Motor control method based on improved composite reaching law and sliding mode observer

Abstract

A motor control method based on an improved composite reaching law and a sliding mode observer belongs to the technical field of permanent magnet synchronous motor system control, and comprises the following steps: firstly, considering motor internal parameter change and external load disturbance, and establishing a disturbance-containing permanent magnet synchronous motor mathematical model and a motor state equation; secondly, providing a new switching function, constructing an improved composite reaching law, completing stability proving, and analyzing rapid convergence and buffeting suppression capability of the improved composite reaching law; then constructing an anti-saturation integral sliding mode surface, and designing a sliding mode speed controller according to the permanent magnet synchronous motor mathematical model containing disturbance, the anti-saturation integral sliding mode surface and the improved composite reaching law; and finally, aiming at disturbance in the controller, designing an improved sliding mode disturbance observer, and completing stability proving. The contradiction between fast convergence and buffeting suppression in an existing sliding mode reaching law scheme is solved, and the provided improved sliding mode observer improves the observation precision and the response speed.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor system control, and particularly to a motor control method based on an improved composite reaching law and a sliding mode observer. Background Art

[0002] Due to its excellent power factor and torque density, the permanent magnet synchronous motor is superior to the synchronous reluctance motor in terms of performance. At the same time, its significant efficiency improvement gives it an advantage in comparison with the induction motor. In addition, due to lower acoustic noise and torque ripple, the permanent magnet synchronous motor is also superior to the switched reluctance motor in terms of running smoothness. These characteristics make the permanent magnet synchronous motor an ideal choice in high-performance AC motor drive systems. At present, permanent magnet synchronous motor drive systems have been widely used in various power range fields, including industrial applications such as wind energy conversion systems, electric ships, hybrid vehicles, and electric vehicles. As a complex nonlinear electromechanical system, the performance of the permanent magnet synchronous motor can be further improved by advanced control strategies. Sliding mode control has been widely applied to motor systems due to its excellent performance in dealing with rapid changes in internal parameters of nonlinear systems, external disturbances, and unmodeled dynamics.

[0003] However, sliding mode control also has a significant limitation: the chattering problem caused by the switching function. This chattering not only reduces the operating performance of the motor system but may even cause system damage in severe cases. Therefore, how to effectively suppress chattering has become a key problem to be solved in the application of sliding mode control in permanent magnet synchronous motors. Currently, some researchers are exploring the use of various continuous functions to reduce the chattering problem in control systems, including activation functions, saturation functions, and hyperbolic tangent functions. Although these methods have achieved certain effects in suppressing chattering, they all seem to come at the cost of prolonging the convergence time of system states.

[0004] In existing sliding mode reaching law schemes, the exponential reaching law has a fast convergence speed but is prone to large chattering when approaching the sliding mode surface; the power reaching law can drive the system state to approach the sliding mode surface more smoothly, thereby reducing chattering, but the approaching speed will be affected. Therefore, it is necessary to solve the contradiction between fast convergence and chattering suppression.

[0005] During the actual operation of the motor, external load disturbances (such as sudden changes in load torque) will have a significant impact on the anti-interference performance of the speed controller. Although traditional sliding mode control has strong robustness, under external disturbances, the dynamic response performance of the system may decline, resulting in speed fluctuations or system instability. Although traditional sliding mode disturbance observers can observe external load disturbances and feed the observed values back to the speed controller, there are still problems such as insufficient observation accuracy and slow response speed. Summary of the Invention

[0006] The object of the present invention is to solve the problems mentioned in the existing background technology, and to provide a motor control method based on an improved composite reaching law and a sliding mode observer.

[0007] A motor control method based on an improved composite reaching law and a sliding mode observer includes the following steps:

[0008] Step 1, considering the internal parameter changes and external load disturbances of the motor, establish a mathematical model of a permanent magnet synchronous motor with disturbances and a motor state equation;

[0009] Step 2, propose a new switching function, construct an improved composite reaching law, complete the stability proof, and analyze the fast convergence and chattering suppression capabilities of the improved composite reaching law;

[0010] Step 3, construct an anti-saturation integral sliding mode surface, and design a sliding mode speed controller according to the mathematical model of the permanent magnet synchronous motor with disturbances, the anti-saturation integral sliding mode surface, and the improved composite reaching law;

[0011] Step 4, design an improved sliding mode disturbance observer for the disturbance in the controller, and complete the stability proof.

[0012] The mathematical model of the permanent magnet synchronous motor with disturbances in Step 1 is where ω m is the mechanical angular velocity of the rotor, J is the moment of inertia, B is the viscous friction coefficient, P n is the number of pole pairs, ψ f is the permanent magnet flux linkage, d is the disturbance value brought by the load torque and parameters, i q is the q-axis current, and where T L is the motor load torque, ΔJ, Δψ f and ΔB are the uncertainties caused by the system parameters J, ψ f and B.

[0013] The motor state equation in Step 1 is where e is the state variable of the system, is the first derivative of e, ω ref is the given mechanical angular velocity of the motor, ω m is the actual mechanical angular velocity of the rotor.

[0014] The new switching function in Step 2 is where sign(s) is the sign function, tanh(s) is the hyperbolic tangent function, σ represents the boundary layer thickness of the function ftanh(s), and 0 < σ < 1.

[0015] The improved composite reaching law in Step 2 is where k 1 and k 2 are both constants greater than zero, and 0 < α < 1; to prove the stability of the improved composite reaching law, define the Lyapunov function V = 0.5s 2 , and by taking the derivative of V, we can obtain Prove that the designed improved composite reaching law is stable.

[0016] In step 2, analyze the fast convergence and chattering suppression capabilities of the improved composite reaching law. To verify the effect of the switching function, take the following controlled object where f(x, t) and b are known, and b > 0; select the sliding mode function as where c > 0, the error e(t) = x d (t) - x(t), x(t) is the target position; adopt the improved composite sliding mode reaching law to obtain the sliding mode controller as To verify the effect of the improved composite sliding mode reaching law, also take the above controlled object and adopt the exponential reaching law where k > 0, q > 0, and the controller is designed as follows Replace the switching function in the improved composite sliding mode reaching law with sign(s) to obtain the controller

[0017] The anti-saturation integral sliding mode surface is where is the current after amplitude limiting, c > 0, K b is the feedback gain of the anti-saturation integral, and K b > 0; based on the designed anti-saturation integral sliding mode surface function and the improved composite reaching law, design the sliding mode controller as where is the pre-estimated value of d.

[0018] In step 3, the sliding mode surface function of the improved sliding mode disturbance observer is where c m is a parameter to be designed, and c m > 0; select the constant velocity reaching law where ε m is the switching gain, and ε m > 0; there is a sign function in the constant velocity reaching law, which will increase the chattering phenomenon of the sliding mode observer. Therefore, replace ftanh(s m ) with sign(s m ), and design the control law of the sliding mode disturbance observer as The observed disturbance can be obtained as where is the observed mechanical angle, To observe the disturbance, \(l\) is the gain of the sliding mode disturbance observer; define the Lyapunov function According to the Lyapunov stability theory, the conditions for the existence and reachability of the sliding mode surface are Therefore, the parameter \(\epsilon\) m needs to satisfy the following conditions where \(e\) d is the disturbance error, and

[0019] Advantages of the present invention:

[0020] 1. The novel switching function proposed by the present invention not only significantly reduces the chattering amplitude but also can quickly converge to the equilibrium point, successfully achieving the balance between stability and rapidity.

[0021] 2. The improved composite sliding mode reaching law proposed by the present invention combines the fast convergence characteristics of the exponential reaching law and the smooth approximation characteristics of the power reaching law, effectively solving the problems of long reaching time and large chattering in traditional sliding mode control. This reaching law not only significantly shortens the time for the system to reach the sliding mode surface, improves the dynamic response speed, but also reduces the high-frequency chattering through the smooth sliding mode surface approximation process, achieving the optimal balance between rapidity and stability.

[0022] 3. The improved sliding mode disturbance observer proposed by the present invention has achieved significant performance improvement, not only improving the observation accuracy of system disturbances, being able to more accurately estimate the system disturbances, but also greatly accelerating the response speed, being able to more quickly capture the changes in system disturbances. Description of the drawings

[0023] Figure 1 is the flowchart of the embodiment of the present invention.

[0024] Figure 2 is the system block diagram of the double closed-loop vector control of the permanent magnet synchronous motor in the embodiment of the present invention.

[0025] Figure 3 is the phase diagram of the switching function in the embodiment of the present invention.

[0026] Figure 4 is the sliding mode function diagram of the switching function in the embodiment of the present invention.

[0027] Figure 5 is the comparison diagram of the phase trajectories of the switching function in the embodiment of the present invention.

[0028] Figure 6 is the sliding mode function diagram of the reaching law in the embodiment of the present invention.

[0029] Figure 7 is the comparison diagram of the phase trajectories of the reaching law in the embodiment of the present invention.

[0030] Figure 8 This is the schematic diagram of speed control based on the improved composite reaching law according to the embodiment of the present invention.

[0031] Figure 9 This is the schematic diagram of the improved sliding mode disturbance observer according to the embodiment of the present invention.

[0032] Figure 10 This is the comparison chart of the rotational speed response in Experiment 1 according to the embodiment of the present invention.

[0033] Figure 11 This is the comparison chart of the torque response in Experiment 1 according to the embodiment of the present invention.

[0034] Figure 12 This is the comparison chart of the rotational speed response in Experiment 2 according to the embodiment of the present invention.

[0035] Figure 13 This is the comparison chart of the current response in Experiment 2 according to the embodiment of the present invention.

[0036] Figure 14 This is the comparison chart of the torque response in Experiment 2 according to the embodiment of the present invention. Detailed implementation manners

[0037] Please refer to Figures 1 to 14 as shown, which is the embodiment of the present invention.

[0038] A motor control method based on the improved composite reaching law and the sliding mode observer. The simulation model of the permanent magnet synchronous motor speed regulation system provided in this embodiment can be seen in Figure 2 , where the improved SMC speed controller and the improved SMO sliding mode disturbance controller are the content disclosed by the present invention.

[0039] Specifically, it includes the following steps:

[0040] Step 1: Considering the internal parameter changes and external load disturbances of the motor, establish a mathematical model of the permanent magnet synchronous motor with disturbances and the motor state equation.

[0041] The mathematical model of the permanent magnet synchronous motor in the d-q coordinate system can be expressed as

[0042]

[0043] In the formula, u d , u q are the d-axis and q-axis voltages respectively, i d , i q are the d-axis and q-axis currents respectively, L d , L q are the d-axis and q-axis inductances respectively, R s is the stator resistance, ω m is the mechanical angular velocity of the rotor, and ψ f is the permanent magnet flux linkage.

[0044] For the surface-mounted permanent magnet synchronous motor, L = L q = L d In addition, the vector control method adopted in the present invention is i d = 0, and thus the speed equation of the permanent magnet synchronous motor can be obtained as

[0045]

[0046] In the formula, J is the moment of inertia, B is the viscous friction coefficient, P n is the number of pole pairs, and T L is the load torque.

[0047] Considering the parameter variations, the dynamic motion equation of the surface-mounted permanent magnet synchronous motor can be expressed as

[0048]

[0049] where ΔJ, Δψ f and ΔB are the uncertainties caused by the system parameters J, ψ f and B.

[0050] Simplifying Equation (3) gives

[0051]

[0052] In the formula, d is the disturbance value caused by the load torque and parameters, and

[0053]

[0054] Define the state variable e of the permanent magnet synchronous motor system

[0055]

[0056] In the formula, ω ref is the given mechanical angular velocity of the motor, and ω m is the actual mechanical angular velocity of the motor.

[0057] Step 2: Propose a new switching function, construct an improved composite reaching law, complete the stability proof, and analyze the fast convergence and chattering suppression capabilities of the improved composite reaching law.

[0058] The new switching function proposed in the present invention is

[0059]

[0060] In the formula, sign(s) is the sign function, tanh(s) is the hyperbolic tangent function, σ represents the boundary layer thickness of the function ftanh(s), and 0 < σ < 1.

[0061] Combined with Figure 3 , the system phase diagrams of the sign function sign(s), the hyperbolic tangent function tanh(s), and the piecewise function ftanh(s) proposed in this chapter are shown, where σ = 0.1. As the absolute value of s decreases and s approaches 0, the sign function sign(s) suddenly changes to 0. At the same time, within the boundary layer defined by σ, the hyperbolic tangent function tanh(s) gradually converges to 0 linearly. However, this causes too long convergence time. The switching function ftanh(s) proposed in this paper converges in advance at the boundary layer, effectively improving the convergence time.

[0062] Based on the new switching function, an improved composite sliding mode reaching law is proposed, and its expression is as follows

[0063]

[0064] where k 1 and k 2 are both constants greater than zero, and 0 < α < 1.

[0065] Under the control of the proposed improved composite sliding mode reaching law, the system state is divided into two stages, namely the variable constant velocity term -k 1 |s| α ftanh(s) and the variable exponential term -k 2 (e |s| -1)s. The power function |s| α helps the system state to gradually stabilize when approaching the sliding mode surface, effectively reducing the oscillation phenomenon of the system, while the exponential function e |s| -1 can prompt the system state to quickly approach the sliding mode surface when far from the sliding mode surface. This reaching law can not only significantly shorten the time to reach the sliding mode surface, improve the dynamic response speed of the system, but also reduce high-frequency chattering through the smooth sliding mode surface approximation process.

[0066] Define the Lyapunov function. Combining with formula (8), we can get

[0067] When |s| > σ, ftanh(s) = sign(s). When s > σ, sign(s) = 1, so s·sign(s) = s > 0; when s < -σ, sign(s) = -1, so s·sign(s) = -s > 0, we get:

[0068]

[0069] When |s| < σ, ftanh(s) = tanh(s / σ). When -σ < s ≤ 0, tanh(s / σ) ≤ 0, so s·tanh(s / σ) ≥ 0; when 0 < s < σ, tanh(s / σ) > 0, so s·tanh(s / σ) > 0.

[0070]

[0071] Therefore, the improved composite sliding mode reaching law satisfies the Lyapunov stability criterion, and the system is asymptotically stable.

[0072] To verify the effect of the above switching function, the following controlled object is taken

[0073]

[0074] where f(x,t) and b are known, b > 0, and x(t) is the target position.

[0075] The sliding mode function is designed as

[0076]

[0077] where c > 0, and the error e(t) = x d (t) - x(t),

[0078] Differentiating the sliding mode function, we get

[0079]

[0080] Using the improved composite reaching law, the sliding mode controller is obtained as

[0081]

[0082] Select b = 133. Take the target position as x d (t) = sin(t), the initial state of the controlled object is [-0.15 0.15], and the controller based on the improved composite reaching law is used. The controller parameters are c = 15, k 1 = 40, k 2 = 20, α = 0.1 and σ = 0.1.

[0083] Combined with Figure 4 , the sliding mode function graph of the novel switching function ftanh(s) proposed by the present invention is compared with the traditional switching functions sign(s) and tanh(s). It can be seen from the figure that the convergence rate of the novel switching function ftanh(s) is higher than that of the switching function tanh(s), and although it is slightly lower than that of the switching function sign(s), its chattering situation is significantly better than that of the switching function sign(s). Combined withFigure 5 The speed at which the switching function ftanh(s) approaches the sliding mode surface is faster than that of the switching function tanh(s). After stabilization, the switching function ftanh(s) can be closer to the sliding mode surface.

[0084] To verify the effect of the improved composite sliding mode reaching law, the above-mentioned controlled object is also taken. The exponential reaching law is adopted where k > 0, q > 0, and the controller is designed as follows

[0085]

[0086] Replace the switching function in the improved composite sliding mode reaching law with sign(s) to obtain the controller

[0087]

[0088] As Figure 6 shown, the improved composite sliding mode reaching law (sign(s)) proposed by the present invention is compared with the exponential reaching law (sign(s)). The convergence speed of the improved composite sliding mode reaching law (sign(s)) is significantly faster than that of the exponential reaching law (sign(s)), which fully proves that the improved composite sliding mode reaching law (ftanh(s)) proposed by the present invention can significantly accelerate the response speed of the system. In addition, although the convergence speed of the improved composite sliding mode reaching law (ftanh(s)) is slightly slower than that of the improved composite sliding mode reaching law (sign(s)), its chattering degree is the smallest, thus effectively reducing the chattering of the system. Combining Figure 7 it can be seen that the improved composite sliding mode reaching law (ftanh(s)) is the most suitable for the sliding mode surface.

[0089] Step 3, construct an anti-saturation integral sliding mode surface. According to the mathematical model of the permanent magnet synchronous motor containing disturbances, the anti-saturation integral sliding mode surface and the improved composite reaching law, design a sliding mode speed controller;

[0090] There is an integral term in the traditional integral sliding mode surface. The existence of this integral term will cause the system to have a more serious overshoot phenomenon when tracking a reference speed with a large mutation degree. To obtain better control effects, the anti-saturation integral sliding mode surface expression is adopted as follows

[0091]

[0092] where is the current after amplitude limiting, c > 0, K b is the feedback gain of the anti-saturation integral.

[0093] Taking the derivative of the formula, we can get

[0094]

[0095] Selecting the improved composite reaching law proposed by the present invention, the control law of the controller can be obtained as

[0096]

[0097] wherein, is the pre-estimated value of d.

[0098] The structure diagram of the above-mentioned improved composite reaching law is as shown in Figure 8 shown.

[0099] Step 4: Design an improved sliding mode disturbance observer for the disturbance in the controller and complete the stability proof.

[0100] As can be seen from the formula, the control law has considered the influence of the total disturbance. However, in order to ensure the robustness of the system to the disturbance, it is often necessary to increase the switching gain of the reaching law, which may cause oscillation of the system. In order to reduce this oscillation while improving the robustness of the system, the present invention proposes a technique based on an observer to estimate and compensate for the mismatched disturbance caused by the parameter fluctuation of the permanent magnet synchronous motor and the external load disturbance, etc. This method can not only enhance the resistance of the system to the disturbance, but also effectively reduce the oscillation problem of the system.

[0101] Taking the mechanical angular velocity ω m and the total system disturbance d as state variables, the electromagnetic torque T e as the system input, and the mechanical angular velocity as the system output, the augmented state space equation is

[0102]

[0103] Taking the mechanical angular velocity ω m and the total system disturbance d as the observation objects, the sliding mode disturbance observer equation can be obtained from the formula

[0104]

[0105] wherein, and are the estimated values of ω m and d respectively, l is the sliding mode disturbance observer gain, g(e m ) is the control law of the sliding mode disturbance observer to be designed, e m is the electrical angular velocity error, and e d is the disturbance error, and Assuming that the disturbance error is bounded, |e d | < M, M ∈ R + . Subtracting Equation (21) from Equation (20) gives the following state equation

[0106]

[0107] Select the integral sliding mode surface

[0108]

[0109] where c m is a parameter to be designed, and c m > 0.

[0110] The ultimate goal of sliding mode control is to make e m and eventually tend to zero. To achieve this goal, take the derivative of the formula to get

[0111]

[0112] Select the constant velocity reaching law

[0113]

[0114] In the formula, ε m is the switching gain, and ε m > 0.

[0115] Combining formula and formula, and taking the term as the disturbance term, the control law of the sliding mode disturbance observer is designed as

[0116]

[0117] There is a sign function in formula (26), which will increase the chattering phenomenon of the sliding mode disturbance observer. Therefore, replace sign(s m ) with ftanh(s m ) proposed by the present invention to obtain the following expression

[0118]

[0119] To ensure that the sliding mode disturbance observer can converge in a finite time, it is necessary to reasonably select the parameters c m , ε m and l. Under the action of the control law, the sliding mode disturbance observer will make e m and tend to 0 in a finite time. When e m and tend to 0, we can get

[0120]

[0121] Integrate formula (28) to get

[0122]

[0123] where c d is a constant greater than zero. From Equation (29), it can be obtained that if the perturbation error e d converges to the equilibrium point within a finite time, then l < 0 in the equation, and the parameter l affects the convergence rate of the observer perturbation error.

[0124] Define the Lyapunov function

[0125]

[0126] Taking the derivative of the above equation gives

[0127]

[0128] Substituting Equations (22), (24), and (27) into it gives

[0129]

[0130] According to the Lyapunov stability theory, the conditions for the existence and reachability of the sliding mode surface are

[0131]

[0132] Therefore, the parameter ε m needs to satisfy the following conditions

[0133]

[0134] The block diagram of the improved sliding mode disturbance observer is as Figure 9 shown.

[0135] To verify the effectiveness of the control method of the present invention, a simulation model of the control method was constructed in the MATLAB / Simulink environment, and the performance of the control method was verified under various different experimental conditions.

[0136] In this embodiment, the parameters of the permanent magnet synchronous motor are shown in Table 1.

[0137] Table 1 Parameters of the permanent magnet synchronous motor

[0138]

[0139] The parameters of the traditional SMC are c = 160, k = 150, q = 200, K b = 600; the parameters of the improved SMC are c = 2.3, k 1 = 150, k 2 = 26, α = 0.8, K b = 10.

[0140] It is verified through two experimental conditions.

[0141] Experiment 1: Starting with load, the initial load is 3 N·m and the target speed is 1000 r / min. At 0.2 s, the load increases to 10 N·m; finally at 0.4 s, the load decreases to 5 N·m.

[0142]

[0143] Combined with Figure 10 , in terms of speed control, the improved sliding mode control (SMC) demonstrates excellent dynamic performance. The speed response time of the improved SMC is shortened to 0.02 s, indicating that its speed response speed is significantly superior to other methods. In the case of sudden load increase, the speed fluctuation amplitude is extremely small and can quickly recover to the set value. Similarly, when the load suddenly drops, the system shows the minimum overshoot, further verifying the excellent performance of the improved SMC under different experimental conditions.

[0144] Combined with Figure 11 , in terms of torque control, the improved SMC also performs excellently. In the case of sudden load increase, the torque recovery speed is faster and the recovery process is smoother, and it can quickly recover to the set value. When the load suddenly drops, the torque can also quickly return to the set value, further demonstrating the significant advantages of the improved SMC in dynamic response and control accuracy. These results indicate that the improved SMC has excellent dynamic performance and anti-disturbance ability in both speed and torque control.

[0145] Experiment 2: The initial speed is 1000 r / min. At 0.2 s, the speed increases to 1200 r / min, and then at 0.4 s, the speed decreases to 900 r / min.

[0146]

[0147] Combined with Figure 12 , the improved SMC shows the fastest dynamic response ability. When the rotational speed suddenly changes to 1200 r / min, the speed overshoot is significantly reduced; when the rotational speed decreases from 1200 to 900, the system can quickly stabilize to the target value, and the transition process is smooth, showing excellent dynamic performance and stability.

[0148] Combined with Figure 13 and Figure 14 , the improved SMC shows significant current stability during the rotational speed change process, and its current fluctuation is significantly smaller than that of the traditional SMC. At the same time, during the rotational speed change process, the torque mutation of the improved SMC is also significantly reduced, which is better than the traditional SMC. This indicates that the improved SMC can effectively suppress the current change and torque fluctuation during the dynamic process, showing stronger dynamic stability and anti-interference ability, further verifying its robustness and superior performance under complex working conditions.

Claims

1. A motor control method based on an improved composite reaching law and a synovial observer, characterized in that: The steps include: Step 1, considering the changes in internal parameters of the motor and external load disturbance, establish a mathematical model of the permanent magnet synchronous motor with disturbance and the motor state equation; Step 2: Propose a new switching function, construct an improved composite reaching law, complete the stability proof, and analyze the fast convergence and chattering suppression capabilities of the improved composite reaching law; Step 3, constructing an anti-saturation integral sliding film surface, and designing a sliding film speed controller according to the permanent magnet synchronous motor mathematical model containing disturbances, the anti-saturation integral sliding film surface and the improved composite reaching law; Step 4: Design an improved synovial disturbance observer for the disturbance in the controller and complete the stability proof.

2. The motor control method based on the improved composite reaching law and the sliding film observer according to claim 1 is characterized in that: The mathematical model of the permanent magnet synchronous motor containing disturbance in step 1 is: In the formula, ω m is the mechanical angular velocity of the rotor, J is the moment of inertia, B is the viscous friction coefficient, P n is the pole pair number, ψ f is the permanent magnet flux, d is the disturbance value caused by load torque and parameters, i q is the q-axis current, and Where, T L is the motor load torque, ΔJ, Δψ f and ΔB are system parameters J, ψ f and the uncertainty caused by B; The motor state equation in step 1 is: In the formula, e is the state variable of the system, is the first derivative of e, ω ref is the given motor mechanical angular velocity, ω m is the actual mechanical angular velocity of the rotor.

3. The motor control method based on the improved composite reaching law and the sliding film observer according to claim 1 is characterized in that: The new switch function in step 2 is: Where sign(s) is the sign function, tanh(s) is the hyperbolic tangent function, σ represents the boundary layer thickness of the function ftanh(s), and 0<σ<1; The improved composite reaching law in step 2 is: In the formula, k1 and k2 are both constants greater than zero, and 0<α<1; Improve the stability proof of the composite reaching law and define the Lyapunov function V=0.5s 2 , taking the derivative of V we get It is proved that the designed improved composite reaching law is stable.

4. The motor control method based on the improved composite reaching law and the sliding film observer according to claim 1 is characterized in that: In step 2, the fast convergence and chattering suppression capabilities of the improved composite reaching law are analyzed. In order to verify the effect of the switching function, the following controlled object is taken In the formula, f(x, t) and b are known, and b>0; the sliding mode function is selected as Where c>0, error e(t)=x d (txt), x(t) is the target position; the sliding film controller is obtained by using the improved composite sliding mode reaching law: In order to verify the effect of improving the composite synovial film reaching law, the same controlled object is taken and the exponential reaching law is adopted. In the formula, k>0, q>0, the controller is designed as follows The controller is obtained by replacing the switching function in the improved composite synovial reaching law with sign(s) The anti-saturation integral synovial surface is In the formula, is the current after limiting, c>0, K b is the feedback gain of the anti-saturation integral, and K b >0; Based on the designed anti-saturation integral sliding film surface function and the improved composite reaching law, the sliding mode controller is designed as In the formula, is the estimated value of d.

5. The motor control method based on improved composite reaching law and sliding film observer according to claim 1, characterized in that: The synovial surface function of the improved synovial disturbance observer in step 3 is: In the formula, c m is the parameter to be designed, and c m >0; select the constant speed approach law In the formula, ε m is the switching gain, and ε m >0; There is a sign function in the constant velocity reaching law, which will increase the chattering phenomenon of the sliding mode observer. Therefore, ftanh(s m ) is replaced by sign(s m ), the control law of the sliding mode disturbance observer is designed as The observed disturbance is In the formula, To observe the mechanical angle, is the observed disturbance, l is the sliding mode disturbance observer gain; define the Lyapunov function According to Lyapunov stability theory, the conditions for the existence and reachability of the sliding surface are: So the parameter ε m The following conditions must be met Where e d is the disturbance error, and

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