Commercial vehicle double-motor electric drive axle synchronous control method considering time lag influence

Abstract

The invention discloses a commercial vehicle double-motor electric drive axle synchronous control method considering a time lag influence, and the method comprises the steps: improving the speed tracking robustness and synchronization precision of double motors of an electric drive axle under the influence of time lag and external disturbance through designing an explicit model prediction controller; meanwhile, a cross coupling control structure is adopted to generate a compensation signal for synchronous control of the two motors, the compensation signal is fused into a combined control framework composed of an explicit model prediction controller and an enhanced Smith predictor, the stability of the dual-motor system is enhanced, meanwhile, the online calculation complexity is remarkably reduced, and the system performance is improved. And the synchronous control capability of the commercial vehicle double-motor electric drive axle influenced by the time lag is improved.

Description

Technical Field

[0001] This invention belongs to the field of electric vehicle electric drive axle control optimization, specifically involving a synchronous control method for dual-motor electric drive axles of commercial vehicles that considers the effects of time delay. Background Technology

[0002] With the continuous development of electrification in commercial vehicles, the electric drive axle, as the core power source of new energy commercial vehicles, not only determines the overall vehicle performance and energy efficiency, but also directly affects the vehicle's range, power response, and overall driving experience. Among them, the dual-motor electric drive axle for commercial vehicles boasts stronger power performance, higher energy efficiency, more flexible power distribution, better handling stability, and stronger system reliability. It performs particularly well in commercial vehicle applications requiring heavy loads, high performance, and complex road conditions, making it suitable for handling diverse and high-intensity operating conditions.

[0003] Currently, synchronous control of dual-motor electric drive axles in commercial vehicles mainly includes independent control, synchronous control, torque distribution control, torque vector control, joint control, and distributed control. However, research on synchronous control of dual-motor electric drive axles in commercial vehicles affected by time lag is not comprehensive. Specifically, Chinese invention patent application number CN201010151009.4, entitled "A Dual-Motor Drive Control System for the Rear Axle of an Electric Vehicle," achieves precise control of the electric vehicle's speed, especially its adaptive differential performance during low-speed driving and turning, by controlling the average speed of the dual motors through closed-loop control. Chinese invention patent application number CN202211428780.0, entitled "A Control Method, System, Device, and Vehicle for a Dual-Motor Drive System," proposes a control method for a dual-motor drive system, along with related systems, devices, and vehicles. Its core is to adjust the power output mode of the dual motors by acquiring the vehicle's current driving state information and power output mode information. Chinese invention patent application number CN202111672154.1, entitled "A method, system and device for synchronous control of two motors", proposes a method for synchronous control of two motors. This method achieves synchronous control of two motors by determining the compensation amount by obtaining the parameter deviation between the two motors, thereby improving the real-time accuracy of motor control and reducing the speed fluctuation rate of the motors, thus realizing real-time synchronization of the two motors.

[0004] However, most existing technical solutions rely heavily on sensor accuracy and real-time control. They have high requirements for vehicle dynamic synchronization and information acquisition, and may be insufficient under sensor inaccuracies or complex operating conditions. Furthermore, they lack consideration for global energy consumption and performance optimization. The complexity of the algorithms increases the computational burden on the controller, leading to control lag in fast-response scenarios, and insufficient consideration of the robustness to mechanical system errors. Due to factors such as control signal transmission and mechanical backlash, time lag may occur in dual-motor control, affecting the synchronous control of the dual-motor electric drive axle. Therefore, considering the impact of time lag in the synchronous control of dual-motor electric drive axles in commercial vehicles is of great significance for improving the dynamics and stability of the dual-motor electric drive axles. Summary of the Invention

[0005] To address the aforementioned problems, the main objective of this invention is to design a synchronous control method for dual-motor electric drive axles in commercial vehicles that considers the effects of time delay, thereby solving the problem of decreased synchronous control performance caused by time delay.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A synchronous control method for a dual-motor electric drive axle in a commercial vehicle that considers the effects of time delay includes the following steps:

[0008] Step 1: Establish a mathematical model of the two motors in the dq rotating coordinate system, and establish a discrete state-space equation that includes time delay factors;

[0009] Step 2: Based on the dual-motor mathematical model established in Step 1, a dual-motor cross-coupled speed synchronization controller is established through a cross-coupled control structure. The speed compensation value is generated during dual-motor speed synchronization control through the speed difference, and the speed compensation value is used as the input of the explicit model predictive controller to perform dual-motor speed synchronization.

[0010] Step 3: Build an enhanced Smith predictor to compensate for time delays and generate a compensation output;

[0011] Step 4: Based on the discrete state-space equations established in Step 1 and the compensation output in Step 3, perform offline calculations and online solutions to establish an explicit model predictive controller. Then, use the binary tree algorithm to quickly query the control laws corresponding to different system states to perform single-motor speed tracking and dual-motor speed synchronization control.

[0012] As a further description of the present invention, in step 1, the mathematical model expression for the dual-motor system is:

[0013]

[0014] Among them, u d u q The stator voltages on the d and q axes are respectively, id i q The stator currents R on the d and q axes are respectively. s L is the stator resistance of the motor. s Let B be the stator inductance of the motor, B be the coefficient of viscous friction, and ψ be the coefficient of friction. f Let J be the permanent magnet flux linkage of the motor rotor, J be the moment of inertia of the motor, p be the number of rotor pole pairs, and ω be the number of permanent magnet flux linkages. r T is the motor speed. L T is the load torque of the electric drive axle gear. E Let dt be the electromagnetic torque, and dt be the differential of time t. The subscripts i = 1 and 2 indicate the first motor and the second motor, respectively.

[0015] As a further description of the present invention, in step 1, the discrete state-space equation of the dual-motor electric drive bridge system is:

[0016] x i (k+1)=A d x i (k)+B d u i (k);

[0017]

[0018] Where x is the state variable of the electric drive bridge motor, x = [i d i q ,ω r i q ,ω r ] T ; k is the discrete time step index; u i (k) represents the control variable of the dual-motor electric drive bridge system, u i (k)=[u d ,u q ] T A d Let B be the system state transition matrix. d Let T be the input matrix of the system. s k is the sampling period. ti is the torque constant.

[0019] As a further description of the present invention, the discrete state-space equation under the influence of time delay in step 1 is as follows:

[0020] x i (k+1)=A d x i (k)+B d u i (kd);

[0021]

[0022] Where τ is the unknown time delay; d is the discrete time delay.

[0023] As a further description of the present invention, step 2, establishing a dual-motor cross-coupled speed synchronization controller to obtain the speed compensation value, includes the following steps:

[0024] Step 2.1: Calculate the speed error of the two motors, the expression is:

[0025] σ = ω1 - ω2;

[0026] Where ω1 is the speed of the first motor and ω2 is the speed of the second motor;

[0027] Step 2.2: Calculate the speed error of each motor, expressed as:

[0028]

[0029] Where, ω * The desired speed of the dual-motor electric drive bridge is given by the subscripts i = 1 and 2, which represent the first motor and the second motor, respectively.

[0030] Step 2.3: Calculate the compensated speed using the PID algorithm, the expression is:

[0031]

[0032] Where, ω comp This is the output speed compensation value for the dual-motor cross-coupled speed synchronization controller, where k is the discrete time step index, K p ,K i ,K d These are the proportional coefficient, integral coefficient, and differential coefficient, respectively.

[0033] As a further description of the present invention, step 3, establishing an enhanced Smith predictor to solve for the compensation output of the system due to the time delay factor, includes the following steps:

[0034] Step 3.1: Establish a prediction model to simulate the dynamics of the time-delay-free system. Its discrete state-space model is as follows:

[0035] x i (k+1)=A d x i (k)+B d u i (k);

[0036] The predicted output model is:

[0037] y i (k)=Cx i (k)+Du i (k);

[0038] Among them, y i To estimate the output, y = [i d i q ] T i d i q , , represent the stator currents along the d and q axes, respectively; C is the output matrix. D is the feedforward matrix.

[0039] Step 3.2: Using the online identification method of stochastic partial differential equation kernel learning, adjust the parameter A in the prediction model in real time based on the actual system operation data. d B d C, D;

[0040] Step 3.3: Calculate the difference between the actual output and the estimated output and perform a first-order low-pass filter. The estimated output is then advanced by d time steps to compensate for the actual output. The expression is:

[0041]

[0042] e f (k)=αe(k-1)+(1-α)e(k);

[0043]

[0044] Where e is the difference between the system's predicted output and the actual output, and e(k) is the difference between the system's predicted output and the actual output at time k. f e is the filtered value of the difference between the system's estimated output and the actual output. f (k) is the filtered value of the difference between the system's predicted output and the actual output at time k. For the system's predicted output, y c The output of the compensated system is α, where α is the filter coefficient.

[0045] As a further description of the present invention, step 4, which involves offline calculation and online solution to establish an explicit model predictive controller, includes the following steps:

[0046] Step 4.1: Replace the actual output with the system output after time delay compensation in the objective function calculation, and establish the cost function for a single motor, the expression of which is:

[0047]

[0048] Where J(k) is the cost function of the motor, Q y Q is the actual output weight matrix. xLet R be the weight matrix of the system parameters, and λ be the weight matrix of the output parameters. q ,λ d λ is the influence coefficient for motor current control. ω λ is the influence coefficient for speed error control of dual motors. u This represents the motor voltage influence coefficient, where j is the future step size index, and N... p To predict the length of the time domain;

[0049] Step 4.2: Transform the circular constraints into rectangular inequalities for constraint design:

[0050]

[0051] In the formula, U s_max I s_max These are the maximum values ​​of the motor bus voltage and current, respectively.

[0052] Step 4.3: Transform the optimization problem into a multi-parameter quadratic programming problem and solve it to obtain the control input sequence u with respect to the initial state x. k The functional relationship;

[0053] Let the Hamiltonian function be:

[0054] H(x,u.λ)=x T Qx+u T Ru+λ T (A d x+B d u);

[0055] Where H() is the Hamiltonian function and λ is the adjoint vector;

[0056] Solve for the partial derivative of the Hamiltonian function with respect to u and set it to 0. get:

[0057]

[0058] The adjoint equations of the electric drive bridge system are established as follows:

[0059]

[0060] By substituting the calculated u into the discrete state control equations and adjoint matrix of the electric drive bridge system, and through matrix operations and iterative calculations, the optimal solution expression is obtained as follows:

[0061] u = -(G T QG+R) -1 G T QFx(k);

[0062] Where G is the coefficient matrix in the constraints, F is the constant coefficient matrix defined by the system parameters, and Q = Q x +Q y This is the weight matrix in the cost function;

[0063] Step 4.4: Solve the system's state partitions offline using the MPT optimization toolbox. Determine the number of state partitions in the system through optimization calculations. Each state partition contains a different control law, represented as follows:

[0064]

[0065] Where u(x) is the control law of the explicit model predictive controller; F i g i For the corresponding optimal control input data; H i K i (i∈{1,...,n}) is the dataset describing the state partitioning of the dual-motor electric drive bridge system; n is the number of state partitions; t represents the solution time; x is the state variable of the electric drive bridge motor.

[0066] Compared with the prior art, the technical advantages of the present invention are as follows:

[0067] This invention provides a synchronous control method for a dual-motor electric drive axle in commercial vehicles that considers the effects of time delay. By designing an explicit model predictive controller, the method improves the speed tracking robustness and synchronization accuracy of the dual motors in the electric drive axle under the influence of time delay and external disturbances. At the same time, a cross-coupled control structure is used to generate compensation signals for the synchronous control of the two motors, which are then integrated into a joint control framework consisting of an explicit model predictive controller and an enhanced Smith predictor. This enhances the stability of the dual-motor system while significantly reducing online computational complexity and improving the synchronous control capability of the dual-motor electric drive axle in commercial vehicles affected by time delay. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the architecture of the present invention. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings:

[0070] In one embodiment of the present invention, a synchronous control method for a dual-motor electric drive axle of a commercial vehicle considering the effect of time delay is disclosed, with reference to... Figure 1 As shown, the method includes the following steps:

[0071] Step 1: Establish a mathematical model of the two motors in the dq rotating coordinate system, and establish a discrete state-space equation that includes time delay factors;

[0072] Step 2: Based on the dual-motor mathematical model established in Step 1, a dual-motor cross-coupled speed synchronization controller is established through a cross-coupled control structure. The speed compensation value during dual-motor speed synchronization control is calculated through the speed difference, and the speed compensation value is used as the input of the explicit model predictive controller to perform dual-motor speed synchronization.

[0073] Step 3: Establish an enhanced Smith predictor to compensate for time delay, generate a compensation output, and reduce the impact of time delay on the system's synchronous control;

[0074] Step 4: Based on the discrete state-space equations established in Step 1 and the compensation output in Step 3, perform offline calculations and online solutions to establish an explicit model predictive controller. Then, use the binary tree algorithm to quickly query the control laws corresponding to different system states to perform single-motor speed tracking and dual-motor speed synchronization control.

[0075] Specifically, this embodiment analyzes the process of each of the above steps, as follows:

[0076] In this embodiment, the mathematical model expression for the dual-motor system in step 1 is as follows:

[0077]

[0078] Among them, u d u q The stator voltages on the d and q axes are respectively, i d i q The stator currents R on the d and q axes are respectively. s L is the stator resistance of the motor. s Let B be the stator inductance of the motor, B be the coefficient of viscous friction, and ψ be the coefficient of friction. f Let J be the permanent magnet flux linkage of the motor rotor, J be the moment of inertia of the motor, p be the number of rotor pole pairs, and ω be the number of permanent magnet flux linkages. r T is the motor speed. L T is the load torque of the electric drive axle gear. E Let dt be the electromagnetic torque, and dt be the differential of time t. The subscripts i = 1 and 2 indicate the first motor and the second motor, respectively.

[0079] Furthermore, the discrete state-space equations of the dual-motor electric drive bridge system are as follows:

[0080] x i (k+1)=A d x i (k)+B d u i (k);

[0081]

[0082] Where x is the state variable of the electric drive bridge motor, x = [id i q ,ω r i q ,ω r ] T ; k is the discrete time step index; u i (k) represents the control variable of the dual-motor electric drive bridge system, u i (k)=[u d ,u q ] T A d Let B be the system state transition matrix. d Let T be the input matrix of the system. s k is the sampling period. ti is the torque constant.

[0083] Furthermore, in step 1, the discrete state-space equation under the influence of time delay is:

[0084] x i (k+1)=A d x i (k)+B d u i (kd);

[0085]

[0086] Where τ is the unknown time delay, including the unknown time delay caused by factors such as sampling, controller calculation, and electric drive axle gear transmission; d is the discrete time delay.

[0087] In this embodiment, step 2, establishing a dual-motor cross-coupled speed synchronization controller to obtain the speed compensation value, includes the following steps:

[0088] Step 2.1: Calculate the speed error of the two motors, the expression is:

[0089] σ = ω1 - ω2;

[0090] Where ω1 is the speed of the first motor and ω2 is the speed of the second motor;

[0091] Step 2.2: Calculate the speed error of each motor, expressed as:

[0092]

[0093] Where, ω * The desired speed of the dual-motor electric drive bridge is given by the subscripts i = 1 and 2, which represent the first motor and the second motor, respectively.

[0094] Step 2.3: Calculate the compensated speed using the PID algorithm, the expression is:

[0095]

[0096] Where, ω comp K is the output speed compensation value of the dual-motor cross-coupled speed synchronization controller. p ,K i ,K d These are the proportional coefficient, integral coefficient, and differential coefficient, respectively.

[0097] In this embodiment, step 3, which involves establishing an enhanced Smith predictor and solving for the compensation output of the system due to time delay factors, includes the following steps:

[0098] Step 3.1: Establish a prediction model to simulate the dynamics of the time-delay-free system. Its discrete state-space model is as follows:

[0099] x i (k+1)=A d x i (k)+B d u i (k);

[0100] The predicted output model is:

[0101] y i (k)=Cx i (k)+Du i (k);

[0102] Among them, y i To estimate the output, y = [i d i q ] T i d i q , , represent the stator currents along the d and q axes, respectively; C is the output matrix. D is the feedforward matrix.

[0103] Step 3.2: Using the online identification method of stochastic partial differential equation kernel learning, adjust the parameter A in the prediction model in real time based on the actual system operation data. d B d C, D;

[0104] Step 3.3: Calculate the difference between the actual output and the predicted output and perform a first-order low-pass filter. Since the prediction model is time-delay-free, the predicted output is advanced by d time steps to compensate for the actual output. The expression is:

[0105]

[0106] e f (k)=αe(k-1)+(1-α)e(k);

[0107]

[0108] Where e is the difference between the system's predicted output and the actual output, and e(k) is the difference between the system's predicted output and the actual output at time k. f e is the filtered value of the difference between the system's estimated output and the actual output. f (k) is the filtered value of the difference between the system's predicted output and the actual output at time k. For the system's predicted output, y c The output of the compensated system is α, where α is the filter coefficient.

[0109] In this embodiment, step 4 involves offline calculation and online solution to establish an explicit model predictive controller, including the following steps:

[0110] Step 4.1: Replace the actual output with the system output after time delay compensation in the objective function calculation, and establish the cost function for a single motor, the expression of which is:

[0111]

[0112] Where J(k) is the cost function of the motor, Q y Q is the actual output weight matrix. x Let R be the weight matrix of the system parameters, and λ be the weight matrix of the output parameters. q ,λ d λ is the influence coefficient for motor current control. ω λ is the influence coefficient for speed error control of dual motors. u This represents the motor voltage influence coefficient, where j is the future step size index, and N... p To predict the length of the time domain;

[0113] Step 4.2: Transform the circular constraints into rectangular inequalities for constraint design:

[0114]

[0115] In the formula, U s_max I s_max These are the maximum values ​​of the motor bus voltage and current, respectively.

[0116] Step 4.3: Transform the optimization problem into a multi-parameter quadratic programming problem and solve it to obtain the control input sequence u with respect to the initial state x. k The functional relationship;

[0117] Let the Hamiltonian function be:

[0118] H(x,u.λ)=xT Qx+u T Ru+λ T (A d x+B d u);

[0119] Where H() is the Hamiltonian function and λ is the adjoint vector;

[0120] Solve for the partial derivative of the Hamiltonian function with respect to u and set it to 0. get:

[0121]

[0122] The adjoint equations of the electric drive bridge system are established as follows:

[0123]

[0124] By substituting the calculated u into the discrete state control equations and adjoint matrix of the electric drive bridge system, and through matrix operations and iterative calculations, the optimal solution expression is obtained as follows:

[0125] u = -(G T QG+R) -1 G T QFx(k);

[0126] Where G is the coefficient matrix in the constraints, F is the constant coefficient matrix defined by the system parameters, and Q = Q x +Q y This is the weight matrix in the cost function;

[0127] Step 4.4: Solve the system's state partitions offline using the MPT optimization toolbox. Determine the number of state partitions in the system through optimization calculations. Each state partition contains a different control law, represented as follows:

[0128]

[0129] Where u(x) is the control law of the explicit model predictive controller; F i g i For the corresponding optimal control input data; H i K i (i∈{1,...,n}) is the dataset describing the state partitioning of the dual-motor electric drive bridge system; n is the number of state partitions; t represents the solution time.

[0130] This invention addresses the speed asynchrony problem of dual-motor electric drive axles in commercial vehicles due to time lag, proposing a synchronous control method for dual-motor electric drive axles in commercial vehicles that considers the effects of time lag. Compared with existing technologies:

[0131] 1. This invention improves the speed tracking robustness and synchronization accuracy of dual motors in an electric drive bridge under the influence of time delay and external disturbances by designing an explicit model predictive controller, thus solving the problem of asynchrony between the two motors caused by time delay.

[0132] 2. This invention uses a cross-coupled control structure to generate compensation signals for the synchronous control of two motors, and integrates them into a joint control framework consisting of an explicit model predictive controller and an enhanced Smith predictor. This enhances the stability of the dual-motor system while significantly reducing online computational complexity and improving the synchronous control capability of the dual-motor electric drive axle of commercial vehicles affected by time delay.

[0133] A cross-coupled control structure is adopted to generate compensation signals for the synchronous control of the two motors. These signals are then integrated into a joint control framework consisting of an explicit model predictive controller and an enhanced Smith predictor. This enhances the stability of the dual-motor system while significantly reducing online computational complexity and improving the synchronous control capability of the dual-motor electric drive axle in commercial vehicles under the influence of time delay.

[0134] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A synchronous control method for a dual-motor electric drive axle in a commercial vehicle considering the effects of time delay, characterized in that, Includes the following steps: Step 1: Establish a mathematical model of the two motors in the dq rotating coordinate system, and establish a discrete state-space equation that includes time delay factors; Step 2: Based on the dual-motor mathematical model established in Step 1, a dual-motor cross-coupled speed synchronization controller is established through a cross-coupled control structure. The speed compensation value is generated during dual-motor speed synchronization control through the speed difference, and the speed compensation value is used as the input of the explicit model predictive controller to perform dual-motor speed synchronization. Step 3: Build an enhanced Smith predictor to compensate for time delays and generate a compensation output; Step 4: Based on the discrete state-space equations established in Step 1 and the compensation output in Step 3, perform offline calculations and online solutions to establish an explicit model predictive controller. Then, use the binary tree algorithm to quickly query the control laws corresponding to different system states to perform single-motor speed tracking and dual-motor speed synchronization control.

2. The synchronous control method for dual-motor electric drive axle of commercial vehicles considering time delay effects according to claim 1, characterized in that: In step 1, the mathematical model expression for the dual-motor system is as follows: Among them, u d u q The stator voltages on the d and q axes are respectively, i d i q The stator currents R on the d and q axes are respectively. s L is the stator resistance of the motor. s Let B be the stator inductance of the motor, B be the coefficient of viscous friction, and ψ be the coefficient of friction. f Let J be the permanent magnet flux linkage of the motor rotor, J be the moment of inertia of the motor, p be the number of rotor pole pairs, and ω be the number of permanent magnet flux linkages. r T is the motor speed. L T is the load torque of the electric drive axle gear. E Let dt be the electromagnetic torque, and dt be the differential of time t. The subscripts i = 1 and 2 indicate the first motor and the second motor, respectively.

3. The synchronous control method for dual-motor electric drive axle of commercial vehicles considering time delay effects according to claim 2, characterized in that: In step 1, the discrete state-space equation of the dual-motor electric drive bridge system is: x i (k+1)=A d x i (k)+B d u i (k); Where x is the state variable of the electric drive bridge motor, x = [i d i q ,ω r i q ,ω r ] T k is the discrete time step index; u i (k) represents the control variable of the dual-motor electric drive bridge system, u i (k)=[u d ,u q ] T A d Let B be the system state transition matrix. d Let T be the input matrix of the system. s k is the sampling period. ti is the torque constant.

4. The synchronous control method for dual-motor electric drive axle of commercial vehicles considering time delay as described in claim 3, characterized in that: The discrete state-space equation under the influence of time delay in step 1 is as follows: x i (k+1)=A d x i (k)+B d u i (k-d); Where τ is the unknown time delay; d is the discrete time delay.

5. The synchronous control method for dual-motor electric drive axles of commercial vehicles considering time delay effects according to claim 1, characterized in that: In step 2, establishing a dual-motor cross-coupled speed synchronization controller to obtain the speed compensation value includes the following steps: Step 2.1: Calculate the speed error of the two motors, the expression is: σ = ω1 - ω2; Where ω1 is the speed of the first motor and ω2 is the speed of the second motor; Step 2.2: Calculate the speed error of each motor, expressed as: Where, ω * The desired speed of the dual-motor electric drive bridge is given by the subscripts i = 1 and 2, which represent the first motor and the second motor, respectively. Step 2.3: Calculate the compensated speed using the PID algorithm, the expression is: Where, ω comp This is the output speed compensation value for the dual-motor cross-coupled speed synchronization controller, where k is the discrete time step index, K p ,K i ,K d These are the proportional coefficient, integral coefficient, and differential coefficient, respectively.

6. The synchronous control method for dual-motor electric drive axles of commercial vehicles considering time delay effects according to claim 3, characterized in that: In step 3, an enhanced Smith predictor is established to solve for the compensation output of the system due to the time delay factor, including the following steps: Step 3.1: Establish a prediction model to simulate the dynamics of the time-delay-free system. Its discrete state-space model is as follows: x i (k+1)=A d x i (k)+B d u i (k); The predicted output model is: y i (k)<Cx i (k)+You i (k); Among them, y i To estimate the output, y = [i d i q ] T i d i q , , represent the stator currents along the d and q axes, respectively; C is the output matrix. D is the feedforward matrix. Step 3.2: Using the online identification method of stochastic partial differential equation kernel learning, adjust the parameter A in the prediction model in real time based on the actual system operation data. d B d C, D; Step 3.3: Calculate the difference between the actual output and the estimated output and perform a first-order low-pass filter. The estimated output is then advanced by d time steps to compensate for the actual output. The expression is: e f (k)=αe(k-1)+(1-α)e(k); Where e is the difference between the system's predicted output and the actual output, and e(k) is the difference between the system's predicted output and the actual output at time k. f e is the filtered value of the difference between the system's estimated output and the actual output. f (k) is the filtered value of the difference between the system's predicted output and the actual output at time k. For the system's predicted output, y c The output of the compensated system is α, where α is the filter coefficient.

7. A synchronous control method for a dual-motor electric drive axle of a commercial vehicle considering time delay, as described in claim 6, is characterized in that: In step 4, offline calculation and online solution are performed to establish an explicit model predictive controller, including the following steps: Step 4.1: Replace the actual output with the system output after time delay compensation in the objective function calculation, and establish the cost function for a single motor, the expression of which is: Where J(k) is the cost function of the motor, Q y Q is the actual output weight matrix. x Let R be the weight matrix of the system parameters, and λ be the weight matrix of the output parameters. q ,λ d λ is the influence coefficient for motor current control. ω λ is the influence coefficient for speed error control of dual motors. u This represents the motor voltage influence coefficient, where j is the future step size index, and N... p To predict the time domain length; Step 4.2: Transform the circular constraints into rectangular inequality descriptions for constraint design: In the formula, U s_max I s_max These are the maximum values ​​of the motor bus voltage and current, respectively. Step 4.3: Transform the optimization problem into a multi-parameter quadratic programming problem and solve it to obtain the control input sequence u with respect to the initial state x. k The functional relationship; Let the Hamiltonian function be: H(x,u.λ)=x T Qx+u T Ru+λ T (A d x+B d u); Where H() is the Hamiltonian function and λ is the adjoint vector; Solve for the partial derivative of the Hamiltonian function with respect to u and set it to 0. get: The adjoint equations of the electric drive bridge system are established as follows: By substituting the calculated u into the discrete state control equations and adjoint matrix of the electric drive bridge system, and through matrix operations and iterative calculations, the optimal solution expression is obtained as follows: u=-(G T QG+R) -1 G T QFx(k); Where G is the coefficient matrix in the constraints, F is the constant coefficient matrix defined by the system parameters, and Q = Q x +Q y This is the weight matrix in the cost function; Step 4.4: Solve the system's state partitions offline using the MPT optimization toolbox. Determine the number of state partitions in the system through optimization calculations. Each state partition contains a different control law, represented as follows: Where u(x) is the control law of the explicit model predictive controller; F i g i For the corresponding optimal control input data; H i K i (i∈{1,...,n}) is the dataset describing the state partitioning of the dual-motor electric drive bridge system; n is the number of state partitions; t represents the solution time; x is the state variable of the electric drive bridge motor.

Images