Predefined time sliding mode rotating speed control method of permanent magnet synchronous motor
By designing a novel predefined time sliding mode controller and a predefined time disturbance observer, the problem that the state tracking error in traditional sliding mode control cannot converge within a finite time is solved, and the permanent magnet synchronous motor servo system achieves rapid convergence within a predefined time, thereby improving the control accuracy and stability of the system.
Patent Information
- Application Number
- CN202511505756.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-21
- Publication Date
- 2025-11-18
AI Technical Summary
In traditional sliding mode control, the state tracking error cannot converge to zero within a finite time, and the convergence time is related to the controller design parameters, making it impossible to achieve stability independently of the initial state within a predefined time.
A novel predefined-time sliding mode controller and a predefined-time disturbance observer are designed. By constructing a kinematic model of a permanent magnet synchronous motor, the speed control is performed using a predefined-time disturbance-resistant sliding mode controller, so that the system state tracking error converges within a predefined time. The disturbance observer is used to estimate and compensate for various disturbances.
This invention achieves rapid convergence of the permanent magnet synchronous motor servo system within a predefined time, independent of the initial state and controller parameters. It solves the problem of complex function-dependent convergence time in traditional methods, thereby improving the control accuracy and stability of the system.
Smart Images
Figure CN120979263A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of permanent magnet synchronous motor, and particularly relates to a predefined time sliding mode speed control method of permanent magnet synchronous motor. BACKGROUND
[0002] Permanent magnet synchronous motor system, with its energy saving, high efficiency and high reliability, is widely used in robots, machine tool processing and aerospace and other high-end equipment. However, the parameter perturbation of the motor, the nonlinearity of the motor model and the uncertainty disturbance existing in the motor control system reduce the control accuracy and stability of the system. At present, the control strategies for solving the nonlinearity, parameter perturbation and uncertain disturbance of the permanent magnet synchronous motor mainly include active disturbance rejection control, intelligent control, model predictive control and sliding mode control. Among them, the sliding mode variable structure control is essentially a special kind of nonlinear control, which can well solve the problem of nonlinear system. In the traditional sliding mode control, a linear sliding mode surface is usually selected, which will make the state tracking error unable to converge to zero in a finite time. In order to obtain better convergence performance, a terminal sliding mode control strategy is usually adopted, and a nonlinear sliding mode surface is designed to make the state tracking error converge to zero in a finite time. However, the finite time convergence cannot guarantee that the system reaches the convergence state within a certain time independently of the initial state. SUMMARY
[0003] The purpose of the present application is to solve the problems existing in the prior art, To achieve the above purpose, the present application provides the following scheme: A predefined time sliding mode speed control method of permanent magnet synchronous motor, comprising: constructing a kinematic model of the permanent magnet synchronous motor; designing a new type of predefined time sliding mode controller based on the kinematic model of the permanent magnet synchronous motor; using a predefined time disturbance observer to centrally estimate and compensate various disturbances of the system to the new type of predefined time sliding mode controller, to obtain a predefined time anti-disturbance sliding mode controller; based on the predefined time anti-disturbance sliding mode controller, performing speed control on the permanent magnet synchronous motor servo system.
[0004] Optionally, the kinematic model of the permanent magnet synchronous motor is: wherein, is the actual value of the speed, i q is the q-axis current of the motor, J is the moment of inertia, B is the sliding friction coefficient, T L is the load torque, is the rotor permanent magnet flux linkage, is the number of motor pole pairs, is the electromagnetic torque, is the derivative of the motor speed.
[0005] Optionally, the new pre-defined time sliding mode controller comprises: a new pre-defined time terminal sliding mode surface: wherein, is the new pre-defined time terminal sliding mode surface, is the difference between the motor reference speed and the actual speed, t is the integral time, is the sliding mode surface parameter, is the sign function, is the sliding mode surface parameter, is the sliding mode surface parameter, is the exponential term for realizing the fast convergence of the system state tracking error ; the pre-defined time sliding mode reaching law is: wherein, is the pre-defined time sliding mode reaching law, is the reaching law parameter, is the reaching law parameter, is the sign function.
[0006] Optionally, the new pre-defined time sliding mode controller is: wherein, is the new pre-defined time sliding mode controller, is the number of motor pole pairs, is the nominal value of the moment of inertia, is the nominal value of the flux linkage.
[0007] Optionally, based on the pre-defined time anti-disturbance sliding mode controller, the speed control of the permanent magnet synchronous motor servo system comprises: the speed control comprises a reaching stage and a sliding stage, and both the reaching stage and the sliding stage converge within the pre-defined time; in the sliding stage when when on the sliding surface, the motion of the permanent magnet synchronous motor servo control system will be limited on the sliding surface , and satisfies ; therefore, wherein, is the motor reference speed, is the derivative of the system error variable, denotes the set of all states falling on the sliding surface, denotes the system once it enters the sliding surface (s(e) = 0), its dynamics on the surface satisfy , si (·) is a sliding surface function or some kind of constraint; if , where, is the derivative of Lyapunov function, is an exponential term to achieve fast convergence of the system state tracking error and ; is a predefined time of the sliding phase, , are all constants; This satisfies the predefined time theory, so the error system will converge to zero within the predefined time in the sliding phase; In the reaching phase, the reaching time is calculated as: Integrating the above equation from zero to t, we get: where, is a predefined time of the reaching phase, is an exponential term to achieve fast convergence of the system state tracking error and ; is a reaching law parameter, is a reaching law parameter; When , , the maximum reaching time is bounded by , and the upper bound of the convergence time of the permanent magnet synchronous motor servo control system is .
[0008] Optionally, the predefined time disturbance observer is: where, is a predefined time disturbance observer, , is an actual value of the speed, is a constant, is an estimated value of the speed, is a constant.
[0009] Optionally, the final controller is: wherein, is the final controller.
[0010] The beneficial effects of the present application are: The present application proposes a predefined time sliding mode speed control method of permanent magnet synchronous motor; a new nonlinear sliding mode surface and a new predefined time reaching law are designed, the motor servo control system is independent of the initial state, the tracking error converges in the predefined time, and the convergence time and the controller design parameters are irrelevant; a predefined time disturbance observer is used to estimate and compensate the total disturbance of the motor servo control system. The present application eliminates the disadvantage that the upper bound of the convergence time in the fixed time is a complex function related to the controller design parameters, at the same time, the convergence time can be obtained by the predefined parameters, and the problem that the traditional observer cannot converge in the predefined time is also solved. BRIEF DESCRIPTION OF DRAWINGS
[0011] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.
[0012] Figure 1 The figure is a flowchart of the predefined time sliding mode speed control method of the permanent magnet synchronous motor of the embodiment of the present application. DETAILED DESCRIPTION
[0013] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.
[0014] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.
[0015] As Figure 1 shown, the present embodiment proposes a predefined time sliding mode speed control method of permanent magnet synchronous motor, which comprises: constructing a kinematic model of permanent magnet synchronous motor; designing a new type of predefined time sliding mode controller based on the kinematic model of the permanent magnet synchronous motor; The predefined time disturbance observer is used to centrally estimate and compensate various disturbances of the system to the new type of predefined time sliding mode controller, so as to obtain a predefined time anti-disturbance sliding mode controller. Based on the predefined time anti-disturbance sliding mode controller, the speed control of the permanent magnet synchronous motor servo system is performed.
[0016] Specifically, in the embodiment, the permanent magnet synchronous motor kinematics model comprises: The permanent magnet synchronous motor kinematics model equation is established as: (1) ; (2) ; Substituting equation (2) into equation (1) can obtain: (3) ; wherein, is the motor speed, i q is the motor q-axis current, J is the rotational inertia, B is the sliding friction coefficient, T L is the load torque, is the rotor permanent magnet flux linkage, is the number of motor pole pairs, is the electromagnetic torque.
[0017] When the motor has parameter perturbation, uncertainty and external disturbance, the motor kinematics equation (3) can be rewritten as: (4) ; wherein , and are the nominal values of the rotational inertia, the flux linkage and the viscous friction coefficient, , and are the mismatched values of the rotational inertia, the flux linkage and the viscous friction coefficient.
[0018] At this time, equation (4) can be rewritten as: (5) ; wherein , is an unknown nonlinear centralized disturbance including parameter mismatch and external load torque. .
[0019] Specifically, in the embodiment, the new type of predefined time terminal sliding mode controller comprises: (1) Predefined time control theory: Consider a system with the following differential equation: (6) ; In equation (6), For the system state, the initial value is , It is known. If formula (6) can achieve global stability within a predefined time , The predefined time is set by the user himself, and it is called a predefined time stable, where the stable time is .
[0020] For system (6), if there is a positive definite Lyapunov function Satisfy the following conditions: (7); Then: 1) If , the system is globally stable within a predefined time and converges to an equilibrium point.
[0021] (8); 2) If , then And it indicates that the system state is always at the equilibrium point.
[0022] In the formula is the predefined time, , , . Then the system (8) is stable in a predefined time, and the convergence time of the system is predetermined and can be adjusted flexibly according to actual needs. It can be obtained and .
[0023] Proof: (9); From which , .
[0024] (2) Design a new type of predefined time terminal sliding mode surface as: (10); In the formula , is the speed reference value, is the actual speed value, , , , .
[0025] (3) Design the predefined time sliding mode approach law as: (11); In the formula , ; Combining formula (10), (11) can be obtained: (12).
[0026] Specifically, in the embodiment, based on the new type of predefined time sliding mode controller, the permanent magnet synchronous motor servo control system is controlled, and the permanent magnet synchronous motor servo control system is independent of the initial state to realize that the state tracking error converges within a predefined time, which includes: The permanent magnet synchronous motor servo control system is controlled by formula (12), so that the controller converges within a predefined time in the sliding mode stage and the approach stage, and the convergence time is independent of the initial state of the system.
[0027] (1) In the sliding mode stage When on the sliding surface, its movement will be limited to the sliding surface , and satisfies ; therefore, (13); represents the set of all states (or error variables) falling on the sliding surface, represents that the system once enters the sliding surface (s(e)=0), and the dynamic on the surface satisfies , si(·) is a sliding surface function or some constraint; If , (14); This satisfies the predefined time theory, so the error system will converge to zero within a predefined time in the sliding stage; In the approach stage, the arrival time is calculated as: (15); Integrate formula (15) from zero to t to obtain: (16); When , , the minimum bound of the maximum arrival time is , so the predefined time stable equilibrium point of the origin (11) is obtained, and the upper bound of the convergence time of the entire PMSM system is .
[0028] Specifically, in the embodiment, the predefined time disturbance observer is designed as follows: The sliding surface of the predefined time disturbance observer (PTDO) is defined as: (17); The proposed predefined time observer is designed as: (18); wherein is the speed estimation value, , ; According to equation (5), it can be obtained that: (19) . (20); The Lyapunov function is constructed as , and the derivative of can be expressed as (21); wherein , , let , it is obvious that , thus the proposed disturbance observer can achieve stability, and equation (21) can be derived as (22); Then, by solving equation (22), the stabilization time of the estimation error from the initial value to zero can be calculated. Similar to the calculation process of equations (14) - (16), it can be obtained that , which indicates that the designed disturbance observer can achieve stability within a predefined time independent of the initial state.
[0029] Specifically, by compensating the predefined time disturbance observer (PTDO) into the predefined time stable sliding mode control law (12), the final controller can be obtained as: (23); wherein, is the final controller.
[0030] The embodiment proposes a fixed time convergence strategy so that the convergence time is independent of the initial conditions of the system and only related to the controller design parameters. However, the upper bound of the convergence time is closely related to the design parameters, and the convergence time estimation is relatively conservative. Therefore, a predefined time stability is proposed. For a predefined time stable system, the upper bound of the convergence time is determined by a single parameter, which can make the system state converge to the equilibrium point within a predetermined designed time, and the convergence time is independent of the initial conditions of the system and the control parameters of the system, which can be set in advance by the designer according to the actual situation.
[0031] The above described embodiments are only to illustrate the preferred modes of the present application, and are not intended to limit the scope of the present application. Any modification and improvement made by those skilled in the art to the technical solutions of the present application without departing from the design spirit of the present application shall fall within the protection scope of the present application as defined by the claims.
Claims
1. A predefined time sliding mode speed control method for a permanent magnet synchronous motor, characterized in that, include: Construct a kinematic model of a permanent magnet synchronous motor; Based on the kinematic model of the permanent magnet synchronous motor, a novel predefined time sliding mode controller is designed. By using a predefined time disturbance observer to centrally estimate and compensate for various disturbances in the system, a predefined time disturbance-resistant sliding controller is obtained. Based on the predefined time-resistant sliding mode controller, the speed control of the permanent magnet synchronous motor servo system is performed.
2. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that, The kinematic model of the permanent magnet synchronous motor is as follows: in, i represents the actual rotational speed. q Let J be the q-axis current of the motor, J be the moment of inertia, B be the coefficient of sliding friction, and T be the coefficient of friction. L For load torque, For rotor permanent magnet flux linkage, This represents the number of pole pairs of the motor. For electromagnetic torque, This is the derivative of the motor speed.
3. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that, The novel predefined time sliding mode controller includes: Novel predefined time-terminal sliding surface: in, For a new type of predefined time terminal sliding surface, Let t be the difference between the motor's reference speed and its actual speed, and t be the integration time. For sliding surface parameters, For symbolic functions, For sliding surface parameters, For sliding surface parameters, The exponential term is used to achieve rapid convergence of system state tracking errors; The predefined time sliding mode reaching law is: in, For a predefined time sliding mode reaching law, For the approach law parameters, For the approach law parameters, It is a symbolic function.
4. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 3, characterized in that, The novel predefined time sliding mode controller is: in, For a new type of predefined time sliding mode controller, This represents the number of pole pairs of the motor. This is the nominal value of the moment of inertia. This is the nominal value of the magnetic flux linkage.
5. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that, Based on the predefined time-resistant sliding mode controller, speed control of the permanent magnet synchronous motor servo system includes: Speed control includes a convergence phase and a sliding phase, both of which converge within a predefined time. During the sliding mode When the permanent magnet synchronous motor servo control system is on the sliding surface, the motion will be limited to the sliding surface. And satisfy ;therefore: in, This is the reference speed for the motor. The derivative of the system error variable. This represents the set of all states that fall on the sliding surface. This indicates that once the system enters the sliding surface (s(e)=0), its dynamics on that surface satisfy... , si (·) represents a sliding surface function or a constraint; if , in, The derivative of the Lyapunov function. The exponential term is used to achieve rapid convergence of system state tracking errors; For the predefined time of the sliding mode phase, , All are constants; This satisfies the predefined time theory, therefore the error system will be in the predefined time during the sliding phase. The convergence is zero. During the approach phase, the arrival time is calculated as follows: Integrating the above equation from zero to t, we get: in, For the predefined time of the approach phase, To achieve rapid convergence of the system state tracking error, the exponential term and ; For the approach law parameters, To approximate the law number; when , Maximum arrival time The minimum bound is The upper bound of the convergence time of the permanent magnet synchronous motor servo control system is .
6. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that, The predefined time-interference observer is: in, For a predefined time disturbance observer, , This is the actual rotational speed. It is a constant. This is an estimated value for the rotational speed. It is a constant.
7. The predefined time sliding mode speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that, The predefined time-resistant sliding mode controller is: in, For a predefined time-resistant sliding mode controller.