Cross coupling double asynchronous motor synchronous control method based on sliding mode control

Abstract

The invention discloses a sliding mode control-based synchronous control method for cross-coupled double asynchronous motors. The method comprises the following steps: firstly, establishing a mathematical model of an asynchronous motor in a two-phase synchronous rotating coordinate system; secondly, on the basis of single-motor vector control, a cross coupling control strategy is introduced, and the output rotating speed of the two motors serves as the input quantity and is fed back to a vector control closed loop through a synchronous controller; finally, a synchronous controller is designed based on sliding mode control, the rotating speed error serves as a control state variable, a proportional-integral sliding mode surface is constructed, compared with a traditional proportional-integral sliding mode surface, the dynamic performance is further improved, and meanwhile a novel reaching law is introduced to reduce buffeting. The method has good dynamic and static performance, good anti-interference capability and robustness to motor parameters.

Description

Technical Field

[0001] The present invention relates to the field of asynchronous motor synchronous control, and particularly to a synchronous control method for cross-coupled dual asynchronous motors based on sliding mode control Background Art

[0002] Due to its advantages such as simple structure, reliable operation, and strong adaptability, asynchronous motors are widely used in various industries of the national economy and daily life. With the development of science and technology, while pursuing high output power, people also pay attention to the coordination among motors in the system, and put forward higher requirements for the synchronization of multiple motors driving and conveying on the production line in industrial production and the front and rear drive multiple motors of new energy vehicles. The synchronous control of multiple motors has gradually developed. In the application scenarios of dual asynchronous motors, it is necessary to design appropriate controllers according to different requirements to meet the actual application requirements. Therefore, the research on the high-performance synchronous control of dual asynchronous motors has profound significance

[0003] In the prior art, the cross-coupling control strategy is widely used in the synchronous control system of dual asynchronous motors due to its good dynamic and static performance in synchronous control. The traditional cross-coupled synchronous controller is designed by PID and is sensitive to external disturbances and motor parameter changes, which affects the synchronous control performance. Therefore, improving the synchronous controller is the key to improving the cross-coupled synchronous control performance. The literature "Yang Dongxu, Jia Shaofeng, Liang Deliang, et al. Coordination control strategy under synchronous conditions of permanent magnet brushless hub motor wheel pair system [J]. Proceedings of the Chinese Society for Electrical Engineering, 2024, 44(6): 2418-2427, Insert 28 at the end." adopts speed loop compensation and current loop compensation to improve the rotational speed synchronization accuracy and accelerate the synchronous response speed, but does not improve the PID synchronous controller. The literature "Jin Hongyan, Zhao Ximei. Elman neural network complementary sliding mode cross-coupled synchronous control for dual linear motor servo systems [J]. Transactions of China Electrotechnical Society, 2018, 33(21): 4971-4978." proposes a synchronous control scheme based on the combination of an Elman neural network complementary sliding mode controller (CSMC) and a cross-coupling controller (CCC), designs an Elman neural network CSMC to estimate system uncertainties and weaken the chattering phenomenon existing in sliding mode control, and enhances the anti-disturbance performance of the system. However, the improvement of this control system is optimized for vector control, indirectly improving the synchronous control accuracy, and there is still room for improvement in its dynamic performance

[0004] The literature "Lin F J, Chou P H, Chen C S. DSP-based synchronous control of dual linear motors via sugeno type fuzzy neural network compensator[C]. 2011 International Conference on Electrical Machines and Systems, Beijing, China, 2011, pp. 1-6." uses a Sugeno type fuzzy neural network as a cross-coupling compensator to enhance the synchronous effect of dual motors with complementary sliding mode control. However, the introduction of the fuzzy network makes the system more complex and increases the computational load. The literature "Li Yuanqing, Cheng Shanmei. Speed synchronization control of dual permanent magnet motors based on sliding mode cross-coupling[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2024(3): 114-118, 123." proposes a cross-coupling synchronous controller based on sliding mode control. However, traditional proportional-derivative sliding mode surfaces and exponential reaching laws are used, and the chattering phenomenon of sliding mode control is not suppressed, which affects the dynamic and static performance of synchronous control.

[0005] The main problems existing in the above control system are as follows: poor dynamic and static performance, strong dependence on the motor mathematical model, etc. Summary of the Invention

[0006] Technical Problem: The purpose of the present invention is to propose a synchronous control method for cross-coupled dual asynchronous motors based on sliding mode control, so as to obtain a synchronous control system with strong anti-disturbance ability and fast dynamic regulation speed, and the control performance is not affected by the change of motor parameters.

[0007] Technical Solution: To achieve the above purpose, a synchronous control method for cross-coupled dual asynchronous motors based on sliding mode control of the present invention includes:

[0008] Step 1. Establish the mathematical model of the asynchronous motor in the two-phase synchronous rotating coordinate system through Clark and Park coordinate transformations, which serves as the basis for designing the parameters of the vector control and the sliding mode controller.

[0009] Step 2. To achieve the speed synchronization of the dual motors, based on vector control, select a cross-coupling control strategy. Use the speeds of the two motors as the inputs of the synchronous controller, and the output is fed back to the vector control closed-loop to construct a dual-motor synchronous control system.

[0010] Step 3. Aiming at the defect that the traditional cross-coupling synchronous controller is vulnerable to system parameter changes and external disturbances, a synchronous controller is designed using sliding mode control to improve the anti-disturbance ability and robustness of the synchronous system.

[0011] Step 4. A new reaching law is designed to weaken the chattering problem inherent in traditional sliding mode control. At the same time, an integral sliding mode surface is adopted to improve the synchronous control performance and reduce the rotational speed synchronization error.

[0012] Among them,

[0013] In Step 1, the mathematical model of the asynchronous motor in the two-phase synchronous rotating coordinate system is established, specifically as follows:

[0014] Through Clark and Park transformations, the three-phase natural coordinate system is converted to the two-phase rotating coordinate system:

[0015]

[0016] where θ e is the electrical angle, and f d represents the direct-axis voltage, current, and flux linkage; f q represents the quadrature-axis voltage, current, and flux linkage; f 0 represents the neutral-point voltage, current, and flux linkage; f A represents the phase-A voltage, current, and flux linkage; f B represents the phase-B voltage, current, and flux linkage; f C represents the phase-C voltage, current, and flux linkage;

[0017] According to the above formula, the voltage equation of the asynchronous motor in the two-phase synchronous rotating coordinate system without considering disturbances is:

[0018]

[0019] where u ds , u qs are the direct-axis and quadrature-axis stator voltages; u dr , u qr are the direct-axis and quadrature-axis rotor voltages; R s , R r are the stator and rotor resistances; i ds , i qs are the direct-axis and quadrature-axis stator currents; i dr , i qr are the direct-axis and quadrature-axis rotor currents; ψ ds , ψ qs are the direct-axis and quadrature-axis stator flux linkages; ψ dr , ψ qr are the direct-axis and quadrature-axis rotor flux linkages; ω e is the electrical angular velocity; ω r is the rotor angular velocity; in a squirrel-cage asynchronous motor, u dr = u qr = 0, and in vector control, with rotor flux linkage orientation, ψ qr = 0, ψ dr = ψr , simplified to:

[0020]

[0021] Where, L s and L r are the equivalent self - inductances of the stator and rotor, and L m is the equivalent mutual inductance between the stator and rotor;

[0022] The electromagnetic torque equation is:

[0023]

[0024] Where, T e is the electromagnetic torque; n p is the number of pole pairs; Since the rotor current is not measurable, the rotor current is expressed in terms of the stator current and simplified to

[0025]

[0026] The rotor motion equation is

[0027]

[0028] Where J is the moment of inertia of the induction motor; ω m is the mechanical angular velocity; T L is the load torque; B is the friction coefficient.

[0029] The specific content of step 2 is:

[0030] Design vector control parameters

[0031]

[0032] Where K pc and K ic are the proportional and integral parameters of the current inner loop; ω cc is the cut - off frequency of the current inner loop; σ is the leakage magnetic coefficient; R is the equivalent resistance; K ps and K is are the proportional and integral parameters of the speed outer loop; ω cs is the cut - off frequency of the speed outer loop; ξ is the damping ratio of the standard second - order system;

[0033] For the synchronous control of dual motors, the cross - coupling control and the deviation - coupling control have the same accuracy. Both are to subtract the output speeds of the two motors and then feedback through a signal compensator to the control loop of this motor. The deviation - coupling control is more suitable for the control of more than two motors; finally, the cross - coupling control strategy is selected. Taking the speeds of the two motors as the input of the synchronous controller, the output is fed back into the vector control closed - loop to construct a dual - motor synchronous control system.

[0034] The specific content of step 3 is:

[0035] Select the rotational speed error x 1 as the state variable of the synchronous controller

[0036]

[0037] where ω r1 and ω r2 are the rotational speeds of motor 1 and motor 2; e ω is the rotational speed difference of the motors, and x 2 is the integral of the rotational speed error;

[0038] Select the proportional-derivative sliding mode surface

[0039]

[0040] where s is the sliding mode surface; c is the sliding mode surface parameter;

[0041] Adopt the exponential reaching law

[0042]

[0043] where k, ε are positive real numbers; sgn(·) is the sign function;

[0044] Let the output compensation of the sliding mode synchronous controller be Compensate the given quadrature axis current of the outer speed loop output and then send it into the vector control current inner loop. The compensated quadrature axis current reference value is

[0045]

[0046] The specific step 4 is as follows:

[0047] Select the proportional-integral sliding mode surface

[0048] s = cx 2 + x 1 = x 1 + c∫x 1

[0049] Design the parameter adjustment function

[0050] f(s) = a·arctan(tanh(|s|))

[0051] where a is a positive real number;

[0052] Select the saturation function

[0053]

[0054] where Δ is the boundary layer thickness;

[0055] Improve the traditional exponential reaching law and design a new reaching law as

[0056]

[0057] For the above formula, when the sliding mode surface s is large, the parameter adjustment function f(s) remains constant, and the reaching speed remains at a large value. When the sliding mode surface s is small, the parameter adjustment function f(s) decreases rapidly, and the reaching speed also decreases rapidly, weakening the chattering caused by the switching along the sliding mode surface. When the sliding mode surface s changes sign, the saturation function sat(s) switches more gently than the sign function sgn(s), avoiding large - amplitude switching and further weakening the chattering of the sliding mode control.

[0058] Beneficial effects: The essential effect of the present invention is: to provide a cross - coupled synchronous control model of dual - asynchronous motors based on sliding mode control with better dynamic performance and strong disturbance rejection ability. The better dynamic performance is reflected in that during the starting stage and when the given speed suddenly changes, the speeds of the two motors can always remain synchronized. The strong disturbance rejection ability is reflected in that when the load is suddenly applied or removed, the speeds of the two motors change synchronously, keeping the speed difference within a certain small range. Description of the drawings

[0059] Figure 1 is the overall control block diagram of the control system;

[0060] Figure 2 is the vector control simulation model;

[0061] Figure 3 is the quadrature - axis compensation current output

[0062] Figure 4 is the overall control system simulation model;

[0063] Figure 5 is the simulated output speed of the present invention;

[0064] Figure 6 is the synchronous error of the output speed of the original cross - coupled control based on PID;

[0065] Figure 7 is the synchronous error of the output speed of the original cross - coupled control based on SMC;

[0066] Figure 8 is the synchronous error of the output speed of the present invention. Detailed implementation manners

[0067] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. Therefore, the detailed description of the embodiments of the present invention provided below is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention.

[0068] The cross-coupled dual-asynchronous motor synchronous control method based on sliding mode control adopted by the present invention provides a vector control method for a squirrel-cage asynchronous motor, including:

[0069] S1: Establish the mathematical model of the asynchronous motor in the two-phase rotating coordinate system.

[0070] S2: Design the vector control parameters, select the cross-coupled control strategy, use the speeds of the two motors as the inputs of the synchronous controller, and feedback the output into the vector control closed-loop to construct a dual-motor synchronous control system.

[0071] S3: Considering that the PID control is vulnerable to external disturbances and changes in motor parameters, design a synchronous controller based on sliding mode control to compensate the quadrature-axis current, improve the anti-disturbance ability and robustness of the synchronous system. Use the speed difference between the two motors as the input, and superimpose the output compensation value on the reference quadrature-axis current signal output by the speed loop, and output the compensated reference current to the current-loop PI controller.

[0072] S4: Aiming at the inherent chattering problem of traditional sliding mode control, design a new reaching law to weaken the chattering. At the same time, adopt an integral sliding surface to improve the synchronous control performance and reduce the speed synchronization error.

[0073] Preferably, S1 of the present invention is specifically as follows:

[0074] Convert the asynchronous motor model in the three-phase natural coordinate system to the two-phase rotating coordinate system. The voltage equation is (squirrel-cage asynchronous motor)

[0075]

[0076] The electromagnetic torque equation is

[0077]

[0078] The motion equation is

[0079]

[0080] Preferably, S2 of the present invention is specifically as follows:

[0081] First, obtain the transfer function of the vector control system. Starting from the inner current loop design, the closed-loop transfer function is

[0082]

[0083] where, I q is the quadrature-axis current, is the given value of the quadrature-axis current. Using the method of zero-pole cancellation, let K ic / K pc = R / σL s , and transform the current loop into a typical first-order system. The closed-loop transfer function can be transformed into

[0084]

[0085] Design the vector control parameters of the current loop from Equation (5), and we can obtain

[0086]

[0087] By determining the cut-off frequency ω cc determine the parameters K pc and K ic .

[0088] When designing the speed loop, regard the current loop as 1, and the closed-loop transfer function of the speed loop can be obtained as

[0089]

[0090] where, is the given value of the mechanical angular velocity of the motor, and ξ, ω n are the parameters of the standard second-order system.

[0091] Equation (7) has an extra zero compared to the standard second-order system, and the zero will increase the overshoot of the system. A correction link needs to be added to eliminate the zero. The designed correction link is

[0092]

[0093] The closed-loop transfer function of the corrected speed loop is

[0094]

[0095] Equation (9) shows that the speed loop is a standard second-order system. After determining the parameter ξ, ω cs = ω n , and further the parameters K ps and K is are

[0096]

[0097] Select the rotational speeds ω of the two motorsr1 and ω r2 are the inputs of the cross - coupled synchronous controller, and the output is fed back into the vector control closed - loop to compensate for the given quantity.

[0098] Preferably, step S3 of the present invention is specifically:

[0099] Select the state error e ω = ω r1 - ω r2 as the control state variable

[0100]

[0101] Select the proportional - derivative sliding mode surface

[0102]

[0103] where s is the sliding mode surface and the parameter c > 0. Taking the derivative of s gives

[0104]

[0105] Adopt the exponential reaching law

[0106]

[0107] From Equation (2) and Equation (3), the derivative of the rotational speed can be obtained as

[0108]

[0109] Combining Equation (13), Equation (14) and Equation (15), the calculation gives

[0110]

[0111] Finally, the calculation gives

[0112]

[0113] According to the Lyapunov function There is

[0114]

[0115] Since sgn(s) has the same sign as s, so - εsgn(s)s ≤ 0 and - ks 2 ≤ 0.

[0116] In summary, This sliding - mode controller can converge to the sliding - mode surface within a finite time, and the control system is stable.

[0117] Preferably, step S4 of the present invention is:

[0118] First, select the state error e ω = ω r1 - ω r2 as the control state variable

[0119]

[0120] Select the integral sliding mode surface

[0121]

[0122] where s is the sliding mode surface and the parameter c > 0. Taking the derivative of s gives

[0123]

[0124] Design the parameter adjustment function

[0125]

[0126] where a is a positive real number.

[0127] Select the quasi-sliding mode dynamic saturation function

[0128]

[0129] where the boundary layer thickness Δ > 0.

[0130] Design the new reaching law

[0131]

[0132] where both k and ε are positive real numbers. The main purpose of this new reaching law is to reduce the chattering phenomenon generated by traditional sliding mode control. A parameter adjustment function is added before the sign function. During the reaching stage, since s is large, the output value of the sign function term is large to ensure the rapid convergence of the rotational speed. When the motion state reaches the sliding mode surface and enters the sliding mode, since the value of s is small, the output of the sign function term can be reduced to reduce chattering.

[0133] In summary, the final calculation gives

[0134]

[0135] where is the cross-axis current compensation value of Motor 1 and Motor 2.

[0136] According to the Lyapunov function There is

[0137] · = · = - 2 -εa·arctan(tanh(|s|))sgn(s)s (28)

[0138] Since sat(s) has the same sign as s and f(s) = a·arctan(tanh(|s|)) is non - negative, thus -ks 2 ≤0 and -εa·arctan(btanh(d|s|))sgn(s)s ≤ 0.

[0139] In summary, This sliding - mode controller can converge to the sliding - mode surface within a finite time, making the control system stable.

[0140] Example:

[0141] A synchronous control method for cross - coupled dual - asynchronous motors based on sliding - mode control of the present invention mainly includes the following steps:

[0142] First, establish the mathematical model of the asynchronous motor in the two - phase rotating coordinate system. According to the voltage equation and torque equation of the asynchronous motor in the three - phase natural coordinate system, we can obtain

[0143]

[0144]

[0145] Combined with the motion equation, we have

[0146]

[0147] Then, design the vector - control parameters, and we have

[0148]

[0149] Next, select the cross - coupling control strategy and design a synchronous controller based on sliding - mode control.

[0150] Select the sliding - mode surface as

[0151] s = x 1 +c∫x 1 (33)

[0152] Design the parameter - adjustment function

[0153] f(s) = a·arctan(tanh(|s|)) (34)

[0154] Select the quasi - sliding - mode dynamic saturation function

[0155]

[0156] Combine Equation (34) and Equation (35) to design a new reaching law

[0157]

[0158] Design the quadrature-axis current compensation values of Motor 1 and Motor 2 by combining Equation (31), Equation (33) and Equation (36).

[0159]

[0160]

[0161] Finally, the stability of the controller was verified using the Lyapunov function.

[0162] A simulation block diagram of the cross-coupled synchronous control system for dual asynchronous motors based on sliding mode control as shown in Figure 4 was established in the simulation software.

[0163] A model-free sliding mode control system simulation model of a permanent magnet synchronous motor with a reduced-order PI observer as shown was established on the Matlab / Simulink simulation platform. The motor parameters were set as shown in Table 1 during the simulation.

[0164] Table 1 Motor parameter settings

[0165]

[0166] Figure 5 The simulated output speed of the present invention is shown. The reference speed was 400 rpm during the start-up phase, increased to 800 rpm at 0.2 s, a load torque of 5×10 4 N·m was applied at 0.3 s, and the torque load was removed at 0.4 s. It can be seen from the figure that the control system provided by the present invention has fast speed regulation and good rotational speed synchronization during the start-up phase. The present invention also maintains good control performance when the reference speed changes from 400 rpm to 800 rpm, and can quickly return to the given speed value after the load is applied and removed.

[0167] Figures 6 - 8 The synchronous error of the output speed of the three control algorithms is shown. It can be seen from the figure that the control system provided by the present invention can maintain good synchronous control performance both dynamically and statically.

Claims

1. A cross-coupled dual asynchronous motor synchronous control method based on sliding mode control, characterized in that: The method includes: Step 1. Establish a mathematical model of the asynchronous motor in a two-phase synchronous rotating coordinate system, and use Clark and Park coordinate transformation as the basis for designing vector control and sliding mode controller parameters; Step 2. To achieve dual motor speed synchronization, based on vector control, a cross-coupling control strategy is selected, the speeds of the two motors are used as the input of the synchronization controller, and the output is fed back to the vector control closed loop to build a dual motor synchronization control system; Step 3. Aiming at the defect that the traditional cross-coupled synchronous controller is easily affected by system parameter changes and external disturbances, it is proposed to design a synchronous controller using sliding mode control to improve the anti-disturbance and robustness of the synchronous system; Step 4. Aiming at the inherent chattering problem of traditional sliding mode control, a new reaching law is designed to reduce the chattering. At the same time, an integral sliding mode surface is used to improve the synchronous control performance and reduce the speed synchronization error.

2. The cross-coupled dual asynchronous motor synchronous control method based on sliding mode control according to claim 1 is characterized in that: The step 1 establishes a mathematical model of an asynchronous motor in a two-phase synchronous rotating coordinate system, specifically: Through Clark and Park transformation, the three-phase natural coordinate system is converted to the two-phase rotating coordinate system: Among them, θ e is the electrical angle, f d represents the direct-axis voltage, current and flux; f q represents the cross-axis voltage, current and flux; f0 represents the neutral point voltage, current and flux; f A Indicates the voltage, current and flux of phase A; f B Indicates the voltage, current and flux of phase B; f C Indicates the voltage, current and flux linkage of phase C; According to the above formula, the voltage equation of the asynchronous motor in the two-phase synchronous rotating coordinate system without considering disturbance is: Among them, u ds 、u qs is the direct-axis and quadrature-axis stator voltage; u dr 、u qr are the direct-axis and quadrature-axis rotor voltages; R s , R r is the stator and rotor resistance; i ds 、i qs are the direct-axis and quadrature-axis stator currents; i dr 、i qr are the direct-axis and quadrature-axis rotor currents; ψ ds , qs is the direct-axis and quadrature-axis stator flux; ψ dr , qr is the direct-axis and quadrature-axis rotor flux; ω e is the electrical angular velocity; ω r is the rotor angular velocity; in a squirrel cage asynchronous motor, u dr =u qr =0, in vector control, according to the rotor flux orientation, there is ψ qr =0,ψ dr =ψ r , which is simplified to: Among them, L s , L r is the equivalent self-inductance of the stator and rotor, L m is the stator-rotor equivalent mutual inductance; The electromagnetic torque equation is: Among them, T e is the electromagnetic torque; n p is the number of pole pairs; since the rotor current cannot be measured, the rotor current is expressed by the stator current and simplified to The rotor motion equation is Where J is the moment of inertia of the asynchronous motor; ω m is the mechanical angular velocity; T L is the load torque; B is the friction coefficient.

3. The cross-coupled dual asynchronous motor synchronous control method based on sliding mode control according to claim 2 is characterized in that: The step 2 is specifically as follows: Design vector control parameters Where K pc , K ic is the current inner loop proportional and integral parameter; ω cc is the cut-off frequency of the inner current loop; σ is the magnetic leakage coefficient; R is the equivalent resistance; K ps , K is is the proportional and integral parameter of the speed outer loop; ω cs is the cut-off frequency of the outer speed loop; ξ is the damping ratio of the standard second-order system; For dual-motor synchronous control, cross-coupling control and deviation coupling control have the same accuracy. Both of them make the output speed of the two motors different and then feed it back to the control loop of the motor through a signal compensator. Deviation coupling control is more suitable for multi-motor control of more than two motors. Finally, the cross-coupling control strategy is selected, with the speed of the two motors as the input of the synchronous controller, and the output is fed back to the vector control closed loop to build a dual-motor synchronous control system.

4. The cross-coupled dual asynchronous motor synchronous control method based on sliding mode control according to claim 3 is characterized in that: Step 3 is as follows: Select the speed error x1 as the state quantity of the synchronous controller where ω r1 ,ω r2 is the speed of motor 1 and motor 2; e ω is the motor speed difference, x2 is the speed error integral; Select proportional-differential sliding surface Where s is the sliding surface; c is the sliding surface parameter; Exponential Reaching Law where k and ε are positive real numbers; sgn(·) is a sign function; Assume that the output compensation of the sliding mode synchronous controller is The output of the speed outer loop is given by the quadrature axis current After compensation, it is sent to the vector control current inner loop. The reference value of the quadrature axis current after compensation is 5. The cross-coupled dual asynchronous motor synchronous control method based on sliding mode control according to claim 4 is characterized in that: The step 4 is specifically as follows: Select proportional-integral sliding surface s=cx2+x1=x1+c∫x1 Design parameter adjustment function f(s) = a·arctan(tanh(|s|)) Where a is a positive real number; Select saturation function Where Δ is the boundary layer thickness; The traditional exponential reaching law is improved and a new reaching law is designed: For the above formula, when the sliding surface s is large, the parameter adjustment function f(s) remains constant and the approach speed is maintained at a large value. When the sliding surface s is small, the parameter adjustment function f(s) decreases rapidly and the approach speed also decreases rapidly, reducing the chattering caused by switching along the sliding surface. When the sliding surface s changes its sign, the saturation function sat(s) switches more gently than the sign function sgn(s), avoiding large-scale switching and further reducing the chattering of the sliding mode control.

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