control input Superimpose it on the control input voltage of the nominal state at time k+i obtained in Step 31), and jointly act on the dual-winding motor to achieve the stability control of the dual-winding motor in the healthy state and the open-phase fault state;

[0186] The expression of the input u(i|k) actually acting on the dual-winding steer-by-wire system is as follows:

[0187]

[0188] There are many specific application ways of the present invention. The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements can still be made, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model, characterized in that, The steps are as follows: Step 1): Design a single-phase open fault diagnosis method to diagnose the faults of the dual-winding motor and obtain the fault diagnosis result; Step 2): Judge the health state of the dual-winding motor according to the fault diagnosis result in Step 1). If the dual-winding motor is in a healthy state, establish a prediction model of the dual-winding motor under the healthy state. If the dual-winding motor is in a single-phase open fault state, reconstruct the prediction model of the dual-winding motor under the single-phase open fault state; Step 3): According to the prediction model of the dual-winding motor in Step 2), solve the objective function to obtain the control input voltage of the nominal state; use the actual state of the dual-winding motor and the updated Tube invariant set to update the objective function and solve to obtain the control input voltage of the nominal state at the k+i moment, and generate the auxiliary control input at the k+i moment; superimpose the control input voltage of the nominal state at the k+i moment and the auxiliary control input at the k+i moment and act on the dual-winding motor together to achieve the stability control of the dual-winding motor under the healthy state and the single-phase open fault state.

2. The fault tolerance control method for a dual-winding steer-by-wire system based on a prediction model according to claim 1, wherein The specific content of Step 1) includes: Step 11): Design the determination conditions for the d-q axis currents of the open-phase fault: If the d-q axis currents \(i_{d}\) d = 0 and \(i_{q}\) q = \(I_{m}\), m then the dual-winding motor is in a healthy state; if the d-q axis currents \(i_{d}'\) d ≠ 0 and \(i_{q}'\) q ' ≠ \(I_{m}\), m then the dual-winding motor is in an open-phase fault state, where \(i_{d}\) d and \(i_{q}\) q are the direct-axis current and the quadrature-axis current in the synchronous rotating coordinate system under the healthy state respectively, \(i_{d}'\) d and \(i_{q}'\) q ' are the direct-axis current and the quadrature-axis current in the synchronous rotating coordinate system under the open-phase fault state respectively, and \(I_{m}\) m is the amplitude of the stator current; Step 12): Design the judgment condition of the single-phase open fault cost function: if the cost function does not generate DC components and second harmonic components, the dual-winding motor is in a healthy state; if the cost function generates DC components and second harmonic components, the dual-winding motor is in a single-phase open fault state, and extract the fault index as the amplitudes of the DC components and second harmonic components generated by the cost function; Step 13): Design the judgment condition for single-phase open fault location: detect the initial phase angle deviation. If the initial phase angle deviation of each winding is equal to 120°, the dual-winding motor is in a healthy state; if the initial phase angle deviation of each winding changes greatly, the dual-winding motor is in a single-phase open fault state, and extract the initial phase angle deviation index as the initial phase angle deviation; Step 14): Design a fault diagnosis algorithm: if the detected fault detection flag is 0, the dual-winding motor is in a healthy state and the six-phase fault location flag is 0; if the detected fault detection flag is 1, the dual-winding motor is in a single-phase open fault state, perform fault location. If the detected single-phase fault location flag is 1 and the other five-phase fault location flags are 0, then this phase is the fault phase.

3. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 2, characterized in that, When the dual-winding motor is in a healthy state in step 11), the d-q axis currents i d and i q are expressed as follows: where, i a , i b , i c , i u , i v , i w are the six-phase stator currents of the double-winding motor; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor.

4. The fault tolerance control method for a dual-winding steer-by-wire system based on a prediction model according to claim 2, wherein In step 11), it is assumed that a certain phase fails, and the dual-winding motor is in a single-phase failure state. The d-q axis currents i′ d and i q ′ are expressed as follows: where ζ is the amplitude coefficient; I m is the amplitude of the stator current; θ e is the electrical angle of the rotor; θ cf is the angle offset.

5. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 2, wherein, The d-q axis currents i′ d and i′ q of the faulty winding in step 12) have the following discretized expressions: Where, i' d (k + 2) and i' q (k + 2) are the d-q axis currents detected at the (k + 2)-th moment under the fault state; i d (k + 2) and i q (k + 2) are the d-q axis currents detected at the (k + 2)-th moment under the healthy state; θ e is the electrical angle of the rotor; θ cf is the angle offset.

6. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 2, wherein The expression of the cost function J in Step 12) is as follows: where Q and R are the weight coefficient matrices of the output quantity and the control increment respectively; ζ is the amplitude coefficient; θ e is the electrical angle of the rotor; θ cf is the angle offset; I m is the amplitude of the stator current; Δu is the difference between the voltage inputs at the k-th sampling instant and the (k - 1)-th sampling instant.

7. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 2, characterized in that The expression of the fault diagnosis algorithm in Step 14) is as follows: Wherein, when the Boolean variable is zero, the value of the counter value counter1 is reset to zero, and if the counter value counter1 is greater than the constant COUNT1, Flag is set from low to high; Flag and Flag mn are the fault detection flag and the fault location flag respectively; counter1 is the count value from the start of detection when the Boolean variable ε = 1 to reaching the constant COUNT1; counter2 is from the Boolean variable ε mn = 1 the count value from the start of detection to reaching the constant COUNT2.

8. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 7, characterized in that The Boolean variables ε, ε in the step 14) mn and the count value expressions are as follows: Where, I dc and I2 are the amplitudes of the DC component and the second harmonic component, respectively; and are the set thresholds; ε and ε mn are Boolean type variables of the generated fault indication and the phase deviation angle indication, respectively; where, T s is the sampling period; T is the stator current period; m is the sensitivity factor, COUNT1 = m1 * T / T s , COUNT2 = m2 * T / T s .

9. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 1, wherein The specific content of reconstructing the prediction model of the dual-winding motor under the single-phase open fault state in Step 2) includes: Step 221): Reconstruct the voltage equation and flux linkage equation in the natural coordinate system under the single-phase open fault state; After one phase of the dual-winding motor is open-circuited, reconstruct the voltage equation and flux linkage equation of the other phases in the natural coordinate system, and the expressions are as follows: ψ s = L s · i s + ψ f · F(θ e ) where, u s = [u A u B u C u U u V T is the stator voltage matrix; i s = [i A i B i C i U i V T is the stator current matrix; R n = RI5 is the winding resistance matrix; F(θ e ) is the flux linkage coefficient matrix; ψ s = [ψ A ψ B ψ C ψ U ψ V T is the flux linkage matrix of each phase; ψ f is the flux linkage amplitude; I5 is the five-dimensional identity matrix; L1 is the leakage inductance of the stator winding; L m is the main self-inductance; L s is the stator inductance matrix; θ e is the electrical angle of the rotor;​​​ Step 222): Reconstruct the prediction model of the dual-winding motor under the single-phase open fault state; Reconstruct the electrical equations in the synchronous rotating coordinate system and the harmonic subspace, and the expressions are as follows: where, u d , u q represent the d-q axis voltages; i d , i q represent the d-q axis currents; u z1 , u z2 , u z3 represent the harmonic subspace voltages; i z1 , i z2 , i z3 represent the currents in the z1, z2, z3 subspaces; L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; V1(θ e ) and W1(θ e ) are the coefficient matrices when one phase is open-circuited, and the expressions are as follows: where θ e is the electrical angle of the rotor; Reconstruct the prediction model of the dual-winding motor under the single-phase open fault state, and the expression is as follows: where, u′ d is the d-axis voltage under the open-phase fault condition, u′ q is the q-axis voltage under the open-phase fault condition, L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; ψ f is the magnetic flux amplitude; ω e is the electrical angular velocity, V1 -1 (θ e ) is the inverse matrix of the coefficient matrix during single-phase open circuit; υ(θ e ) represents the rotor flux offset vector caused by current imbalance in the d-q axis coordinate system.

10. The fault-tolerant control method for a dual-winding steer-by-wire system based on a prediction model according to claim 1, wherein The specific content of Step 3) includes: Step 31): Solve the model predictive control objective function to obtain the control input voltage of the nominal state Define the model predictive control objective function J as the sum of the absolute value of the current error and the control increment, and the expression is as follows: where y p (k + i|k) is the predicted value of the control output, N c is the control step size, i = 0, 1, …, N c −1; G and R are the weight coefficient matrices of the output quantity and the control increment respectively; y ref (k + i|k) is the reference value of the control output; N p is the prediction step size; Set the constraint conditions as: u min u(k + i) ≤ u max where i = 0, 1, …, N c -1 where u min is the minimum output voltage, and u max is the maximum output voltage; According to the above model predictive control objective function and constraint conditions, the model predictive control is transformed into an optimization problem that minimizes the model predictive control objective function under the premise of satisfying the constraint conditions. The expression is as follows: The linear matrix inequality method is used to solve the model predictive control objective function, and the voltage control signal at time k is obtained. The expression is as follows: where, u d (k), u q (k) are the stator voltages in the d-q plane at time k; u x (k), u y (k) are the stator voltages in the x-y plane at time k; the control input voltage at the nominal state at time k is obtained Step 32): Obtain the rotor electrical angle θ of the open-phase fault dual-winding motor at time k e (k), and update the Tube invariant set; The compensation control gain K is designed to make the trajectory of the actual dual-winding motor system lie in the Tube sequence X, which is centered on the optimal trajectory of the nominal model without disturbance terms, so as to ensure that the dual-winding motor can asymptotically and stably converge within the Tube invariant set Z. The expression of the Tube sequence X is as follows: X := {X1, X2, ···, X N} In the formula, is the nominal model state; From time k, the expression of the Tube invariant set Z at the i-th step is as follows: Among them, \(Z(i|k)\) is a Tube invariant set containing the origin; \(N\) c is the control step size; \(w(i - 1|k)\) is the disturbance suffered by the system at time \(k + i - 1\); \(Z(i - 1|k)\) is the Tube invariant set of the system at time \(k + i - 1\); \(A\) K is the parameter matrix of the system at time \(k + i - 1\), and the expression is as follows: A K = A 0 + QK where A 0 is the nominal state matrix without considering the change of electrical rotation angle, and Q is the control matrix, and the expressions are as follows: where θ e (k) is the rotor electrical angle at time k; L d , L q are the inductances in the d-q coordinate system; L1 is the leakage inductance of the stator winding; T s is the sampling period; R s is the stator resistance; Step 33): Update the objective function and constraint conditions using the Tube invariant set Z at the i-th step starting from time k obtained in Step 32), and use the linear matrix inequality method to solve the model predictive control objective function to obtain the control input voltage at time k + i; The updated objective function and constraint conditions are as follows: where x ref (i|k) is the reference current, G and R are the weight coefficient matrices of the reference current and the nominal state respectively, P is the weight coefficient matrix of the control input voltage, X m is the terminal constraint and X m ∈ X; Step 34): Obtain the actual system state x(i|k), and calculate the error between the actual system state and the center trajectory of the Tube invariant set Generate an auxiliary control input Superimpose it on the control input voltage of the nominal state at time k+i obtained in Step 31), and jointly act on the dual-winding motor to achieve stability control of the dual-winding motor in both healthy state and single-phase open fault state; The expression of the input u(i|k) actually acting on the dual-winding steer-by-wire system is as follows:

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