Double permanent magnet synchronous motor rotating speed synchronization method based on active disturbance rejection technology

Abstract

The invention provides a double-permanent-magnet synchronous motor rotating speed synchronization method based on an active-disturbance-rejection technology. The method comprises the following steps that 1, a linear active-disturbance-rejection controller replaces a traditional PI controller to serve as a speed ring controller of a double-permanent-magnet synchronous motor; and 2, taking the sliding mode cross coupling controller as a rotating speed synchronous controller between the double motors. The method has the beneficial effects that the control strategy and the control structure are improved, and high-precision synchronization of the rotating speed is realized. A linear active-disturbance-rejection controller is designed according to a mathematical model of the permanent magnet synchronous motor, so that the disturbance rejection and the dynamic response speed of the system are improved; a sliding-mode cross-coupling controller is designed based on the cross-coupling control structure, and high-precision synchronization of the rotating speed is realized through the sliding-mode cross-coupling controller.

Description

Technical Field

[0001] The present invention relates to the technical field of synchronous motors, and in particular to a speed synchronization method for a dual permanent magnet synchronous motor based on an anti-disturbance technology. Background Art

[0002] With the continuous improvement of production efficiency and the increasingly stringent requirements for the quality of industrial products, the control power of a single motor is limited and often cannot meet the needs of the project, which has led to the introduction of dual-motor and even multi-motor control applications, and the application of dual-motor control has become more and more widespread. For example, in traditional industries, traditional deep well hoists usually use a single motor, but to increase the depth, a higher power motor is required. High-power motors are large in size and not easy to disassemble and transport. Dual-motor synchronous control technology connects two motors to the shaft instead of a single motor control, which can solve important problems such as the large size and insufficient power of a single motor. At the same time, traditional industries such as printing, textiles, papermaking, and CNC machine tools have begun to use dual-motor and multi-motor synchronous control.

[0003] In some high-power follow-up systems, such as ship-borne guns and vehicle-borne guns, these devices are mainly capable of precise guidance and rapid launch tracking. In today's combat systems, the requirements for weapons and equipment are getting higher and higher, and they must be able to achieve the goal of "fast, accurate and ruthless". In vehicle-borne gun devices, due to the heavy weight of the turret, high control accuracy is required. The elevation angle and rotation azimuth of the turret are driven by dual motors to effectively improve the control accuracy and adjustment time. Therefore, the control of dual motors has application value in the military.

[0004] In the field of new energy vehicles, dual motor control has been widely used. For example, BYD Tang, BYD Qin and other products use dual permanent magnet synchronous motor drive systems with reliable and stable performance. Tesla Model Y uses a dual motor drive system that combines permanent magnet motors and induction motors, which has good safety and driving performance. Unlike applications in other industrial occasions, the motor drive system of an automobile, in addition to providing basic driving force, should also meet some specific working conditions of the automobile: it can run smoothly at high speed, and meet other speed regulation performance requirements such as fast start and stop, braking, etc., so it has extremely high requirements for the synchronization performance of dual motor control.

[0005] In summary, dual motor synchronization technology has been used in many control devices, whether in traditional industries, emerging industries, new energy vehicles, or military. The precision of the speed synchronization of dual motor control directly affects the working efficiency, power size, lifespan and other performances of the equipment. Therefore, a dual motor synchronization control method has been developed to achieve high-precision synchronization of speeds, which has important theoretical and engineering application value. Summary of the invention

[0006] In order to solve the above problems, especially to address the deficiencies in the prior art, the present invention provides a dual permanent magnet synchronous motor speed synchronization method based on an anti-disturbance technology to solve the above problems.

[0007] To achieve the above purpose, the present invention adopts the following technical means:

[0008] A speed synchronization method for a dual permanent magnet synchronous motor based on an auto-disturbance rejection technology comprises the following steps:

[0009] Step 1: The linear active disturbance rejection controller replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor:

[0010] A linear active disturbance rejection controller is designed based on the mathematical model of the permanent magnet synchronous motor. The linear active disturbance rejection controller replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor. The linear active disturbance rejection controller is composed of a PD linear combination and a linear extended state observer. The linear active disturbance rejection controller mainly observes the disturbance of the speed loop through the linear extended state observer, and dynamically compensates the observed disturbance, thereby generating a control quantity to eliminate the influence of the disturbance on the system.

[0011] Step 2: Sliding mode cross-coupling controller as the speed synchronization controller between the dual motors:

[0012] A sliding mode cross-coupling controller is designed based on a cross-coupling control structure, and a sliding mode cross-coupling controller is used as a speed synchronization controller between dual motors. The sliding mode cross-coupling controller obtains a dual-axis current reference compensation amount of the dual motors through a controller according to the speed synchronization error between the dual motors, thereby enhancing the robustness of the motor when disturbed. That is, when the motor is disturbed and the speed fluctuates, the dual-axis current reference compensation amount of the dual motors is obtained by coupling the speed difference between the motors, which accelerates the convergence speed of the speed synchronization error, thereby improving the synchronization performance of the dual-motor drive system.

[0013] A further preferred embodiment of the present invention is as follows: the linear anti-disturbance controller models the permanent magnet synchronous motor in a synchronous rotating coordinate system, and establishes differential equations related to the q-axis current, d-axis current, rotor spatial electrical angle, electrical angular velocity and electronic torque.

[0014] A further preferred embodiment of the present invention is as follows: the specific form of the mathematical model of the permanent magnet synchronous motor is as follows:

[0015]

[0016] Among them, i d and i q are the d-axis and q-axis currents, θ m is the rotor space electrical angle, ωe is the electrical angular velocity, ω m is the rotor angle, J is the moment of inertia, B is the viscous friction coefficient, T L is the torque load, Rs is the stator resistance, L d and Lq are the equivalent d-axis and q-axis inductances, ψ r is the permanent magnet flux, T e is the electromagnetic torque, p n is the number of motor pole pairs, represents the time derivative of a variable, u d 、u q is the d, q axis stator voltage.

[0017] A further preferred embodiment of the present invention is as follows: the mathematical model of the permanent magnet synchronous motor is selected to use i in a synchronous rotating coordinate system. d = 0 control strategy simplifies the differential equation and converts i d = 0 is substituted into formula (1) and equivalent transformation is performed to obtain the simplified mathematical model of permanent magnet synchronous motor in the following form:

[0018]

[0019] Electromagnetic torque equation:

[0020]

[0021] Mechanical equation of motion:

[0022]

[0023] Arranging equations (3) and (4) yields:

[0024]

[0025] set up -(Bω m +T L ) / J=f 内 , f 外 is the unknown disturbance outside the system, let y=x1,x1=ω m , x2=f 内 +f 外 , while x2 is differentiable, its derivative Then the system state equation can be obtained:

[0026]

[0027] In this system, the output is y, which is the rotor angular velocity; the input is i q , that is, the q-axis current.

[0028] A further preferred embodiment of the present invention: the system state equation (6) can be used to obtain the observer state equation:

[0029]

[0030] In the formula, C = [1 0], according to the principle of the classical linear extended state observer, the following observer model can be obtained:

[0031]

[0032] P control feedback and compensation control are:

[0033]

[0034] A further preferred solution of the present invention: the design method of the sliding mode cross-coupling controller comprises the following steps:

[0035] Step 1: Design the sliding surface:

[0036] The torque equations of the two motors are:

[0037]

[0038] Where, T ei is the electromagnetic torque of the motor, p i is the number of motor pole pairs, ψ fi is the permanent magnet flux of the motor’s rotor, is the q-axis current component of the motor, i is the motor number;

[0039] The equation of motion for a PMSM is:

[0040]

[0041] Where, T Li is the load torque of the motor, ΔT Li is the load disturbance on the motor, J i , B i is the moment of inertia and friction coefficient on the motor shaft, ω ei is the rotor electrical angular velocity of the motor, i is the motor number;

[0042] The state variables of the speed synchronization control system are taken as:

[0043]

[0044] Combining equations (22) and (23), the state equation of the speed synchronization control system is obtained as follows:

[0045]

[0046] Select the system integral sliding surface s as:

[0047] s=x1+cx2 (26)

[0048] Where s is the sliding surface function, c is the positive integral constant;

[0049] Step 2: Design a sliding mode cross-coupling controller based on step 1:

[0050] In order to realize sliding mode control, the constant velocity reaching law is selected, as shown in formula (28):

[0051]

[0052] In the formula, is the derivative of s;

[0053] Formula (28) combined with formula (25) and formula (26) in step 1 can obtain the output of the sliding mode speed synchronization controller as follows:

[0054]

[0055] In the formula, J = J1 = J2, p = p1 = p2, ψ f =ψ f1 =ψ f2 , B=B1=B2, ΔT L =T L1 -T L2 ;

[0056] Δi q-ref is the dual-axis current reference compensation output by the dual-motor sliding mode cross-coupling control, i q1 、i q2 are the q-axis components of the dual motor stator currents, ψ f is the permanent magnet flux, T L is the load torque of the motor, ΔT is the load torque difference of the dual motors, J is the moment of inertia of the motor, B is the friction coefficient of the motor, and p is the number of pole pairs.

[0057] A further preferred embodiment of the present invention also includes proving the system stability of the sliding mode cross-coupling control method.

[0058] A further preferred embodiment of the present invention: The specific process of proving the system stability is as follows:

[0059] Choose the Lyapunov function as:

[0060]

[0061] The derivative is:

[0062]

[0063] Since ε and q are both constants greater than zero, no matter s is positive or negative, s and Always different signs, that is Meeting the sliding mode reachability condition can ensure that the system enters the sliding mode.

[0064] A further preferred embodiment of the present invention: The specific process of proving the system stability is as follows:

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention takes the dual permanent magnet synchronous motor system based on vector control as the research object, and improves the control strategy and control structure to solve the asynchronous speed problem of the dual motors caused by load disturbance, so as to achieve high-precision synchronization of the speed. Firstly, a linear anti-disturbance controller is designed according to the mathematical model of the permanent magnet synchronous motor to improve the anti-disturbance and dynamic response speed of the system. Then, a sliding mode cross-coupling controller is designed based on the cross-coupling control structure. The sliding mode cross-coupling controller achieves high-precision synchronization of the speed, and the stability of the closed-loop system is analyzed by using the Lyapunov function. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a principle block diagram of the linear active disturbance rejection controller of the present invention;

[0068] Figure 2 It is a principle block diagram of the sliding mode cross-coupling controller of the present invention;

[0069] Figure 3 It is a simulation waveform diagram of dual motor speed synchronization control based on sliding mode cross-coupling control structure of the present invention;

[0070] Figure 4 This is a speed error waveform diagram of a dual permanent magnet motor based on a sliding mode cross-coupling control structure of the present invention. DETAILED DESCRIPTION

[0071] The present invention is further described below in conjunction with the accompanying drawings:

[0072] A speed synchronization method for a dual permanent magnet synchronous motor based on an auto-disturbance rejection technology comprises the following steps:

[0073] Step 1: The linear active disturbance rejection controller replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor:

[0074] like Figure 1As shown in the figure, the linear active disturbance rejection controller (LADRC) replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor, and the cross-coupling controller is used as the speed synchronization controller between the dual motors. Specifically:

[0075] Linear Active Disturbance Rejection Controller (LADRC)

[0076] A linear active disturbance rejection controller (LADRC) is designed based on the mathematical model of permanent magnet synchronous motor (PMSM). The linear active disturbance rejection controller (LADRC) replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor.

[0077] The permanent magnet synchronous motor (PMSM) is modeled in a synchronous rotating coordinate system, and differential equations related to the q-axis current, d-axis current, rotor space electrical angle, electrical angular velocity and electronic torque are established. The specific form of the mathematical model of the permanent magnet synchronous motor (PMSM) is as follows:

[0078]

[0079] Among them, i d and i q are the d-axis and q-axis currents, θ m is the rotor space electrical angle, ω e is the electrical angular velocity, ω m is the rotor angle, J is the moment of inertia, B is the viscous friction coefficient, T L is the torque load, Rs is the stator resistance, L d and Lq are the equivalent d-axis and q-axis inductances, ψ r is the permanent magnet flux, T e is the electromagnetic torque, p n is the number of motor pole pairs, represents the time derivative of a variable, u d 、u q is the d, q axis stator voltage.

[0080] According to the above mathematical model, in the synchronous rotating coordinate system, we choose to use i d = 0 control strategy simplifies the differential equation and converts i d = 0 is substituted into formula (1) and equivalent transformation is performed to obtain the simplified permanent magnet synchronous motor (PMSM) mathematical model in the following form:

[0081]

[0082] Electromagnetic torque equation:

[0083]

[0084] Mechanical equation of motion:

[0085]

[0086] Arranging equations (3) and (4) yields:

[0087]

[0088] set up -(Bω m +T L ) / J=f 内 , f 外 is the unknown disturbance outside the system, let y=x1,x1=ω m , x2=f 内 +f 外 , while x2 is differentiable, its derivative Then the system state equation can be obtained:

[0089]

[0090] In this system, the output is y, which is the rotor angular velocity; the input is i q , that is, the q-axis current.

[0091] The observer state equation can be obtained from formula (6):

[0092]

[0093] In the formula, C = [1 0], according to the principle of the classical linear extended state observer, the following observer model can be obtained:

[0094]

[0095] P control feedback and compensation control are:

[0096]

[0097] The LADRC speed control structure diagram of the dual permanent magnet synchronous motor is obtained, as shown in Figure 2 shown.

[0098] According to the above simulation model built in MATLAB, given the reference speed n of the dual motor system ref =1000r / min, simulation time 0.5s. When the two motors reach the given value, PMSM1 and PMSM2 are suddenly added with load disturbances of 7N·m and 10N·m at 0.3s, respectively, and the simulation waveforms are as follows Figure 3 and Figure 4 shown.

[0099] The linear active disturbance rejection controller (LADRC) consists of a PD linear combination and a linear extended state observer (LESO). The linear active disturbance rejection controller (LADRC) mainly observes the disturbances in the speed loop through the linear extended state observer (LESO), and dynamically compensates the observed disturbances to generate control quantities to eliminate the impact of the disturbances on the system.

[0100] Taking the second-order system as an example, the basic mathematical model of LADRC is derived. First, it is assumed that the mathematical model of the controlled object is:

[0101]

[0102] In the formula, y and u are the output and input of the controlled object, ω is the disturbance of the system, a0 and a1 are unknown coefficients, and b is the controller gain. Simplifying formula (10) we get

[0103]

[0104] In the formula is the disturbance of the system.

[0105] Select state variable x1=y, Then formula (11) can be converted to:

[0106]

[0107] Where: x=[x1x2 x3] T .

[0108] According to formula (12), the expression of LESO can be established as:

[0109]

[0110] When the observer parameters β1, β2, and β3 are selected with appropriate values, the system state variables can be accurately tracked, i.e., z1→y, z2→y.

[0111] The output of the controller can be expressed as:

[0112]

[0113] If the estimation error of LESO on the system disturbance is ignored, equation (11) can be simplified to a standard integral series structure, that is,

[0114]

[0115] According to the above formula, the PD linear combination can be designed as:

[0116] u0=kp (r-z1)-k d z2 (16)

[0117] In the formula, k p , k d is the controller parameter, and r is the reference given signal.

[0118] Substituting formula (16) into formula (15), we get:

[0119]

[0120] By performing Laplace transformation on equation (17), the closed-loop transfer function of the controlled object can be obtained as follows:

[0121]

[0122] Selecting appropriate controller parameters kp and kd can make the system stable, and then the characteristic equation of LESO can be obtained as:

[0123] λ(s)=(s+ω0) 3 s 3 +β1s 2 +β2s+β3 (19)

[0124] Select the ideal characteristic equation λ(s)=(s+ω0) 3 , then the unknown parameters of the characteristic equation are:

[0125]

[0126] Where ω0 is the observer bandwidth.

[0127] According to the parameter setting rules of previous studies, the controller parameters of equation (18) are selected as:

[0128]

[0129] Where ω c is the controller bandwidth.

[0130] Step 2: Sliding mode cross-coupling controller as the speed synchronization controller between the dual motors:

[0131] A sliding mode cross-coupling controller is designed based on a cross-coupling control structure, and a sliding mode cross-coupling controller is used as a speed synchronization controller between dual motors. The sliding mode cross-coupling controller obtains a dual-axis current reference compensation amount of the dual motors through a controller according to the speed synchronization error between the dual motors, thereby enhancing the robustness of the motor when disturbed. That is, when the motor is disturbed and the speed fluctuates, the dual-axis current reference compensation amount of the dual motors is obtained by coupling the speed difference between the motors, which accelerates the convergence speed of the speed synchronization error, thereby improving the synchronization performance of the dual-motor drive system;

[0132] The design method of the sliding mode cross-coupling controller includes the following steps:

[0133] Step 1: Design the sliding surface:

[0134] The torque equations of the two motors are:

[0135]

[0136] Where, T ei is the electromagnetic torque of the motor, p i is the number of motor pole pairs, ψ fi is the permanent magnet flux of the motor’s rotor, is the q-axis current component of the motor, i is the motor number;

[0137] The equation of motion for a PMSM is:

[0138]

[0139] Where, T Li is the load torque of the motor, ΔT Li is the load disturbance on the motor, J i , B i is the moment of inertia and friction coefficient on the motor shaft, ω ei is the rotor electrical angular velocity of the motor, i is the motor number;

[0140] The state variables of the speed synchronization control system are taken as:

[0141]

[0142] Combining equations (22) and (23), the state equation of the speed synchronization control system is obtained as follows:

[0143]

[0144] Select the system integral sliding surface s as:

[0145] s=x1+cx2 (26)

[0146] Where s is the sliding surface function, c is the positive integral constant;

[0147] Step 2: Design a sliding mode cross-coupling controller based on step 1:

[0148] In order to realize sliding mode control, the constant velocity reaching law is selected, as shown in formula (28):

[0149]

[0150] In the formula, is the derivative of s;

[0151] Formula (28) combined with formula (25) and formula (26) in step 1 can obtain the output of the sliding mode speed synchronization controller as follows:

[0152]

[0153] In the formula, J = J1 = J2, p = p1 = p2, ψ f =ψ f1 =ψ f2 , B=B1=B2, ΔT L =T L1 -T L2 ;

[0154] Δi q-ref is the dual-axis current reference compensation output by the dual-motor sliding mode cross-coupling control, i q1 、i q2 are the q-axis components of the dual motor stator currents, ψ f is the permanent magnet flux, T L is the load torque of the motor, ΔT is the load torque difference of the dual motors, J is the moment of inertia of the motor, B is the friction coefficient of the motor, and p is the number of pole pairs;

[0155] Let A = 3pψ f / 2J, the principle block diagram of the sliding mode cross-coupling speed synchronization controller is obtained, as shown in Figure 2 shown.

[0156] System stability proof:

[0157] In order to make the system meet the stability requirements, the Lyapunov function is used to prove the system, and the Lyapunov function is selected as:

[0158]

[0159] The derivative is:

[0160]

[0161] Since ε and q are both constants greater than zero, no matter s is positive or negative, s and Always different signs, that is Meeting the sliding mode reachability condition can ensure that the system enters the sliding mode;

[0162] Taking the tracking error of the system entering the sliding mode (s=0) as an example, the derivative of its motion equation is:

[0163]

[0164] Solving the differential equation yields:

[0165] x1=ω1-ω2=x0e -ct , x0=x1(0) (32)

[0166] Formula (32) shows that once the system enters the sliding surface, the velocity tracking error will rapidly approach zero according to the exponential law with a time constant of 1 / c, and finally reach stability. The dynamic quality of the system tracking error can be controlled by selecting an appropriate c.

[0167] Given the reference speed n of the dual motor system ref =1000r / min, simulation time 0.5s. When the two motors reach the given value, PMSM1 and PMSM2 are suddenly added with load disturbances of 7N·m and 10N·m at 0.3s, respectively, and the simulation waveforms are as follows Figure 3 and Figure 4 shown.

[0168] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A speed synchronization method for a dual permanent magnet synchronous motor based on an anti-disturbance technology, characterized in that: The steps include: Step 1: The linear active disturbance rejection controller replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor: A linear active disturbance rejection controller is designed based on the mathematical model of the permanent magnet synchronous motor. The linear active disturbance rejection controller replaces the traditional PI controller as the speed loop controller of the dual permanent magnet synchronous motor. The linear active disturbance rejection controller is composed of a PD linear combination and a linear extended state observer. The linear active disturbance rejection controller mainly observes the disturbance of the speed loop through the linear extended state observer, and dynamically compensates the observed disturbance, thereby generating a control quantity to eliminate the influence of the disturbance on the system. Step 2: Sliding mode cross-coupling controller as the speed synchronization controller between the dual motors: A sliding mode cross-coupling controller is designed based on a cross-coupling control structure, and a sliding mode cross-coupling controller is used as a speed synchronization controller between dual motors. The sliding mode cross-coupling controller obtains a dual-axis current reference compensation amount of the dual motors through a controller according to the speed synchronization error between the dual motors, thereby enhancing the robustness of the motor when disturbed. That is, when the motor is disturbed and the speed fluctuates, the dual-axis current reference compensation amount of the dual motors is obtained by coupling the speed difference between the motors, which accelerates the convergence speed of the speed synchronization error, thereby improving the synchronization performance of the dual-motor drive system.

2. According to claim 1, a dual permanent magnet synchronous motor speed synchronization method based on auto-disturbance rejection technology is characterized in that: The linear active disturbance rejection controller models the permanent magnet synchronous motor in a synchronous rotating coordinate system, and establishes differential equations related to q-axis current, d-axis current, rotor space electrical angle, electrical angular velocity and electronic torque.

3. The speed synchronization method of a dual permanent magnet synchronous motor based on the auto-disturbance rejection technology according to claim 2 is characterized in that: The specific form of the mathematical model of the permanent magnet synchronous motor is as follows: Among them, i d and i q are the d-axis and q-axis currents, θ m is the rotor space electrical angle, ω e is the electrical angular velocity, ω m is the rotor angle, J is the moment of inertia, B is the viscous friction coefficient, T L is the torque load, Rs is the stator resistance, L d and Lq are the equivalent d-axis and q-axis inductances, ψ r is the permanent magnet flux, T e is the electromagnetic torque, p n is the number of motor pole pairs, represents the time derivative of a variable, u d 、u q is the d, q axis stator voltage.

4. The speed synchronization method of a dual permanent magnet synchronous motor based on the auto-disturbance rejection technology according to claim 3 is characterized in that: The mathematical model of the permanent magnet synchronous motor is selected to use i in the synchronous rotating coordinate system. d = 0 control strategy simplifies the differential equation and converts i d = 0 is substituted into formula (1) and equivalent transformation is performed to obtain the simplified mathematical model of permanent magnet synchronous motor in the following form: Electromagnetic torque equation: Mechanical equation of motion: Arranging equations (3) and (4) yields: set up -(Bω m +T L ) / J=f 内 , f 外 is the unknown disturbance outside the system, let y=x1,x1=ω m , x2=f 内 +f 外 , while x2 is differentiable, its derivative Then the system state equation can be obtained: In this system, the output is y, which is the rotor angular velocity; the input is i q , that is, the q-axis current.

5. The speed synchronization method of a dual permanent magnet synchronous motor based on the auto-disturbance rejection technology according to claim 4 is characterized in that: The system state equation (6) can be used to obtain the observer state equation: In the formula, C = [1 0], according to the principle of the classical linear extended state observer, the following observer model can be obtained: P control feedback and compensation control are:

6. The speed synchronization method of a dual permanent magnet synchronous motor based on the auto-disturbance rejection technology according to claim 1 is characterized in that: The design method of the sliding mode cross-coupling controller comprises the following steps: Step 1: Design the sliding surface: The torque equations of the two motors are: Where, T ei is the electromagnetic torque of the motor, p i is the number of motor pole pairs, ψ fi is the permanent magnet flux of the motor rotor, i qi is the q-axis current component of the motor, i is the motor number; The equation of motion for a PMSM is: Where, T Li is the load torque of the motor, ΔT Li is the load disturbance on the motor, J i , B i is the moment of inertia and friction coefficient on the motor shaft, ω ei is the rotor electrical angular velocity of the motor, i is the motor number; The state variables of the speed synchronization control system are taken as: Combining equations (22) and (23), the state equation of the speed synchronization control system is obtained as follows: Select the system integral sliding surface s as: s=x1+cx2 (26) Where s is the sliding surface function, c is the positive integral constant; Step 2: Design a sliding mode cross-coupling controller based on step 1: In order to realize sliding mode control, the constant velocity reaching law is selected, as shown in formula (28): In the formula, is the derivative of s; Formula (28) combined with formula (25) and formula (26) in step 1 can obtain the output of the sliding mode speed synchronization controller as follows: In the formula, J = J1 = J2, p = p1 = p2, ψ f =ψ f1 =ψ f2 , B=B1=B2, ΔT L =T L1 -T L2 ; Δi q-ref is the dual-axis current reference compensation output by the dual-motor sliding mode cross-coupling control, i q1 、i q2 are the q-axis components of the dual motor stator currents, ψ f is the permanent magnet flux, T L is the load torque of the motor, ΔT is the load torque difference of the dual motors, J is the moment of inertia of the motor, B is the friction coefficient of the motor, and p is the number of pole pairs.

7. A sliding mode cross-coupling control method according to claim 6, characterized in that: It also includes proving the system stability of the sliding mode cross-coupling control method.

8. The sliding mode cross-coupling control method according to claim 7, characterized in that: The specific process of the system stability proof is as follows: Choose the Lyapunov function as: The derivative is: Since ε and q are both constants greater than zero, no matter s is positive or negative, s and Always different signs, that is Meeting the sliding mode reachability conditions can ensure that the system enters the sliding mode.

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