Permanent magnet synchronous motor control method based on second-order discrete time sliding mode

Abstract

The invention provides a permanent magnet synchronous motor control method based on a second-order discrete time sliding mode. The permanent magnet synchronous motor control method comprises the steps of establishing a current and speed equation of a permanent magnet synchronous motor and a state-space equation of the permanent magnet synchronous motor; based on the established state-space equation of the permanent magnet synchronous motor, a second-order discrete time sliding-mode control law design is carried out on a speed ring in combination with the Lyapunov criterion of a discrete time non-smooth control system; based on a second-order discrete time sliding mode control law design, a tracking error trajectory of the permanent magnet synchronous motor system is converged in finite time, and through a discrete time non-smooth control system Lyapunov function, conditions which should be met by system parameters when the permanent magnet synchronous motor system is stable in finite time are deduced. The method provided by the invention is suitable for a scene with a relatively long sampling period and relatively rough equipment, the motor can have better dynamic performance, and the chattering condition is reduced.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and specifically to a permanent magnet synchronous motor control method based on second-order discrete-time sliding mode. Background Technology

[0002] A permanent magnet synchronous motor (PMSM) is a synchronous motor that uses permanent magnets to generate a magnetic field, synchronizing the rotor speed with the stator winding current frequency. It features high power density, high efficiency, and simple structure, and is widely used in servo control, automotive, aerospace, and wind power generation. PI control technology is widely used in PMSM systems due to its simple digital implementation. However, when faced with system uncertainties and external disturbances, traditional PI controllers often struggle to meet the stringent requirements of high-precision control.

[0003] With the advancement of modern control theory, various nonlinear control methods have been applied to practical systems. Sliding mode control is a control method based on modern control theory. Its basic idea is to establish a sliding surface and guide the controlled system onto and along the sliding surface. Sliding mode control is insensitive to system uncertainties and disturbances, thus becoming an effective strategy for improving the robustness and tracking accuracy of permanent magnet synchronous motor systems. However, currently commonly used sliding mode control theories and methods are mainly designed for continuous systems. In motor equipment, they need to be converted into discrete systems for implementation. This conversion inevitably leads to errors and performance degradation in actual operation. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a control method for permanent magnet synchronous motors based on second-order discrete-time sliding mode.

[0005] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0006] A control method for a permanent magnet synchronous motor based on second-order discrete-time sliding mode includes:

[0007] Step 1: Perform electrical and mechanical analysis on the permanent magnet synchronous motor, establish the current and speed equations of the permanent magnet synchronous motor, and establish the state-space equations of the permanent magnet synchronous motor based on the current and speed equations of the permanent magnet synchronous motor.

[0008] Step 2: Based on the state-space equation of the permanent magnet synchronous motor established in Step 1, and combined with the Lyapunov criterion for discrete-time non-smooth control systems, design a second-order discrete-time sliding mode control law for the speed loop, and use PI control for the current loop.

[0009] Step 3: Based on the design of the second-order discrete-time sliding mode control law in Step 2, the tracking error trajectory of the permanent magnet synchronous motor system converges in a finite time. Through the Lyapunov function of the discrete-time non-smooth control system, the conditions that the system parameters β1, β2, and L should satisfy when the permanent magnet synchronous motor system is stable in a finite time are derived, and the parameters L, speed and sampling period T are adjusted within these conditions.

[0010] Furthermore, the current and speed equations of the permanent magnet synchronous motor are expressed as follows:

[0011]

[0012] Among them, i d i q These are the stator currents on the dq axis, u d u q These are the stator voltages on the dq axis, L s Where B is the stator inductance, B is the coefficient of viscous friction, and R is the stator inductance. s n is the stator resistance. p Let ω be the number of pole pairs, ω be the rotor angular velocity, and ψ be the number of pole pairs. f Let J be the magnetic flux linkage, J be the moment of inertia, and T be the moment of inertia. L It is the load torque.

[0013] Furthermore, the state-space equation of the permanent magnet synchronous motor is expressed as follows:

[0014]

[0015] Where, ω e , Let ω be the derivative of angular velocity error and angular velocity error, respectively. * For reference rotor angular velocity, For reference current, d0(t) represents the sum of the error between the reference current and the stator current, as well as external disturbances.

[0016] Furthermore, the design of the second-order discrete-time sliding mode control law includes: rewriting the state-space equation of the permanent magnet synchronous motor, proposing the Lyapunov criterion for discrete-time non-smooth control systems, and designing the second-order discrete-time sliding mode control law.

[0017] Furthermore, the specific process of rewriting the state-space equations of the permanent magnet synchronous motor is as follows:

[0018] First, differentiate the state-space equations of the permanent magnet synchronous motor:

[0019]

[0020] in, Let represent a concentrated perturbation, and |d(t)|≤D, where D is a positive constant.

[0021] Secondly, we add an intermediate parameter, a positive integer L, and let α1 = ω. e , The state-space equations of the permanent magnet synchronous motor after differentiation are rewritten as follows:

[0022]

[0023] Among them, t k This represents the time corresponding to the kth sampling period.

[0024] Furthermore, the proposed Lyapunov criterion for discrete-time nonsmooth control systems is as follows:

[0025] Consider permanent magnet synchronous motor system Where, x∈R N Let u ∈ R be the system state variable, u ∈ R be the system control input, and u(t) = u(t) k ),t∈[t k ,t k +T);

[0026] Suppose there exists a positive definite continuous function W(x) that is differentiable with respect to time t and satisfies:

[0027]

[0028] in, Coefficient k0 > 0, k i >0, a i >0, 0<b i <b0<1; a i / (b0-b i ) = a, N is a positive integer, a is a positive constant, and T is the sampling period; then the state of the permanent magnet synchronous motor system will converge to the following region:

[0029] Ω={x|W(x)≤cT a}

[0030] in,

[0031] Furthermore, the second-order discrete-time sliding mode control law is expressed as:

[0032]

[0033] in, sign(·) is the standard sign function, where β1 and β2 are positive real numbers.

[0034] Furthermore, the transfer function of the PI control is:

[0035]

[0036] Where, k p For proportional adjustment parameters; k i is the integral adjustment parameter; s is the complex parameter in the Laplace transform.

[0037] Furthermore, the system parameters β1, β2, and L should satisfy the following conditions: And L≥1, h1 is the maximum value of |h(t,m)|.

[0038] The beneficial effects of this invention are as follows:

[0039] (1) The present invention adopts the control law based on Lyapunov's theorem for discrete-time non-smooth control systems. It can not only be used for the stability analysis of second-order discrete sliding mode control, but also extended to the stability analysis of more general finite-time control systems under sampling control, thereby improving the dynamic performance of the system on permanent magnet synchronous motors.

[0040] (2) This invention differs from the traditional design method based on discrete time model. Instead, in the design of second-order discrete sliding mode control law, it adopts the idea of ​​directly discretizing the controller after designing based on a general model. This is more in line with the actual experimental environment, enhances the adaptability to different sampling periods, and reduces chattering compared with traditional discrete systems. Attached Figure Description

[0041] Figure 1 This is a flowchart of the permanent magnet synchronous motor control method based on second-order discrete-time sliding mode as described in this invention.

[0042] Figure 2 This is a schematic diagram of the deployment of the experimental equipment described in this invention.

[0043] Figure 3 This is a comparison diagram of the speed control effects of the method described in this invention with PI control and first-order discrete sliding mode control methods during motor startup.

[0044] Figure 4 This is a comparison diagram of the current control effects of the method described in this invention with PI control and first-order discrete sliding mode control methods during motor startup.

[0045] Figure 5 This is a comparison chart of the speed control effects of the method described in this invention with PI control and first-order discrete sliding mode control methods under sudden load.

[0046] Figure 6This is a comparison chart of the current control effects of the method described in this invention with PI control and first-order discrete sliding mode control methods under sudden load conditions.

[0047] Figure 7 This is a graph showing the effect of parameter L variation on speed control in the method described in this invention.

[0048] Figure 8 This is a diagram showing the effect of parameter L variation on current control in the method described in this invention.

[0049] Figure 9 This is a graph showing the effect of the sampling period T variation on the speed control effect in the method described in this invention.

[0050] Figure 10 This is a graph showing the effect of the sampling period T variation on the current control effect in the method described in this invention. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0052] The present invention proposes a control method for permanent magnet synchronous motors based on second-order discrete-time sliding mode, the specific process of which is as follows: Figure 1 As shown, it includes the following steps:

[0053] Step 1: Perform electrical and mechanical analysis on the permanent magnet synchronous motor, establish the current and speed equations of the permanent magnet synchronous motor, and establish the state-space equations of the permanent magnet synchronous motor based on the current and speed equations. The specific process is as follows:

[0054] Step 1.1: Establish the current and speed equations for the permanent magnet synchronous motor, expressed as:

[0055]

[0056] Among them, i d i q These are the stator currents on the dq axis, u d u q These are the stator voltages on the dq axis, L s Where B is the stator inductance, B is the coefficient of viscous friction, and R is the stator inductance. s n is the stator resistance. p Let ω be the number of pole pairs, ω be the rotor angular velocity, and ψ be the number of pole pairs. f Let J be the magnetic flux linkage, J be the moment of inertia, and T be the moment of inertia. L It is the load torque;

[0057] Step 1.2: Perform state transformation on the current and speed equations of the permanent magnet synchronous motor to obtain the state-space equations of the permanent magnet synchronous motor, as shown below:

[0058]

[0059] Where, ω e , Let ω be the derivative of angular velocity error and angular velocity error, respectively. * The reference rotor angular velocity is used, and the reference current is used. Replaced stator current i q , d0(t) represents the sum of the error between the reference current and the stator current, as well as external disturbances.

[0060] Step 2: Based on the state-space equation of the permanent magnet synchronous motor established in Step 1, design a second-order discrete-time sliding mode control law for the speed loop and use PI control for the current loop.

[0061] Step 2.1: Differentiate the state-space equations of the permanent magnet synchronous motor:

[0062]

[0063] in, This represents a concentrated disturbance, and |d(t)|≤D, where D is a positive constant or intermediate quantity.

[0064] To facilitate the design of the second-order discrete-time sliding mode control law, subsequent debugging of the permanent magnet synchronous motor system parameters, and corresponding stability proofs, an intermediate parameter of positive integer L is added, let α1 = ω. e , The differentiated state-space equations of the permanent magnet synchronous motor can be rewritten as follows:

[0065]

[0066] Among them, t k This represents the time corresponding to the kth sampling period.

[0067] Step 2.2: To better apply this criterion to practical discrete-time permanent magnet synchronous motor applications, the newly proposed Lyapunov criterion for discrete-time nonsmooth control systems is used as the stability criterion. The Lyapunov criterion for discrete-time nonsmooth control systems is as follows:

[0068] Consider permanent magnet synchronous motor system Where, x∈R N Let u ∈ R be the system state variable, u ∈ R be the system control input, and u(t) = u(t) k ),t∈[t k ,t k +T).

[0069] Suppose there exists a positive definite continuous function W(x) that is differentiable with respect to time t and satisfies:

[0070]

[0071] in, k0>0, k i >0, a i >0, 0<b i <b0<1, both are freely selectable coefficients; a i / (b0-b i ) = a, N is a positive integer, a is a positive constant, and T is the sampling period. The state of the permanent magnet synchronous motor system will then converge to the following region:

[0072] Ω={x|W(x)≤cT a}

[0073] in,

[0074] Step 2.3: Based on the state-space equations of Step 2.1 and the Lyapunov criterion for discrete-time nonsmooth control systems from Step 2.2, design a second-order discrete-time sliding mode control law, expressed as:

[0075]

[0076] in, sign(·) is the standard sign function, where β1 and β2 are positive real numbers that can be adjusted as needed.

[0077] Step 2.4: The current loop design uses PI control, and the transfer function is... Where, k p The proportional adjustment parameter determines the sensitivity of the permanent magnet synchronous motor system to errors; a larger value results in faster adjustment, but excessively large values ​​can lead to overshoot or oscillation. i is the integral adjustment parameter used to eliminate steady-state error and make the output approach the target value by continuously correcting the deviation; s is the complex parameter in the Laplace transform.

[0078] Step 3: Based on the design in Step 2, the tracking error trajectory of the permanent magnet synchronous motor system can converge in finite time. Furthermore, using the Lyapunov function of the discrete-time non-smooth control system, the conditions that the system parameters β1, β2, and L must satisfy when the permanent magnet synchronous motor system is stable in finite time are derived. And L≥1, h1 is the maximum value of |h(t,m)|, and L, speed and sampling period T are adjusted within this condition to optimize the control performance of permanent magnet synchronous motor.

[0079] Step 4: To better verify the control effect of the permanent magnet synchronous motor system based on the second-order discrete sliding mode control law, this embodiment conducted a practical experiment based on the MiG motor 130ST-M10015. The experimental equipment was deployed as follows: Figure 2 As shown.

[0080] In this embodiment, under the condition of a step change in speed, the effects of three different control methods (PI control, first-order discrete sliding mode control, and the second-order discrete sliding mode control proposed in this embodiment) on speed control are as follows: Figure 3 As shown, the effect on current control is as follows: Figure 4 As shown. The motor speed reference setting is 500 rpm, with no additional load torque. Figure 3 As shown, compared to the three different control methods, the linear PI control method exhibits the largest overshoot in the speed curve, while the second-order discrete sliding mode control method has the shortest controller settling time. Meanwhile, as... Figure 4 As shown, in terms of current control, second-order discrete sliding mode control is basically equivalent to PI control, but compared with first-order discrete sliding mode control, it significantly reduces chattering. In summary, second-order discrete sliding mode control exhibits better dynamic performance under step speed changes.

[0081] Figure 5 Experimental results show the speed response of a permanent magnet synchronous motor system to a sudden load under three different control methods. Figure 6 Experimental results demonstrate the current response to a sudden load in a permanent magnet synchronous motor system under three different control methods. Figure 5 It can be seen that the upper and lower limits of the observed speed under the second-order discrete sliding mode control method differ by only 14 rpm, which is much smaller than that of the other two methods. This shows that when subjected to sudden external disturbances, the speed of this method is less affected by the disturbance and has better anti-disturbance performance. Figure 6 As can be seen from the data, the current performance of the second-order discrete sliding mode control is basically equivalent to that of the PI control under external disturbances, and the chattering is significantly reduced compared to the first-order discrete sliding mode control.

[0082] To evaluate the impact of parameter L within the framework of a permanent magnet synchronous motor system based on a second-order discrete sliding mode control law, Figure 7 The paper describes the speed results of a permanent magnet synchronous motor system during a step speed change for three different L values ​​(L=2, L=3, and L=4). Figure 8 This paper describes the current results of a permanent magnet synchronous motor (PMSM) system during a speed step change at three different L values. The speed and current response curves of the PMSM speed control system at L=2, L=3, and L=4 are shown. Although from... Figure 8 It can be seen from this that a smaller L value can reduce current chattering, but at the same time... Figure 7It is also evident that a smaller L value leads to a larger speed overshoot and an increased settling time. Therefore, a larger L value can be chosen for scenarios requiring faster settling time and smaller overshoot, while a smaller L value can be chosen for scenarios requiring reduced current jitter.

[0083] To investigate the influence of the sampling period T within the framework of a permanent magnet synchronous motor system based on a second-order discrete sliding mode control law, the rotational speeds of the permanent magnet synchronous motor system under three different T values ​​(T = 0.001s, T = 0.0002s, and T = 0.0001s) under a step speed change are shown below. Figure 9 As shown, the current results of the permanent magnet synchronous motor system at three different T values ​​under a step speed change are as follows: Figure 10 As shown in the figure, it can be seen that with the increase of parameter T, the dynamic performance of the permanent magnet synchronous motor system in terms of speed and the vibration suppression capability of the current are improved to varying degrees.

[0084] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A control method for a permanent magnet synchronous motor based on second-order discrete-time sliding mode, characterized in that: Step 1: Perform electrical and mechanical analysis on the permanent magnet synchronous motor, establish the current and speed equations of the permanent magnet synchronous motor, and establish the state-space equations of the permanent magnet synchronous motor based on the current and speed equations of the permanent magnet synchronous motor. Step 2: Based on the state-space equation of the permanent magnet synchronous motor established in Step 1, and combined with the Lyapunov criterion for discrete-time non-smooth control systems, design a second-order discrete-time sliding mode control law for the speed loop, and use PI control for the current loop. Step 3: Based on the design of the second-order discrete-time sliding mode control law in Step 2, the tracking error trajectory of the permanent magnet synchronous motor system converges in a finite time. Through the Lyapunov function of the discrete-time non-smooth control system, the conditions that the system parameters β1, β2, and L should satisfy when the permanent magnet synchronous motor system is stable in a finite time are derived, and the parameters L, speed and sampling period T are adjusted within these conditions.

2. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 1, characterized in that, The current and speed equations of the permanent magnet synchronous motor are expressed as follows: Among them, i d i q These are the stator currents on the dq axis, u d u q These are the stator voltages on the dq axis, L s Where B is the stator inductance, B is the coefficient of viscous friction, and R is the stator inductance. s n is the stator resistance. p Let ω be the number of pole pairs, ω be the rotor angular velocity, and ψ be the number of pole pairs. f Let J be the magnetic flux linkage, J be the moment of inertia, and T be the moment of inertia. L It is the load torque.

3. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 2, characterized in that, The state-space equation of the permanent magnet synchronous motor is expressed as follows: Where, ω e , Let ω be the derivative of angular velocity error and angular velocity error, respectively. * For reference rotor angular velocity, For reference current, d0(t) represents the sum of the error between the reference current and the stator current, as well as external disturbances.

4. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 3, characterized in that, The design of the second-order discrete-time sliding mode control law includes: rewriting the state-space equation of the permanent magnet synchronous motor, proposing the Lyapunov criterion for discrete-time non-smooth control systems, and designing the second-order discrete-time sliding mode control law.

5. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 4, characterized in that, The specific process of rewriting the state-space equations of the permanent magnet synchronous motor is as follows: First, differentiate the state-space equations of the permanent magnet synchronous motor: in, Let represent a concentrated perturbation, and |d(t)|≤D, where D is a positive constant. Secondly, we add an intermediate parameter, a positive integer L, and let α1 = ω. e , The state-space equations of the permanent magnet synchronous motor after differentiation are rewritten as follows: Among them, t k This represents the time corresponding to the kth sampling period.

6. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 5, characterized in that, The proposed Lyapunov criterion for discrete-time nonsmooth control systems is as follows: Consider permanent magnet synchronous motor system Where, x∈R N Let u ∈ R be the system state variable, u ∈ R be the system control input, and u(t) = u(t) k ),t∈[t k ,t k +T); Suppose there exists a positive definite continuous function W(x) that is differentiable with respect to time t and satisfies: in, Coefficient k0 > 0, k i >0, a i >0, 0<b i <b0<1; a i / (b0-b i ) = a, N is a positive integer, a is a positive constant, and T is the sampling period; then the state of the permanent magnet synchronous motor system will converge to the following region: Ω={x|W(x)≤cT a } in, 7. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 6, characterized in that, The second-order discrete-time sliding mode control law is expressed as: in, sign(·) is the standard sign function, where β1 and β2 are positive real numbers.

8. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 1, characterized in that, The transfer function of the PI control is: Where, k p For proportional adjustment parameters; k i is the integral adjustment parameter; s is the complex parameter in the Laplace transform.

9. The permanent magnet synchronous motor control method based on second-order discrete-time sliding mode according to claim 7, characterized in that, The system parameters β1, β2, and L should satisfy the following conditions: And L≥1, h1 is the maximum value of |h(t,m)|.

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