Sliding mode control method based on disturbance observation, improved reaching law and switching function

Abstract

The invention relates to the technical field of electronic control, in particular to a sliding mode control method based on disturbance observation, an improved reaching law and a switching function, and the method comprises the following steps: defining state variables of a permanent magnet synchronous motor, and building a mathematical model; designing a sliding mode controller; designing an expansion observer; and introducing an estimation result of the expansion observer into a sliding mode controller to realize control of the system. According to the invention, the system has the advantages of no overshoot, fast response speed, short adjustment time and strong anti-interference capability. The estimated torque can be smoother than the actual torque. Therefore, buffeting can be well weakened by introducing the estimated motor parameter change observed by the expansion observer and the disturbance value of the load torque into the sliding mode controller. Therefore, the problem of buffeting in traditional sliding mode control is solved.

Description

Technical Field

[0001] The present invention relates to the field of electronic control technology, and in particular to a sliding mode control method based on disturbance observation, improved reaching law and switching function. Background Art

[0002] In new energy vehicles, permanent magnet synchronous motors (PMSMs) have become one of the mainstream drive motors due to their high efficiency, high power density, and excellent dynamic performance. PMSM control technology directly impacts vehicle power, energy efficiency, and driving experience. New energy vehicles require motor control with high efficiency, high dynamic performance, strong robustness, and low harmonics and noise. To achieve these goals, researchers have developed a variety of control methods, among which sliding mode control (SMC) has garnered widespread attention due to its unique advantages.

[0003] Sliding mode control is a nonlinear control method based on variable structure control theory. By designing a sliding surface and switching control laws, the system state converges to the sliding surface within a finite time and then slides along the sliding surface to the target state. The core idea of ​​sliding mode control is to design a sliding surface to guide the system state onto it and then use switching control laws to slide the system state to the target value on the sliding surface. The sliding surface is typically designed based on the system error. For example, in speed control, the sliding surface can be designed as a combination of the speed error and its integral. The control law consists of a reaching law and a switching control law. The reaching law is used to guide the system state along the sliding surface, while the switching control is used to overcome system uncertainties and external disturbances. The main advantages of sliding mode control include strong robustness, fast response, and simple implementation. Due to its nonlinear characteristics, sliding mode control is highly robust to system parameter changes and external disturbances, effectively addressing the uncertainties and nonlinearities in motor control. In addition, sliding mode control has a fast dynamic response and can quickly track the target value, making it suitable for the frequently changing operating conditions of new energy vehicles.

[0004] However, sliding mode control also has some drawbacks, the most notable of which is chattering. Due to the use of sign functions in switching control, the control signal will produce high-frequency jitter, which may cause motor torque pulsation and mechanical vibration, affecting system stability and comfort. Summary of the Invention

[0005] The purpose of the present invention is to provide a sliding mode control method based on disturbance observation and improved reaching law and switching function, aiming to solve the chattering problem of traditional sliding mode control.

[0006] To achieve the above object, the present invention provides a sliding mode control method based on disturbance observation, improved reaching law and switching function, comprising the following steps:

[0007] Define the state variables of permanent magnet synchronous motor and establish a mathematical model;

[0008] Design sliding mode controller;

[0009] Design dilation observer;

[0010] The estimation results of the extended observer are introduced into the sliding mode controller to realize the control of the system. In the step of "defining the state variables of the permanent magnet synchronous motor and establishing a mathematical model", the following steps are included:

[0011] List the three-phase voltage equations of motor abc;

[0012] The dq axis voltage equation is derived through Clark transformation and Park transformation;

[0013] Establish the voltage equations of the dq axis, including the voltage, current, inductance, stator winding resistance, and flux linkage on the dq axis;

[0014] Derive the equations of motion, including torque and speed equations.

[0015] The "Design Sliding Mode Controller" step includes the following steps:

[0016] Establish the system state space equation based on the torque equation;

[0017] Taking the speed and disturbance as observation objects, the speed error gain feedback is established;

[0018] The observer is output to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference ability.

[0019] The "Designing an Expanded Observer" step includes the following steps:

[0020] Establish the system state space equation based on the torque equation;

[0021] Taking the speed and disturbance as observation objects, the speed error gain feedback is established;

[0022] The observer is output to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference ability.

[0023] The present invention's sliding mode control method, based on disturbance observation, an improved reaching law, and a switching function, includes the following steps: defining the state variables of a permanent magnet synchronous motor and establishing a mathematical model; designing a sliding mode controller; designing an extended observer; and integrating the estimated results of the extended observer into the sliding mode controller to achieve system control. This method enables the system to achieve zero overshoot, fast response, short settling time, and strong anti-interference capabilities. The estimated torque can be smoother than the actual torque. Therefore, incorporating the estimated motor parameter changes and load torque disturbance values ​​observed by the extended observer into the sliding mode controller effectively reduces chattering. This solves the chattering problem associated with traditional sliding mode control. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 It is the algorithm block diagram.

[0026] Figure 2 is the speed change curve; (a) is the system response; (b) is the load startup comparison; (c) is the speed change curve when the load is suddenly increased.

[0027] Figure 3 These are the actual and observed values ​​of the sudden load increase and unload torque.

[0028] Figure 4 is the graph of the function f(s).

[0029] Figure 5 is the image of the function sgn(s)*.

[0030] Figure 6 This is a flow chart of the sliding mode control method based on disturbance observation, improved reaching law and switching function provided by the present invention.

[0031] Figure 7 It is a flow chart for defining the state variables of a permanent magnet synchronous motor and establishing a mathematical model.

[0032] Figure 8 It is a flow chart for designing sliding mode controller.

[0033] Figure 9 This is a flowchart for designing an extended observer. DETAILED DESCRIPTION

[0034] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0035] See also Figures 1 to 9 The present invention provides a sliding mode control method based on disturbance observation, improved reaching law and switching function, comprising the following steps:

[0036] S1 defines the state variables of the permanent magnet synchronous motor and establishes a mathematical model;

[0037] S11 lists the three-phase voltage equations of motor abc;

[0038] S12 is transformed by Clark and Park to derive the dq axis voltage equation;

[0039] S13 establishes the voltage equations of the dq axis, including the voltage, current, inductance, stator winding resistance, and flux linkage on the dq axis;

[0040] S14 derives the equations of motion, including torque and speed equations.

[0041] Specifically, by establishing a mathematical model of the permanent magnet synchronous motor, the voltage equation can be obtained as follows:

[0042]

[0043] Where: u d ,i d , L d is the voltage, current, and inductance on the d-axis; u q ,i q , L q are the voltage, current and inductance on the q axis; R is the stator winding resistance; ω m is the electrical angular velocity; ψ f is the magnetic flux; c is the number of pole pairs;

[0044] Since it is a surface permanent magnet synchronous motor, L d =L q , T e is the target torque, the torque equation is as follows:

[0045]

[0046] PMSM motion equation:

[0047]

[0048] Where: B is the viscous friction coefficient; J is the moment of inertia; TL is the load torque;

[0049] Considering the system parameters and torque changes:

[0050]

[0051] Where: Δα1, Δα2, Δα3 represent the parameter changes of the motor, β represents the disturbance value caused by the load torque and parameters; and

[0052]

[0053] S2 designs a sliding mode controller;

[0054] S21 establishes the system state space equation based on the torque equation;

[0055] S22 takes the speed and disturbance as observation objects and establishes the speed error gain feedback;

[0056] S23 outputs the observer to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference capabilities.

[0057] Specifically, the PMSM state variables are taken as

[0058]

[0059] Where: ωref is the target speed, ωm is the motor output speed; Combined with formula (5), and derived from formula (6), we can get

[0060]

[0061] The sliding surface function of the system is defined as:

[0062] s=cx1+x2(8)

[0063] Derivative the sliding surface function and substitute Equation (6) into it to obtain

[0064]

[0065] An improved new convergence rate will be introduced, and its improved convergence rate is

[0066]

[0067] Where: ε, q are constants, and ε>0, q>0 isokinetic approach term is -εsgn * (s)f(s), and the exponential approach term is qs. When the error increases, the constant velocity approach term makes the system state variable approach the sliding surface. At the same time, the exponential approach term reduces the system state variable to 0.

[0068] It can be seen that compared with the traditional approach, the improved approach law proposed in this paper adds a function f(s). From a formal point of view, the improved exponential approach law does not add new parameters, but only further utilizes the existing data. According to the change of s, it can be seen that the function has the following characteristics: (1) When |s| approaches 0, the function f(s) approaches a value greater than 0 and less than 1, which can improve the stability near the sliding surface; (2) When |s| approaches ∞, the function f(s) approaches ∞, thereby further increasing the driving speed. In summary, the use of the function f(s) can further improve the dynamic response capability of the sliding mode control.

[0069] The image of the function f(s) is as follows Figure 4 As shown in the figure, by adjusting the a and b parameters, the trend of the image is adjusted, thereby affecting the change of the convergence law.

[0070] The proposed switching function sgn(s)* is as follows Figure 5 As shown in Figure 2, compared with the sgn sign function, adjusting the k parameter can make the step smoother, thereby alleviating the chattering problem.

[0071] definition Combining equations (9) and (10), the output equation of the controller is:

[0072]

[0073] Select Lyapunov function

[0074]

[0075] According to the Lyapunov stability theorem, we only need to prove Then the system is asymptotically stable, and from equations (10) and (12) we can get

[0076] V=-εsgn * (s)f(s)-qs 2 (13)

[0077] Where: ε>0, q>0, and sgn * (s)f(s)>0; hence we can get Therefore, the system error can converge to 0 in a finite time, making the system stable.

[0078] S3 designs an expansion observer;

[0079] S31 establishes the system state space equation based on the torque equation;

[0080] S32 takes the speed and disturbance as observation objects and establishes the speed error gain feedback;

[0081] S33 outputs the observer to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference capabilities.

[0082] Specifically, in the actual motor speed control system, the PMSM system parameter disturbance changes slowly, and the first-order derivative of the disturbance can be approximated to 0. Then, the system state space equation can be established by formula (4) to obtain

[0083]

[0084] Taking ωm, β as observation objects, the gain feedback of the speed estimation error e1 is established, where the extended disturbance observer is designed based on formula (14):

[0085]

[0086] Where: are the estimated values ​​of electrical angular velocity and load parameter perturbation respectively; λ1, λ2, η are positive real numbers; in order to achieve high gain, η should be very small; using this observer, we can not only estimate the disturbance terms of motor parameter changes and load torque As feedforward compensation for sliding mode control, it can also achieve Approaching β, Approaching ωm;

[0087] From equations (15) and (16), the error equation of the extended observer is as follows:

[0088]

[0089] Where: represents the speed estimation error, Represents the estimation error of system parameters and load torque;

[0090] Therefore, the error state equation of the extended observer can be expressed as

[0091]

[0092] Where:

[0093] From this we can see that by configuring Located in the left half plane, the error e can be asymptotically approached to 0, which makes the system error approach 0;

[0094] The observed disturbance and the perturbation value of the load torque are Substituting into formula (11) we can get

[0095]

[0096] In order to verify the feasibility of combining the sliding mode control and disturbance observer proposed in this paper, a field-oriented control system of PMSM was built. In order to quickly respond to the continuous output of the speed loop, a current sliding mode controller with improved reaching law and switching function was designed. The designed speed controller and observer were verified and analyzed. The parameters of the PMSM used in the simulation model are shown in Table 1. The system block diagram is shown in Figure 1 shown.

[0097] S4 introduces the estimation result of the extended observer into the sliding mode controller to realize the control of the system.

[0098] In order to verify the feasibility of combining the sliding mode control and disturbance observer proposed in this paper, a field-oriented control system of PMSM was built. In order to quickly respond to the continuous output of the speed loop, a current sliding mode controller with improved reaching law and switching function was designed. The designed speed controller and observer were verified and analyzed. The parameters of the PMSM used in the simulation model are shown in Table 1. The system block diagram is shown in Figure 1 shown.

[0099] Table 1 PMSM parameters

[0100]

[0101] The parameters of the sliding mode controller and the extended observer in this design are c = 759, ε = 189, λ1 = 13, λ2 = 10, η = 0.00039, k = 4.8, a = 0.000007, b = 0.000006. The traditional sliding mode parameter configuration is c = 27, ε = 180, k = 270; the PI parameter configuration is k p =0.129,k i =6;

[0102] Simulation result analysis: Set the target speed to 1200r / min, DC side voltage U dc The voltage is 320V and the initial load is 5N.m. Figure 2 The speed response curves of the system under PI, traditional sliding mode, and traditional sliding mode are shown when a load of 10 N.m is suddenly added in 0.5 s. Tables 2 and 3 show the dynamic performance and anti-interference ability of the control methods.

[0103] Table 2 Dynamic performance comparison

[0104]

[0105] Table 3 Comparison of anti-interference performance

[0106]

[0107] Depend on Figure 2 As shown in Tables 2 and 3, the proposed sliding mode control method, based on a combination of an improved reaching law, a switching function, and a disturbance observer, outperforms traditional control methods in improving the dynamic performance and anti-interference performance of the speed regulation system. This method enables the system to achieve zero overshoot, fast response, short adjustment time, and strong anti-interference capabilities.

[0108] In order to verify that the designed extended sliding mode observer has good robustness to the system, the torque is suddenly increased by 10N / m at 0.3s and the torque of 10N / m is removed at 0.8s. Figure 3 The expanded observer is shown to estimate the torque change in real time when the load is suddenly added or removed.

[0109] Conventional sliding mode control, traditional PI and other control methods will produce large vibrations when the load is suddenly added or unloaded. Figure 3 It can be seen that when the torque changes suddenly, the estimated torque is smoother than the actual torque. Therefore, introducing the estimated motor parameter changes and the load torque disturbance observed by the extended observer into the sliding mode controller can effectively reduce the chattering.

[0110] The algorithm flow:

[0111] Enter an ω ref , represents the input target speed of the speed loop of the sliding mode control with improved reaching law and switching function. The whole system is ultimately designed to achieve this target speed. The output of the speed loop is i qref , is the input of the PI current loop, representing the input of the q-axis current. dref is the input current of the d-axis. Since the controlled permanent magnet synchronous motor is a surface-mount type, it can be directly set to 0 here.

[0112] The output of the current loop represents the voltage of the dq axis, which is u q 、u d After the inverse Park transformation u q 、u d Converted to u in the two-phase stationary coordinate system α 、u β , and then convert it into SVPWM output to the three-phase full-bridge inverter, U dc is the input DC drive voltage, and the output three-phase current i a 、i b 、i c Used to drive permanent magnet synchronous motors.

[0113] Three-phase current i a 、i b 、i c The current in the three-phase stationary coordinate system is converted into i by Clarke transformation α 、i βTwo-phase stationary coordinate system, and then through Park transformation, i α 、i β Transformed into the two-phase synchronous rotating coordinate system i q 、i d , which is used as feedback to the speed loop and current loop to form a closed-loop system.

[0114] The current angle θ obtained by the speed position sensor participates in Park transform and inverse Park transform, and then differentiates to obtain the current speed ω m , fed back to the speed loop. i q and ω m The output load torque compensation d is fed back to the sliding mode speed controller through the expansion observer to improve the anti-interference ability of the speed loop.

[0115] The above disclosure is only a preferred embodiment of the sliding mode control method based on disturbance observation, improved reaching law and switching function of the present invention. Of course, this cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that implementing all or part of the processes of the above embodiment and making equivalent changes in accordance with the claims of the present invention still fall within the scope of the invention.

Claims

1. A sliding mode control method based on disturbance observation, improved reaching law and switching function, characterized in that: The following steps are involved: Define the state variables of permanent magnet synchronous motor and establish a mathematical model; Design sliding mode controller; Design dilation observer; The estimation result of the extended observer is introduced into the sliding mode controller to realize the control of the system.

2. The sliding mode control method based on disturbance observation, improved reaching law and switching function according to claim 1, characterized in that: The process of "defining the state variables of a permanent magnet synchronous motor and establishing a mathematical model" includes the following steps: List the three-phase voltage equations of motor abc; The dq axis voltage equation is derived through Clark transformation and Park transformation; Establish the voltage equations of the dq axis, including the voltage, current, inductance, stator winding resistance, and flux linkage on the dq axis; Derive the equations of motion, including torque and speed equations.

3. The sliding mode control method based on disturbance observation, improved reaching law and switching function according to claim 2, characterized in that: In "Designing a Sliding Mode Controller," you need to: Establish the system state space equation based on the torque equation; Taking the speed and disturbance as observation objects, the speed error gain feedback is established; The observer is output to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference ability.

4. The sliding mode control method based on disturbance observation, improved reaching law and switching function according to claim 3, characterized in that: In "Designing a Dilated Observer," you need to: Establish the system state space equation based on the torque equation; Taking the speed and disturbance as observation objects, the speed error gain feedback is established; The observer is output to the sliding mode controller as compensation to improve the system's dynamic response and anti-interference ability.

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