Model-free preset time sliding mode control method of permanent magnet synchronous motor

Abstract

The invention discloses a model-free predetermined time sliding mode control method for a permanent magnet synchronous motor, and the method specifically comprises the steps: building a rotating speed ring super-local model according to the system characteristics of the permanent magnet synchronous motor and in combination with a model-free theory; a model-free preset time sliding mode disturbance observer is designed to estimate the lumped disturbance, including design of an observer sliding mode surface function and design of a lumped disturbance estimated value change law, and stability analysis is carried out; and designing a model-free preset time sliding mode controller, namely designing a sliding mode surface function of the controller, designing a sliding mode reaching law, and performing stability analysis. According to the method, the model-free theory, the preset time stability theory, the sliding mode controller and the sliding mode disturbance observer are combined, the complexity of a system model and the sensitivity to motor parameters are reduced, finally, the system can be stable within preset time, and buffeting of a traditional sliding mode control method can be effectively weakened. The problem of stable tracking control of the permanent magnet synchronous motor under lumped disturbance can be effectively solved.

Description

Technical Field

[0001] The invention relates to the field of nonlinear system control of permanent magnet synchronous motors, and in particular to a model-free scheduled time sliding mode control method based on a model-free scheduled time sliding mode disturbance observer for permanent magnet synchronous motors. Background Art

[0002] Permanent magnet synchronous motors are widely used in military industry, aerospace and other fields due to their high efficiency and high reliability. However, the military industry, aerospace and other fields have extremely high requirements for the accuracy, stability and reliability of permanent magnet synchronous motors. At present, PID control method is widely used in the control of permanent magnet synchronous motors, but because it is a complex nonlinear system, PID is difficult to deal with these nonlinear factors, which makes it difficult for PID control to accurately control permanent magnet synchronous motors. Model predictive control is also used in the control of motors, which can make more accurate predictions of future states, but the performance of model predictive control depends to a large extent on the accuracy of the controlled object model, and the calculation amount is large, and the parameter adjustment process is complicated. These problems make it difficult for model predictive control to achieve high accuracy in the control of strongly coupled nonlinear systems such as permanent magnet synchronous motors. The sliding mode control algorithm is widely used in the field of nonlinear system control because of its simple structure and insensitivity to the control parameters of the controlled object. However, the traditional sliding mode control algorithm has a significant problem, that is, it is easy to produce chattering, which seriously limits its application scope in practical engineering. Therefore, it is of great significance to study how to suppress the chattering of the sliding mode control algorithm and apply it to the control of permanent magnet synchronous motors. Reference ["Anti-disturbance speed control of low-speed high-torque PMSM based on second-order non-singular terminal sliding mode load observer."ISA transactions 88(2019):142-152.] designed a sliding mode controller and a second-order non-singular terminal sliding mode disturbance observer to estimate the disturbance caused by the load torque in the permanent magnet synchronous motor, so as to compensate it in the sliding mode controller, which can effectively suppress the jitter caused by the traditional sliding mode control algorithm. Reference ["Sliding mode control for synchronization of fractional permanent magnet synchronous motors with finite time."Optik-InternationalJournal for Light and Electron Optics 127.6(2016):3329-3332] proposed a sliding mode control method based on fractional order stability theory, which can make the system stable within a finite time. However, the permanent magnet synchronous motor is a complex nonlinear system with characteristics such as parameter drift, unmodeled dynamics, friction and load disturbance, which leads to certain limitations of the constructed mathematical model and affects the motor control accuracy.Because the model-free theory does not rely on the mathematical model of the controlled system, it reduces the complexity of the system model and the sensitivity to the motor parameters, and effectively overcomes certain limitations of the mathematical model of the permanent magnet synchronous motor. In recent years, the scheduled time stability method has been proposed. The system convergence time is independent of the initial state of the system. The convergence time can be set according to the requirements. The system can be stable within the scheduled time, which can meet the requirements of the military industry and aerospace for control system performance. Therefore, based on the model-free theory, the study designs the super-local mathematical model of the permanent magnet synchronous motor, and combines it with the scheduled time stability method to design a model-free scheduled time sliding mode controller and a model-free scheduled time sliding mode disturbance observer, so as to reduce the control algorithm's dependence on the mathematical model of the permanent magnet synchronous motor, achieve system stability within the scheduled time, and effectively weaken the jitter phenomenon in the traditional sliding mode control technology, improve the anti-interference and robustness of the permanent magnet synchronous motor system, and achieve precise control of the permanent magnet synchronous motor, which is of great significance. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of the prior art and provide a model-free scheduled time sliding mode control method for a permanent magnet synchronous motor. By establishing a local model of the permanent magnet synchronous motor speed loop based on the model-free theory and combining it with the scheduled time stability method, a model-free scheduled time sliding mode controller and a model-free scheduled time sliding mode disturbance observer are designed, so as to reduce the dependence of the control algorithm on the mathematical model of the permanent magnet synchronous motor, and make the system convergence time independent of the initial state of the system. The convergence time can be set according to demand and can finally be stabilized within the scheduled time. At the same time, it can effectively weaken the chattering phenomenon of the traditional sliding mode control method, improve the anti-interference and robustness of the permanent magnet synchronous motor system, so that the motor can operate with high precision.

[0004] To achieve the above-mentioned object of the invention, the present invention provides a model-free predetermined time sliding mode control method for a permanent magnet synchronous motor, characterized in that it comprises the following steps:

[0005] Step 1: Based on the characteristics of the permanent magnet synchronous motor system and combined with the model-free theory, a speed loop local model is established;

[0006] Step 2: Design a model-free scheduled time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the observer sliding surface function, the design of the variation law of the lumped disturbance estimation value, and perform stability analysis;

[0007] Step 3: Design a model-free scheduled time sliding mode controller, including the design of the controller sliding surface function, the design of the sliding mode reaching law, and perform stability analysis.

[0008] The object of the present invention is achieved in this way.

[0009] The present invention provides a model-free scheduled time sliding mode control method for a permanent magnet synchronous motor, which specifically includes: according to the system characteristics of the permanent magnet synchronous motor, combining the model-free theory, establishing a speed loop super local model; designing a model-free scheduled time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the sliding mode surface function of the observer, the design of the variation law of the lumped disturbance estimation value, and performing stability analysis; designing a model-free scheduled time sliding mode controller, including the design of the controller sliding mode surface function, the design of the sliding mode convergence law, and performing stability analysis. The present invention combines the model-free theory, the scheduled time stability theory with the sliding mode controller and the sliding mode disturbance observer, reducing the complexity of the system model and the sensitivity to the motor parameters. Finally, the system can be stable within the scheduled time, and can effectively weaken the chattering of the traditional sliding mode control method. The present invention can effectively solve the problem of stable tracking control of permanent magnet synchronous motors under lumped disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of the steps of a specific implementation of a model-free predetermined time sliding mode control method for a permanent magnet synchronous motor of the present invention.

[0011] Figure 2 It is a schematic diagram of the principle of a specific implementation method of a model-free predetermined time sliding mode control method of a permanent magnet synchronous motor of the present invention. DETAILED DESCRIPTION

[0012] In order to make the technical solutions and advantages of the present invention clearer, the specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0013] Considering that the permanent magnet synchronous motor is a complex nonlinear system, it is easily affected by uncertainty factors such as parameter drift, unmodeled dynamics, friction and load disturbance during actual operation, which leads to certain limitations of the mathematical model of the motor. Therefore, based on the model-free theory, a local model of the permanent magnet synchronous motor speed loop is designed, which is designed as follows: w is the sum of unknown disturbances and some uncertain parts in the system. According to the speed equation of permanent magnet synchronous motor, α is defined as P n is the number of pole pairs of the motor, Φ is the permanent magnet flux, and J is the moment of inertia. The speed loop local model is further designed as: h is defined as B m is the viscous friction coefficient, and p is defined as the lumped disturbance of the system.

[0014] For the lumped disturbance p in the local model of the speed loop, a model-free scheduled time sliding mode disturbance observer is designed to estimate p. Based on the estimated value of the motor mechanical angular velocity The actual mechanical angular velocity ω m The error, defined The sliding surface function of the designed observer is defined as: Where c1>0. The expression of the variation law of the estimated value of the lumped disturbance is designed as: In the formula, 0<ε<1, b3>0, T p The system preset time means that the designed observer will be p Internal stability. Then choose a Lyapunov function Taking the derivative of V1, we get Right now Then we can get the system convergence time Prove that the model-free scheduled time sliding mode disturbance observer will p Internal stability.

[0015] Finally, based on the established local model of the permanent magnet synchronous motor speed loop, a model-free scheduled time sliding mode controller is designed. The actual mechanical angular velocity ω m The error, defined The sliding surface function of the designed controller is: Where, f1>0, f2>0, f3>0, 0<λ<1, and the speed loop model-free scheduled time sliding mode controller is designed as: Where ξ is the control input of the controller, In order to estimate the lumped disturbance p obtained by the model-free scheduled time sliding mode disturbance observer, a scheduled time sliding mode control reaching law is designed: Where, d1>0, d2>0, d3>0, c>0, 0<λ<1, T m is the scheduled time, which means that the designed controller will m The control input ξ of the controller can be obtained by internal stability. To prove the stability of the model-free scheduled time sliding mode controller, a Lyapunov function is selected, and the expression is: Can get Assume the convergence time is T q ,but It is proved that the designed model-free scheduled time sliding mode controller will m Internal stability.

[0016] Combination Figure 1The present invention discloses a model-free predetermined time sliding mode control method for a permanent magnet synchronous motor, and the specific implementation steps are as follows:

[0017] Step 1: Based on the characteristics of the permanent magnet synchronous motor system and combined with the model-free theory, a speed loop local model is established;

[0018] Step 2: Design a model-free scheduled time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the observer sliding surface function, the design of the variation law of the lumped disturbance estimation value, and perform stability analysis;

[0019] Step 3: Design a model-free scheduled time sliding mode controller, including the design of the controller sliding surface function, the design of the sliding mode reaching law, and perform stability analysis.

[0020] Combination Figure 2 The present invention relates to the establishment of a local model of a permanent magnet synchronous motor speed loop, a sliding mode surface function s1 of a model-free predetermined time sliding mode disturbance observer, and a lumped disturbance variation law. Design, stability proof of model-free scheduled time sliding mode disturbance observer, sliding surface function s2 of model-free scheduled time sliding mode controller and reaching law of sliding mode controller Design of a model-free scheduled time sliding mode controller Design and stability proof.

[0021] Step 1: Based on the characteristics of the permanent magnet synchronous motor system and combined with the model-free theory, a speed loop local model is established;

[0022] First, the speed equation of the permanent magnet synchronous motor is:

[0023]

[0024] In the formula, ω m is the mechanical angular velocity of the rotor, P n is the number of pole pairs of the motor, Φ is the permanent magnet flux, i q is the q-axis component of the stator current, J is the moment of inertia, T L is the load torque, B m is the viscous friction coefficient.

[0025] For model-free theory, the hyperlocal mathematical model of a single-input single-output nonlinear system can be expressed as:

[0026]

[0027] In the formula, u is the input signal, y is the output signal, Dis is an unknown nonlinear bounded function that satisfies Lipschitz boundedness.

[0028] Based on the motor speed equation (1) and the model-free theoretical equation (2), the local mathematical model of the permanent magnet synchronous motor speed loop is established, and the expression is:

[0029]

[0030] In the formula, w is the sum of unknown disturbances and some uncertain parts in the system, and α is designed as

[0031] According to formula (1), the local mathematical model of the speed loop (3) can be further defined as:

[0032]

[0033] In the formula, h is designed to be p is defined as the lumped disturbance of system parameter drift, unmodeled dynamics, friction, and load disturbances.

[0034] Step 2: Design a model-free scheduled time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the observer sliding surface function, the design of the variation law of the lumped disturbance estimation value, and perform stability analysis.

[0035] First, define At the same time, based on formula (4), we can get:

[0036]

[0037] Based on formula (5), the predetermined time sliding mode disturbance observer is designed, and the expression is:

[0038]

[0039] Where c1>0,0<ε<1, b3>0,e ω Estimated value of the motor mechanical angular velocity The actual mechanical angular velocity ω m The error, defined T p The system preset time means that the designed observer will be p Internal stability.

[0040] Subtracting equation (5) from equation (6) yields the error observation equation of the sliding mode disturbance observer:

[0041]

[0042] The sliding surface function of the sliding mode disturbance observer with a predetermined time is designed as:

[0043]

[0044] By taking the derivative of formula (8), we can get:

[0045]

[0046] To prove the stability of the model-free scheduled time sliding mode observer, a Lyapunov function is chosen:

[0047]

[0048] For formula (7) Taking the derivative we get:

[0049]

[0050] By taking the derivative of formula (10), we can obtain:

[0051]

[0052] By transforming formula (12), we can get:

[0053]

[0054] Where, T o is the system convergence time. Further transformation of formula (13) can be obtained as follows:

[0055]

[0056] Assume that there is a nonlinear system (15), let x be the system state variable, is a continuous nonlinear function with the initial condition x(t0)=x0. Wherein, t represents time, and satisfies g(0)=0.

[0057]

[0058] Definition of finite-time stability: Assume that the origin of the nonlinear system (15) is asymptotically stable if, for any initial state x(t0) = x0, the following conditions are satisfied: when When x(t)=0, T(x0) is the system convergence time, which is determined by the initial state x0. The nonlinear system (15) is called finite-time stable.

[0059] Definition of fixed-time stability: Assume that the origin of the nonlinear system (15) is finite-time stable, and let the system convergence time be T(x0), there exists a positive constant T max , T max Regardless of the initial state of the system, if T(x0)≤T max, then the nonlinear system (15) is said to be fixed-time stable.

[0060] Definition of predetermined time stability: Assume that the origin of the nonlinear system (15) is fixed time stable, and let the system convergence time be T(x0). If there exists a positive constant T c ,when Satisfies T(x0)≤T c , then the nonlinear system (15) is said to be stable in the predetermined time.

[0061] Therefore, according to the definition of scheduled time stability, the designed scheduled time sliding mode observer will be p Internal stability.

[0062] Step 3: Design a model-free scheduled time sliding mode controller, including the design of the controller sliding surface function, the design of the sliding mode reaching law, and perform stability analysis.

[0063] The speed loop super local model can be written as:

[0064]

[0065] According to the system given reference motor mechanical angular velocity The actual mechanical angular velocity ω m The error, defined The sliding surface function of the model-free scheduled time sliding mode controller is designed as:

[0066]

[0067] In the formula, f1>0, f2>0, f3>0, 0<λ<1.

[0068] The speed loop model-free scheduled time sliding mode controller is designed as:

[0069]

[0070] Subtracting equation (16) from equation (18) yields is the lumped disturbance estimate obtained by the model-free scheduled-time sliding mode disturbance observer.

[0071] By taking the derivative of the sliding surface function s2, we can obtain:

[0072]

[0073] Design a reaching law for a predetermined time sliding mode control, which is expressed as:

[0074]

[0075] Where, d1>0, d2>0, d3>0, c>0, 0<λ<1, T m is the scheduled time, which means that the designed controller will m Internal stability.

[0076] According to equations (19) and (20), the control input expression of the controller can be obtained:

[0077]

[0078] That is, the expression of the speed loop model-free scheduled time sliding mode controller is:

[0079]

[0080] The stability of the model-free scheduled-time sliding mode controller is proved.

[0081] First, choose a Lyapunov function, expressed as:

[0082]

[0083] By taking the derivative of the Lyapunov function (23), we can obtain:

[0084]

[0085] Formula (24) can be rewritten as:

[0086]

[0087] Further transformation can be obtained:

[0088]

[0089] Where, T q is the system convergence time.

[0090] Further transformation of formula (26) can be obtained:

[0091]

[0092] Right now x0 is the initial state of the system.

[0093] Therefore, the designed model-free scheduled time sliding mode controller will be m Internal stability, assuming the convergence time is T q , then T q ≤T m .

[0094] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A model-free predetermined time sliding mode control method for a permanent magnet synchronous motor, characterized in that: The following steps are involved: Step 1: Based on the characteristics of the permanent magnet synchronous motor system and combined with the model-free theory, a speed loop local model is established; Step 2: Design a model-free scheduled time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the observer sliding surface function, the design of the variation law of the lumped disturbance estimation value, and perform stability analysis; Step 3: Design a model-free scheduled time sliding mode controller, including the design of the controller sliding surface function, the design of the sliding mode reaching law, and perform stability analysis; 2. According to claim 1, a model-free predetermined time sliding mode control method for a permanent magnet synchronous motor is characterized in that: In step 1, based on the characteristics of the permanent magnet synchronous motor system and combined with the model-free theory, a speed loop local model is established, which is designed as follows: w is the sum of unknown disturbances and some uncertain parts in the system. According to the speed equation of permanent magnet synchronous motor, α is defined as P n is the number of pole pairs of the motor, Φ is the permanent magnet flux, and J is the moment of inertia; The speed ring super local model is further designed as: h is defined as B m is the viscous friction coefficient, and p is the lumped disturbance of system parameter drift, unmodeled dynamics, friction, and load disturbances.

3. The method for model-free predetermined time sliding mode control of a permanent magnet synchronous motor according to claim 1, characterized in that: The step 2 designs a model-free predetermined time sliding mode disturbance observer to estimate the lumped disturbance, including the design of the observer sliding mode surface function and the design of the variation law of the lumped disturbance estimation value, according to the estimated value of the motor mechanical angular velocity. The actual mechanical angular velocity ω m The error, defined The sliding surface function of the predetermined time sliding mode disturbance observer is designed as: Where c1>0; Design lumped disturbance estimated value variation law Then, the predetermined time sliding mode disturbance observer is designed, and the expression is: Where, 0<ε<1, b3>0,T p The system preset time means that the designed observer will be p Internal convergence and stability.

4. The method for model-free predetermined time sliding mode control of a permanent magnet synchronous motor according to claim 1, characterized in that: The step 2 performs stability analysis on the model-free scheduled time sliding mode disturbance observer and selects a Lyapunov function, which is expressed as: Taking the derivative of it, we can get It can be proved that the designed scheduled time sliding mode disturbance observer will p Internal stability, assuming the system convergence time is T o , 5. The method for model-free predetermined time sliding mode control of a permanent magnet synchronous motor according to claim 1, characterized in that: The step 3 designs a model-free predetermined time sliding mode controller, including the design of the controller sliding mode surface function and the design of the predetermined time sliding mode reaching law, according to the given reference motor mechanical angular velocity of the system. The actual mechanical angular velocity ω m The error, defined The sliding surface function of the model-free scheduled time sliding mode controller is designed as: Wherein, f1>0, f2>0, f3>0, 0<λ<1; The speed loop model-free scheduled time sliding mode controller is designed as: Where ξ is the control input of the controller, is the estimated value of the lumped disturbance p obtained by the model-free scheduled time sliding mode disturbance observer; a scheduled time sliding mode control reaching law is designed, which is expressed as: Where, d1>0, d2>0, d3>0, c>0, 0<λ<1, T m is the scheduled time, indicating that the controller will m Internal stability; Then the control input expression of the controller is obtained as: That is, the expression of the speed loop model-free scheduled time sliding mode controller is:

6. The method for model-free predetermined time sliding mode control of a permanent magnet synchronous motor according to claim 1, characterized in that: The step 3 proves the stability of the model-free scheduled time sliding mode controller, and selects a Lyapunov function, which is expressed as: Can get Assume the system convergence time is T q , It is proved that the designed model-free scheduled time sliding mode controller will m Internal stability.

Images