Permanent magnet synchronous motor speed control algorithm based on adaptive sliding mode reaching law

Abstract

The invention relates to a permanent magnet synchronous motor speed control algorithm based on an adaptive sliding mode reaching law, and belongs to the technical field of motor control algorithms. The algorithm comprises the following steps: step 1, establishing a mathematical model of the surface-mounted permanent magnet synchronous motor under a rotating coordinate system; 2, designing an integral sliding mode surface; 3, designing a self-adaptive sliding mode approaching rate; and 4, designing a sliding mode speed ring controller based on the self-adaptive approaching rate. According to the permanent magnet synchronous motor speed control algorithm based on the self-adaptive sliding mode reaching law, during large-range speed regulation, the problems that a permanent magnet synchronous motor speed regulation control method based on a traditional sliding mode reaching law is low in response speed and long in time can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control algorithms, and in particular to a permanent magnet synchronous motor speed control algorithm based on an adaptive sliding mode reaching law. Background Art

[0002] Permanent magnet synchronous motors have the advantages of high efficiency, high power density, fast response speed and brushless design, and are widely used in various fields such as aerospace, industrial automation, and new energy. PID control is one of the most classic control methods. It has the advantages of simple structure and convenient parameter adjustment, and is widely used in various motor control systems. It adjusts the output of the controller through three links: proportional, integral and differential, thereby achieving speed control of the permanent magnet synchronous motor. However, it also has some limitations, such as weak adaptability to nonlinear and time-varying systems, and difficult parameter adjustment.

[0003] In order to further improve the control accuracy of the speed loop of the permanent magnet synchronous motor control system and the robust performance of the system, domestic and foreign researchers have proposed many innovative nonlinear permanent magnet synchronous motor speed control strategies. Among them, sliding mode control is widely used in the field of permanent magnet synchronous motor speed control due to its simple design, strong robustness and strong dynamic response ability. Sliding mode control introduces a sliding surface to drive the system state to slide quickly onto the surface and keep moving on the sliding surface, thereby achieving precise control of the system. Its principle is based on the design of the sliding mode curve and the sliding surface. By switching the structure of the controller (control law or controller parameters), the system state is purposefully changed according to the current state (such as deviation and its derivatives of various orders) during the dynamic process, thereby forcing the system to move according to the predetermined "sliding mode" state trajectory. However, the traditional sliding mode control method still has certain limitations: for example, the initial state of the system affects the maximum time required for the system to reach the sliding surface. When the initial state is far away from the sliding surface, the sliding mode function needs more time to converge. Therefore, in order to solve the problems of slow convergence and easy overshoot in traditional sliding mode control, it is urgent to design a new sliding mode reaching law. Summary of the invention

[0004] The present invention aims to provide a permanent magnet synchronous motor speed control algorithm based on an adaptive sliding mode reaching law in order to solve the technical problems of slow response speed and long time consumption of the traditional sliding mode reaching law in the speed control of a permanent magnet synchronous motor in a wide range of speed regulation scenarios.

[0005] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0006] A permanent magnet synchronous motor speed control algorithm based on an adaptive sliding mode reaching law comprises the following steps:

[0007] Step 1: Establish a mathematical model of the surface-mounted permanent magnet synchronous motor in a rotating coordinate system;

[0008] Step 2: Design the integral sliding surface;

[0009] Step 3: Design the adaptive sliding mode approach rate;

[0010] Step 4: Design a sliding mode speed loop controller based on adaptive sliding mode approaching rate.

[0011] In the above technical solution, the mathematical model of the surface-mounted permanent magnet synchronous motor in step 1 is:

[0012]

[0013] Where: u d 、u q are the d-axis and q-axis stator voltage components respectively, i d 、i q are the d-axis and q-axis stator current components, ψ d , q are the d-axis and q-axis stator flux respectively, are the derivatives of the stator flux of the d and q axes respectively, t is the time, L d , L q are the d-axis and q-axis stator inductances, ω e is the synchronous speed in electrical angle, R s is the stator resistance, ψ f Replace the permanent magnet flux.

[0014] In the above technical solution, the torque model equation of the surface-mounted permanent magnet synchronous motor in step 1 is:

[0015]

[0016] Where: T L is the external load torque, B is the viscous friction coefficient, ω r is the mechanical angular velocity.

[0017] In the above technical solution, the integral sliding surface s in step 2 is:

[0018]

[0019] Where: c 1 is the proportional coefficient of the integral sliding surface, c 2 is the integral coefficient of the integral sliding surface, e is the speed error, e=ω r -ω f ,ω r is the command speed, ω f is the actual speed, and t is the time.

[0020] In the above technical solution, the adaptive sliding mode approach rate in step 3 is for:

[0021]

[0022] Where: f(s,x) is the adaptive switching gain function, sign(s) is the sign function, s is the sliding surface; k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function; h(x) and g(s) are both variable function items in the adaptive switching gain function; α, β, λ, μ are all variable item coefficients in the variable function item; k t >0, δ>0, α>1, β>0, 0<μ<2, λ>0, x is the system state.

[0023] In the above technical solution, the sliding mode speed loop controller based on the adaptive sliding mode approaching rate in step 4 is:

[0024]

[0025] Where: iqref is the controller output, J is the motor moment of inertia, n p is the number of motor pole pairs, is the motor flux, f(s,e) is the adaptive switching gain function, k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function; h(e) and g(s) are the variable function terms in the adaptive switching gain function, α, β, λ, μ are the variable term coefficients in the variable function term; k t >0, δ>0, α>1, β>0, 0<μ<2, λ>0, s is the system sliding surface, and e is the speed error.

[0026] The present invention has the following beneficial effects:

[0027] The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention can solve the problems of slow response speed and long time of the permanent magnet synchronous motor speed control method based on the traditional sliding mode reaching law when adjusting the speed in a large range.

[0028] The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention has a better suppressive effect on load disturbances. When the load is suddenly added, the speed fluctuation is smaller and the given speed can be converged more quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0030] Figure 1The structural block diagram of the system applicable to the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention. Based on the vector control framework, the speed loop controller is designed, and the adaptive sliding mode reaching rate is constructed based on the adaptive sliding mode gain, which solves the problems of slow convergence and easy overshoot in traditional sliding mode control.

[0031] Figure 2 It is a schematic diagram of speed response curves of PI control and the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention when the command speed is 100 rpm and 1000 rpm.

[0032] Figure 3 It is a schematic diagram of the speed response curve of the load disturbance of the command speed of 1000rpm, PI control and the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention.

[0033] Figure 4 It is a schematic diagram of the speed response curve of the load disturbance of the command speed of 100 rpm, PI control and the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention.

[0034] Figure 5 The command speed is 1000 rpm, and the motor torque output curve schematic diagram when the load is added or subtracted according to the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention. DETAILED DESCRIPTION

[0035] The inventive concept of the present invention is:

[0036] The present invention is described in detail below with reference to the accompanying drawings.

[0037] The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention comprises the following steps:

[0038] Step 1: Establish a mathematical model of the surface-mounted permanent magnet synchronous motor in a rotating coordinate system;

[0039]

[0040] Where: u d 、u q ——respectively, the d-axis and q-axis stator voltage components (V);

[0041] i d 、i q ——respectively, the d-axis and q-axis stator current components (A);

[0042] ψ d , q ——respectively, the d-axis and q-axis stator flux (Wb);

[0043] L d , L q ——d-axis and q-axis stator inductances (H) respectively;

[0044] ω e ——Represents the synchronous speed in electrical angle (rad / s);

[0045] R s ——Represents stator resistance (Ω);

[0046] ψ f ——Represents the permanent magnet flux (Wb);

[0047] t——stands for time.

[0048] The speed loop outputs the command current as the control input of the current loop. For the surface-mounted permanent magnet synchronous motor, its torque model equation is:

[0049]

[0050] Where: T L is the external load torque, B is the viscous friction coefficient, ω r is the mechanical angular velocity.

[0051] Step 2: Design the integral sliding surface;

[0052] Specifically:

[0053]

[0054] Where: c 1 is the proportional coefficient of the integral sliding surface, c 2 is the integral coefficient of the integral sliding surface, e is the speed error, e=ω r -ω f ,ω r is the command speed, ω f is the actual speed, and t is the time.

[0055] Step 3: Design a new adaptive sliding mode approach rate;

[0056]

[0057] Where: f(s,x) is the adaptive switching gain function, sign(s) is the sign function, s is the sliding surface; k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function. h(x) and g(s) are both variable function items in the adaptive switching gain function, and α, β, λ, and μ are all variable item coefficients in the variable function items. k t>0, δ>0, α>1, β>0, 0<μ<2, λ>0, x is the system state.

[0058] Step 4: Design a sliding mode speed loop controller based on adaptive approaching rate;

[0059]

[0060] Where: iqref is the controller output, J is the motor moment of inertia, n p is the number of motor pole pairs. is the motor flux, f(s,e) is the adaptive switching gain function, k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function. h(e) and g(s) are both variable function items in the adaptive switching gain function, and α, β, λ, and μ are all variable item coefficients in the variable function items. k t >0, δ>0, α>1, β>0, 0<μ<2, λ>0, s is the system sliding surface, and e is the speed error.

[0061] The design of the new reaching law is based on the exponential term e -δ|s| , terminal term βs μ , system state x|, variable term λ and linear gain k. When |s| is large, f(s,x)=k / g(s)=k(α+βs μ ), which is much larger than the original gain k. At this time, the system has a smaller approach time and stronger robustness. The terminal term βs μ The addition of makes the system have better dynamic response performance when the |s| value is relatively large. When |s| is small, f(s,x)=1 / h(x)=kx / (x+λ), which is less than the original gain k, and can effectively suppress system chattering. Under the action of the control law, the system state |x| gradually approaches zero, f(s,x) gradually approaches zero, and the system trajectory gradually approaches the sliding surface. Therefore, the controller based on this new approach law can dynamically adapt to the changes of the system state and the sliding surface s, and can obtain better control performance.

[0062] The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention is described in detail below with reference to specific examples.

[0063] In this embodiment, Figure 1 As shown, based on the vector control framework, the speed loop controller is designed, and the adaptive sliding mode reaching rate is constructed based on the adaptive sliding mode gain, which solves the problems of slow convergence and easy overshoot in traditional sliding mode control. In the system where the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention is applicable, the parameters in the speed controller based on the adaptive sliding mode reaching law are set to: c 1 =1.5, c2 =200, k=80.0, k t =150, δ=100, α=1.1, β=0.1, μ=1, λ=0.1, and the reference speeds are set to 100 rpm and 1000 rpm respectively.

[0064] The speed response curve is as follows Figure 2 As shown, it can be seen that compared with the PID control method, the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention has a faster response time and can converge to the command speed with a smaller overshoot.

[0065] A disturbance torque of 10 Nm is applied at 0.25 s, and a disturbance torque of 5 Nm is applied at 1 s to test the robustness of the speed controller. At 1.5 s, the disturbance torque is suddenly reduced by 7 Nm. The response curve is as follows: Figure 3 Shown and Figure 4 Compared with the PID control method, the permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention has a better suppression effect on load disturbances. When the load is suddenly added, the speed fluctuation is smaller and the given speed can be converged faster.

[0066] Figure 5 This is the motor torque output curve when the load is suddenly added at a given speed of 1000rpm. It can be seen that the torque output is smooth.

[0067] The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law of the present invention can solve the problems of slow response speed and long time of the permanent magnet synchronous motor speed control method based on the traditional sliding mode reaching law when adjusting the speed in a large range.

[0068] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A permanent magnet synchronous motor speed control algorithm based on adaptive sliding mode reaching law, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the surface-mounted permanent magnet synchronous motor in a rotating coordinate system; Step 2: Design the integral sliding surface; Step 3: Design the adaptive sliding mode approach rate; Step 4: Design a sliding mode speed loop controller based on adaptive sliding mode approaching rate.

2. The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law according to claim 1 is characterized in that: The mathematical model of the surface-mounted permanent magnet synchronous motor in step 1 is: Where: u d 、u q are the d-axis and q-axis stator voltage components respectively, i d 、i q are the d-axis and q-axis stator current components, ψ d , q are the d-axis and q-axis stator flux respectively, are the derivatives of the stator flux of the d and q axes respectively, t is the time, L d , L q are the d-axis and q-axis stator inductances, ω e is the synchronous speed in electrical angle, R s is the stator resistance, ψ f Replace the permanent magnet flux.

3. The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law according to claim 2 is characterized in that: The torque model equation of the surface-mounted permanent magnet synchronous motor in step 1 is: Where: T L is the external load torque, B is the viscous friction coefficient, ω r is the mechanical angular velocity.

4. The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law according to claim 1 is characterized in that: The integral sliding surface s in step 2 is: Where: c1 is the proportional coefficient of the integral sliding surface, c2 is the integral coefficient of the integral sliding surface, e is the speed error, e = ω r -ω f ,ω r is the command speed, ω f is the actual speed, and t is the time.

5. The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law according to claim 1 is characterized in that: The adaptive sliding mode approach rate s in step 3 is: Where: f(s,x) is the adaptive switching gain function, sign(s) is the sign function, s is the sliding surface; k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function, h(x) and g(s) are the variable function items in the adaptive switching gain function; α, β, λ, μ are the variable item coefficients in the variable function item; k t >0, δ>0, α>1, β>0, 0<μ<2, λ>0, x is the system state.

6. The permanent magnet synchronous motor speed control algorithm based on the adaptive sliding mode reaching law according to claim 1 is characterized in that: The sliding mode speed loop controller based on the adaptive sliding mode approaching rate in step 4 is: Where: iqref is the controller output, J is the motor moment of inertia, n p is the number of motor pole pairs, is the motor flux, f(s,e) is the adaptive switching gain function, k is the original switching gain, k t is the linear gain, δ is the switching coefficient in the adaptive switching gain function; h(e) and g(s) are both variable function items in the adaptive switching gain function, α, β, λ, μ are all variable item coefficients in the variable function item; k t >0, δ>0, α>1, β>0, 0<μ<2, λ>0, s is the system sliding surface, and e is the speed error.

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