Control method based on ESMDO and model-free adaptive sliding mode

Abstract

The invention discloses a control method based on ESMDO and a model-free adaptive sliding mode, and the method comprises the steps: firstly building an SPMSM mathematical model, and obtaining a rotating speed loop state equation; the method comprises the following steps: designing a model-free adaptive sliding mode controller, firstly establishing a hyperlocal model of a nonlinear system, and introducing a rotating speed ring state equation to obtain an SPMSM rotating speed ring extended hyperlocal model; based on a model-free control theory and the hyper-local model, designing an integral differential sliding mode surface and a rotating speed ring model-free adaptive sliding mode control rate; an extended sliding mode disturbance observer is designed, the model-free adaptive sliding mode controller outputs a reference current to the motor module according to an input reference rotating speed, and the motor module outputs an actual current and an actual rotating speed; and the expansion sliding mode disturbance observer observes uncertain and unknown disturbance parts of output system parameters and inputs the uncertain and unknown disturbance parts into the model-free self-adaptive sliding mode controller, and the actual rotating speed is also used for carrying out feedforward compensation on the reference rotating speed, so that control is completed. According to the invention, the anti-interference capability and robustness of the motor system are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a control method based on ESMDO and model-free adaptive sliding mode. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in numerous industries, including electric vehicles, medical devices, and aerospace, due to their simple structure, high efficiency, low noise, and high reliability. Traditional PI control is often used in PMSM systems due to its simple principle, excellent dynamic performance, and ease of implementation. However, PMSMs are multivariable, strongly coupled, nonlinear systems. Parameter changes and external disturbances can affect the control performance of PMSM systems, making it difficult to achieve efficient, precise, and stable operation of the motor in high-performance applications using traditional PI control.

[0003] With the long-term development of control theory, advanced control methods such as model reference adaptive control, robust control, predictive control, and sliding mode control have been applied to permanent magnet synchronous motor systems. Among them, sliding mode control (SMC) has attracted widespread attention due to its robustness and insensitivity to system parameters.

[0004] Some literature has described designing an integral time-varying sliding mode variable structure speed loop controller to achieve precise control of motor speed. Others have proposed combining exponential functions with power term piecewise functions to design a compound reaching law to accelerate system response. However, the controller gain is too large to guarantee system stability. However, sliding mode control, due to its discontinuous nature, can produce chattering. Therefore, minimizing chattering is crucial in designing sliding mode control.

[0005] Based on the above scheme, another proposal adds an exponential term to the power-approaching law and introduces the system state variable into the exponent of the power term. This not only improves the sliding mode approach speed but also suppresses system chattering. Another paper proposes an adaptive fuzzy sliding mode control method based on a disturbance observer, which effectively reduces tracking error, reduces chattering, and improves system control performance.

[0006] However, all of the above control algorithms are model-based, and their performance depends on accurate modeling of the controlled object. Since motor parameters do not remain constant during actual operation, these algorithms have certain limitations. Therefore, designing a robust controller that is independent of specific models is crucial for achieving high precision and fast response. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a control method based on ESMDO and model-free adaptive sliding mode, which effectively improves the anti-interference ability and robustness of the motor system.

[0008] In order to solve the above technical problems, the present invention provides a control method based on ESMDO and model-free adaptive sliding mode, comprising the following steps:

[0009] Establish the SPMSM mathematical model and obtain the speed loop state equation;

[0010] A model-free adaptive sliding mode controller is designed. First, a hyperlocal model of a single-input, single-output nonlinear system is established. The speed loop state equation is introduced to obtain the SPMSM speed loop extended hyperlocal model. Based on model-free control theory and the SPMSM speed loop extended hyperlocal model, the integral-differential sliding mode surface and the speed loop model-free adaptive sliding mode control rate are designed.

[0011] Design an extended sliding mode disturbance observer, based on the SPMSM speed loop extended super-local model, establish a disturbance observer model and design the observer sliding mode control rate;

[0012] The model-free adaptive sliding mode controller outputs a reference current to the motor module based on the input reference speed. The motor module outputs the actual current and actual speed. The actual current and actual speed are observed by the extended sliding mode disturbance observer to output the uncertain and unknown disturbance parts of the system parameters and input them into the model-free adaptive sliding mode controller. The actual speed is also used to perform feed-forward compensation on the reference speed to control the motor module.

[0013] Furthermore, in the mathematical model of SPMSM, the core saturation effect is ignored, eddy current and hysteresis losses are not considered, and internal parameter perturbations and load disturbances are introduced to obtain the torque equation and mechanical motion equation of the motor. Based on the torque equation and mechanical motion equation, the speed loop state equation is obtained.

[0014] Furthermore, the torque equation of the motor is: Among them, T e is the electromagnetic torque, i q is the q-axis stator current component, n p is the pole pair number, ψ f is the permanent magnet flux, ΔT e is the change of electromagnetic torque;

[0015] The mechanical motion equation of the motor is: Among them, T L is the load torque, B is the viscous friction coefficient; ω m is the mechanical angular velocity, ω e is the electrical angular velocity, ΔP nis the disturbance caused by the change of the moment of inertia and viscous friction coefficient, The whole represents the differential of electrical angular velocity; J is the moment of inertia;

[0016] The speed loop state equation of the motor is: where ΔT L is the unknown disturbance caused by the change of load torque.

[0017] Furthermore, the hyperlocal model of the nonlinear system is Among them, α1 is the design parameter to be determined, β1 is the state gain of the system; F1 is a nonlinear bounded function that satisfies the Lebesgue measurability theorem, u represents the system input, and x is the nonlinear system input.

[0018] Furthermore, the SPMSM speed loop extended super-local model is: Among them, α is the q-axis current gain that has yet to be determined, β is the speed gain that has yet to be determined, F is the uncertainty and unknown disturbance part of the system parameters, ξ(t) is the rate of change of F, i q is the q-axis stator current component.

[0019] Furthermore, the integral differential sliding surface is: Where x1 is the speed error, and c and m are both constants greater than 0.

[0020] Furthermore, based on the integral differential sliding surface, the adaptive exponential reaching law is designed as in, a>0, η is the adaptive factor, and k is any positive real number.

[0021] Furthermore, the model-free adaptive sliding mode control rate of the speed loop is:

[0022] in, is the online estimation of F using the extended sliding mode disturbance observer, is the reference speed of the motor, ω e is the electrical angular velocity, and α is the q-axis current coefficient which has yet to be determined.

[0023] Furthermore, the disturbance observer model is: in, is the observed value of the rotational speed; is the observed value of the uncertain and unknown disturbance part of the system parameters; yes The rate of change of χ is the gain of the disturbance observer, u ESMDO is the observer sliding mode control law.

[0024] Furthermore, based on the disturbance observer model and the SPMSM speed loop extended super-local model, the error equation is obtained as follows: Among them, e s is the speed observation error, e f is the observation error of F,

[0025] The sliding surface of the selected observer is:

[0026] The exponential reaching law of the selected observer is: Among them, ε ω is the switch gain to be designed; k ω is the coefficient of the exponential term to be designed; ε ω and k ω All greater than 0;

[0027] According to the error equation and the observer exponential reaching law, the observer sliding mode control law u is obtained ESMDO For: u ESMDO =-ε ω sigmoid(e s )-k ω e s -βe s .

[0028] Beneficial effects of the present invention:

[0029] Based on the motor's hyperlocal model, an integral-differential sliding mode surface is designed to reduce the system's steady-state error. An adaptive factor, η, is also introduced to achieve rapid system convergence. The designed model-free sliding mode controller with adaptive switching gain serves as the speed loop feedback controller, reducing motor system chatter and improving system robustness.

[0030] Based on the hyperlocal model, an extended sliding mode disturbance observer is designed to achieve accurate observation of the system. Compared with the ordinary sliding mode observer, it can effectively reduce system chattering and improve system control accuracy.

[0031] The present invention combines an extended sliding mode disturbance observer with a model-free adaptive sliding mode and applies it to the motor speed loop. Through simulation and comprehensive comparison with the traditional PI control method and the model-free sliding mode control method in terms of motor load addition and reduction, speed increase and decrease, and forward and reverse rotation, the simulation results show that the method of the application has strong anti-interference and robustness, better tracking performance, and faster dynamic response speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a block diagram of the model-free adaptive sliding mode algorithm of the present invention;

[0033] Figure 2This is a comparison chart of the sgn function and the sigmoid function;

[0034] Figure 3 It is the convergence form of the sigmoid function of the present invention under different a values;

[0035] Figure 4 It is a block diagram of the SPMSM system structure of the present invention;

[0036] Figure 5 This is a speed simulation curve diagram during no-load starting of the present invention;

[0037] Figure 6 This is a simulation curve diagram of the rotation speed when a sudden load is applied according to the present invention;

[0038] Figure 7 This is a simulation curve diagram of the rotation speed when the load suddenly drops according to the present invention;

[0039] Figure 8 This is a simulation curve diagram of the rotation speed when the speed is increased or decreased according to the present invention;

[0040] Figure 9 It is a speed simulation curve diagram of the present invention during forward and reverse rotation. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0042] Reference Figure 1 As shown in the figure, an embodiment of the control method based on ESMDO and model-free adaptive sliding mode of the present invention is presented. A surface-mounted permanent magnet synchronous motor (hereinafter referred to as the motor) is a complex system with multiple variables, strong coupling, and nonlinearity. When the motor system is affected by uncertain factors such as load disturbances, the motor will experience speed fluctuations and instability. This application can effectively solve the above problems and improve the anti-interference ability and robustness of the motor system.

[0043] Specifically, we first need to establish a mathematical model for the SPMSM, ignoring the core saturation effect, eddy current and hysteresis loss. The stator voltage equation of the motor in the dq rotating coordinate system is:

[0044]

[0045] Among them, u d 、u q are the d-axis and q-axis stator voltage components respectively; R S is the stator resistance; L d 、L q It is divided into d-axis and q-axis stator inductance components. For surface-mounted permanent magnet synchronous motors, Ld =L q ;i d 、i q are the d-axis and q-axis stator current components respectively; ω e is the electrical angular velocity; ψ f is the permanent magnet flux.

[0046] At this time, the torque equation of the surface-mounted permanent magnet synchronous motor is:

[0047]

[0048] Among them, T e is the electromagnetic torque; n p is the pole pair number.

[0049] The mechanical motion equation of the motor is:

[0050]

[0051] Among them, T L is the load torque, B is the viscous friction coefficient; ω m is the mechanical angular velocity.

[0052] However, in actual operation, the SPMSM will be affected by internal parameter perturbations and load disturbances. At this time, the stator voltage equation in the dq rotating coordinate system is:

[0053]

[0054] Where Δu d , Δu q is the change in the d-axis and q-axis stator voltage caused by the motor parameter perturbation, as shown in formula (5):

[0055]

[0056] Where, ΔR s is the stator resistance R s The change in ΔL d , ΔL q is the change in the d-axis and q-axis inductance; Δψ f is the change in the permanent magnet flux.

[0057] Considering the influence of internal parameter perturbation and load disturbance, the torque equation of the motor is designed as:

[0058]

[0059] Where, ΔT e is the change in electromagnetic torque. At this time, the motor mechanical motion equation is:

[0060]

[0061] Where ΔP n is the disturbance caused by the change of the moment of inertia and the viscous friction coefficient.

[0062] Combining equations (6) and (7), we can get the speed loop state equation as follows:

[0063]

[0064] Where, ΔT L is the unknown disturbance caused by the change of load torque.

[0065] Then the model-free adaptive sliding mode controller is designed: The block diagram of the model-free adaptive sliding mode algorithm designed in this application is as follows: Figure 1 As shown. The feedback controller in the figure is an adaptive sliding mode controller, u c As the output of the controller, the extended sliding mode disturbance observer observes and estimates the uncertain system parameters and the unknown disturbance part F.

[0066] Specifically, a hyperlocal model of the speed loop is first established. The hyperlocal model of the single-input, single-output nonlinear system (SISO) is:

[0067]

[0068] Where y represents the system output; n represents the order of differentiation, and n≥1 ; g(x) only depends on the unknown nonlinear function of x and satisfies the boundedness of the Lipschitz function; b represents a nonzero constant parameter; u represents the system input.

[0069] Combining equations (8) and (9), we can get the typical super-local model of the SPMSM speed loop:

[0070]

[0071] Among them, α1 is the design parameter that has yet to be determined; g is the uncertain and unknown disturbance part of the motor parameter.

[0072] According to the new hyperlocal model theory, g in Equation (10) is g(x), which is the motor parameter uncertainty and unknown disturbance part, and can be further decomposed into two parts: a linear system state and a nonlinear disturbance part, as shown in Equation (11): g(x) = β1x + F1 (11)

[0073] Among them, β1 is the state gain of the system; F1 is a nonlinear bounded function that satisfies the Lebesgue measurability theorem.

[0074] Substituting Equation (11) into Equation (9), we can obtain the new hyperlocal model of the nonlinear system:

[0075]

[0076] According to the SPMSM speed loop state equation described by formula (8) and the hyperlocal model of formula (12), the following speed loop extended new hyperlocal model is designed:

[0077]

[0078] Among them, α is the q-axis current gain that has yet to be determined, β is the speed gain that has yet to be determined, F is the uncertainty and unknown disturbance part of the system parameters, and ξ(t) is the rate of change of F.

[0079] Design of Model-Free Adaptive Sliding Mode Controller:

[0080] Based on the model-free control theory and combined with the SPMSM speed loop super-local model of formula (13), when n=1, the designed speed loop model-free control rate is:

[0081]

[0082] in, is the given q-axis current component; is the reference speed of the motor; u c is the output of the feedback controller.

[0083] The reference speed value and the actual value are selected as the state variables of the controller, and the state variables x1 and x2 are introduced at the same time:

[0084]

[0085] Combining equations (13) and (14), we can obtain:

[0086]

[0087] After taking the derivative of formula (15), we can combine it with formula (16) to get:

[0088]

[0089] In order to reduce the steady-state error, the integral differential sliding surface with the independent variable x1 is selected:

[0090]

[0091] Wherein, c and m are both constants greater than 0.

[0092] After taking the derivative of formula (18), we can substitute formula (17) to obtain:

[0093]

[0094] The mathematical expression of the traditional exponential reaching law (ERL) is shown in formula (20):

[0095] Wherein, ε and k are positive real numbers.

[0096] As can be seen from the above formula, the traditional exponential reaching law approaches the sliding surface at a constant speed when it is far away from the sliding surface. This results in: when ε is too small, the approach speed becomes slower, the approach time becomes longer, and the adjustment time also becomes longer; on the contrary, when ε is too large, the approach speed becomes faster, the approach time becomes shorter, the adjustment time becomes shorter, and the speed of reaching the sliding surface is too fast, causing large chattering and affecting the stability of the system. Therefore, to solve the above problems, an adaptive exponential reaching law is designed as shown in formula (21):

[0097]

[0098] in, a>0.

[0099] Since the sgn(x) function is discontinuous and prone to chattering, this application selects the function sigmoid(x) to replace the original switching function sgn(x). The comparison images of the two functions are as follows: Figure 2 As shown, Figure 3 It is the convergence form of the sigmoid function under different a values.

[0100] from Figure 2 and Figure 3 As can be seen, the sigmoid function converges within the range [-1, 1], and its convergence speed depends on the value of a. When a > 1, the sigmoid function is monotonically increasing. The sigmoid function's convergence speed increases with increasing a, and the system's response speed also increases. However, when a is too large, the sigmoid function (sgn function) increases chattering. Conversely, when a is too small, the curve becomes smoother, improving system robustness, but the system's response speed slows down, and dynamic performance deteriorates.

[0101] To ensure the system convergence speed and reduce chattering, it is necessary to select a suitable a value. This application selects a value of 18.

[0102] From equations (19) and (21), we can get the feedback controller u c for:

[0103]

[0104] Combining Equation (14) and Equation (22), the speed loop model-free adaptive sliding mode control rate can be obtained as follows:

[0105]

[0106] Where, It is an online estimation of F using an extended sliding mode disturbance observer.

[0107] Prove stability: Select Lyapunov function V1 as:

[0108] Taking the derivative of formula (24), we can get:

[0109]

[0110] Substituting formula (21) into formula (25) yields:

[0111] According to Lyapunov stability theory, a model-free adaptive sliding mode controller is adopted to achieve asymptotic stability.

[0112] Then the extended sliding mode disturbance observer is designed:

[0113] In order to improve the rapid response capability of the disturbance observer and the accuracy of its estimation, this application adopts an extended sliding mode disturbance observer to expand the parameter uncertainty and unknown disturbance F in the system input into state variables and accurately estimate them.

[0114] The disturbance observer model is established based on the extended hyperlocal model of the speed loop described by formula (13):

[0115]

[0116] in, is the observed value of the rotational speed; is the observed value of the uncertain and unknown disturbance part of the system parameters; yes The rate of change of χ is the gain of the disturbance observer, u ESMDO is the sliding mode control law.

[0117] Combining equations (13) and (27), we can get the error equation:

[0118]

[0119] Among them, e s is the speed observation error, e f is the observation error of F,

[0120] Select the following observer sliding surface:

[0121]

[0122] Select the observer exponential reaching law:

[0123]

[0124] Among them, ε ω is the switch gain to be designed; k ω is the coefficient of the exponential term to be designed; ε ω and k ω Both are greater than 0.

[0125] Combining equations (28) and (30), we can obtain the sliding mode control law u ESMDO for:

[0126] u ESMDO =-ε ω sgn(e s )-k ω e s -βe s (31)

[0127] Prove stability: Select Lyapunov function V2 as:

[0128] Taking the derivative of V2, we get:

[0129] Substituting formula (28) into formula (33), we can obtain:

[0130]

[0131] Formula (34) satisfies: ε ω ≥|e f |, then The observer is asymptotically stable, and the system state quantity can reach the sliding surface in a finite time. According to the sliding mode equivalence principle, Substitute into formula (28):

[0132]

[0133] Solving equation (35) yields:

[0134]

[0135] Among them, C>0, the size of χ affects the convergence speed of the system error.

[0136] In order to weaken the chattering of the extended sliding mode disturbance observer, the sigmoid function is also used instead of the sgn function, that is, the sliding mode control law u ESMDO The final result is: uESMDO =-ε ω sigmoid(e s )-k ω e s -βe s .

[0137] The model-free adaptive sliding mode controller and extended sliding mode disturbance observer are applied to the motor module for effective control. Specifically, the model-free adaptive sliding mode controller outputs a reference current to the motor module according to the input reference speed. The motor module outputs the actual current and actual speed. The actual current and actual speed are observed by the extended sliding mode disturbance observer to output the uncertain and unknown disturbance parts of the system parameters and input them into the model-free adaptive sliding mode controller. The actual speed is also used to perform feedforward compensation on the reference speed.

[0138] Simulation verification and analysis were also carried out

[0139] The algorithm simulation model of model-free adaptive sliding mode control based on extended sliding mode disturbance observer was built in Simulink, and the control strategy adopted was i d * =0, the system structure diagram is as follows Figure 4 To verify the effectiveness of the proposed method, the proposed method was simulated and compared with PI control and model-free sliding mode control. The motor parameters in the experiment are shown in Table 1, and the parameters of the PI control, MFSMC control, and MFASMC+ESMDO controller are shown in Table 2.

[0140] Table 1 SPMSM parameters

[0141]

[0142]

[0143] Table 2 Control system parameters

[0144]

[0145] Load addition and reduction simulation:

[0146] The simulation is set to a total time of 1 s, a given speed of 400 rpm, and a no-load start. A load of 10 N·m is suddenly added at 0.4 s and then suddenly reduced to 0 at t = 0.6 s. Figure 5 Table 3 shows the speed curves of the three control methods during no-load starting. Table 3 shows the specific performance comparison of the three control methods.

[0147] Table 3 Performance comparison of three control methods during no-load starting

[0148]

[0149] Note 1: The adjustment time in Table 3 is defined as the time it takes for the absolute value of the difference between the given speed and the actual speed to converge to 1 r / min.

[0150] from Figure 5 As shown in Table 3, PI control exhibits significant overshoot during motor startup, while MFASMC+ESMDO and MFSMC+SMO exhibit virtually no overshoot. Compared to PI control and MFSMC+SMO, the proposed method achieves faster stability, faster response, and smaller speed fluctuations. Figure 6 and Figure 7 The speed simulation curves for sudden load increase and sudden load decrease are shown in Table 4. The control performance data of the three control methods are shown in Table 4.

[0151] Table 4 Performance comparison of three control methods when the load increases and decreases suddenly

[0152]

[0153] When the motor is loaded at 0.4s, the overshoot generated by MFASMC+ESMDO is 86.6% less than that of PI and 25.7% less than that of MFSMC+SMO. MFASMC+ESMDO recovers to the desired speed in just 0.0036s, compared to 0.064s for PI and 0.026s for MFSMC+SMO. Furthermore, while PI exhibits significant jitter, MFASMC+ESMDO exhibits less jitter and a faster response than the other two algorithms. When the motor is unloaded at 0.6s, the speed overshoot of MFASMC+ESMDO is 92.1% less than that of PI and 53.5% less than that of MFSMC+SMO. MFASMC+ESMDO reaches steady state in 0.002s, a time reduction of 96.9% and 66.7% compared to PI and MFSMC+SMO, respectively. Speed fluctuation is also smaller than that of the other two control methods.

[0154] The above simulation results show that compared with other methods, MFASMC+ESMDO has a faster response speed. When the load is added or reduced, the speed can not only recover to the given value more quickly, but also the speed fluctuation is more stable, the anti-interference ability is stronger, and the robustness is better.

[0155] Speed ​​up and down simulation:

[0156] The motor runs at 100r / min without load. At 0.5s, the speed is set to 200r / min. After the motor runs stably for a period of time, the speed is changed to the given value of 100r / min at t=1s. The speed simulation curves of the three control methods are shown in the figure below. Figure 8 Table 5 shows the performance comparison of these three control methods.

[0157] Table 5 Performance comparison of three control methods when increasing or decreasing speed

[0158]

[0159] Depend on Figure 8 As shown in Table 5, compared with the other two control methods, MFASMC+ESMDO produces almost no speed overshoot throughout the entire operation process and exhibits better dynamic response characteristics. During the speed increase phase, MFASMC+ESMDO reaches the given speed value in just 0.009 seconds, which is 73.4% faster than the PI control method and 82% faster than the MFSMC+SMO control method. During the speed reduction phase, the overshoot produced by MFASMC+ESMDO and MFSMC+SMO is much smaller than that of the PI control method, and the speed fluctuation is also smoother than that of the PI control method. However, the response speed of MFSMC+SMO is far slower than that of MFASMC+ESMDO. The MFASMC+ESMDO method exhibits superior performance.

[0160] Forward and reverse simulation:

[0161] The total simulation time is set to 2s, the initial speed is set to 300r / min, and the speed is set to -300r / min at t=1s. The speed simulation curves of the three control methods are as follows Figure 9 shown.

[0162] Table 6 Performance comparison of three control methods in forward and reverse rotation

[0163]

[0164] Depend on Figure 9 As can be seen, the speed overshoot generated by the PI control method is consistently much larger than that generated by the other two control methods, regardless of forward or reverse rotation, indicating lower motor stability. Furthermore, the MFASMC+ESMDO method achieves a smoother transition and reaches steady-state much faster than the PI and MFSMC+SMO methods. Its forward motor regulation time is 85.7% shorter than the PI method and 80% shorter than the MFSMC+SMO method; its reverse motor regulation time is 84.1% shorter than the PI method and 78.1% shorter than the MFSMC+SMO method. Table 6 shows that the MFSMC+SMO method exhibits minimal fluctuations throughout the entire operation process, demonstrating high steady-state control accuracy.

[0165] This application addresses the vulnerability of permanent magnet synchronous motor control systems to uncertainties such as load disturbances. Using surface-mounted permanent magnet synchronous motors as the target, this application designs a model-free adaptive sliding mode controller based on model-free control theory and an adaptive sliding mode algorithm. Furthermore, an extended sliding mode disturbance observer is designed to accurately observe the uncertainties and unknown disturbances of the motor parameters in real time. Feedforward compensation is then applied to the model-free adaptive sliding mode controller to improve precise motor control. Simulation results demonstrate that the proposed method achieves superior dynamic performance, enhanced anti-interference capabilities, and effectively enhances the robustness of the motor system.

[0166] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or modification made by those skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A control method based on ESMDO and model-free adaptive sliding mode, characterized in that: The following steps are involved: Establish the SPMSM mathematical model and obtain the speed loop state equation; A model-free adaptive sliding mode controller is designed. First, a hyperlocal model of a single-input, single-output nonlinear system is established. The speed loop state equation is introduced to obtain the SPMSM speed loop extended hyperlocal model. Based on model-free control theory and the SPMSM speed loop extended hyperlocal model, the integral-differential sliding mode surface and the speed loop model-free adaptive sliding mode control rate are designed. Design an extended sliding mode disturbance observer, based on the SPMSM speed loop extended super-local model, establish a disturbance observer model and design the observer sliding mode control rate; The model-free adaptive sliding mode controller outputs a reference current to the motor module based on the input reference speed. The motor module outputs the actual current and actual speed. The actual current and actual speed are observed by the extended sliding mode disturbance observer to output the uncertain and unknown disturbance parts of the system parameters and input them into the model-free adaptive sliding mode controller. The actual speed is also used to perform feed-forward compensation on the reference speed to control the motor module.

2. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: In establishing the mathematical model of SPMSM, the core saturation effect, eddy current and hysteresis loss are ignored. At the same time, internal parameter perturbation and load disturbance are introduced to obtain the torque equation and mechanical motion equation of the motor. Based on the torque equation and mechanical motion equation, the speed loop state equation is obtained.

3. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: The torque equation of the motor is: Among them, T e is the electromagnetic torque, i q is the q-axis stator current component, n p is the pole pair number, ψ f is the permanent magnet flux, ΔT e is the change of electromagnetic torque; The mechanical motion equation of the motor is: Among them, T L is the load torque, B is the viscous friction coefficient; ω m is the mechanical angular velocity, ω e is the electrical angular velocity, ΔP n is the disturbance caused by the change of the moment of inertia and viscous friction coefficient, The whole represents the differential of electrical angular velocity; J is the moment of inertia; The speed loop state equation of the motor is: where ΔT L is the unknown disturbance caused by the change of load torque.

4. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: The hyperlocal model of the nonlinear system is Among them, α1 is the design parameter to be determined, β1 is the state gain of the system; F1 is a nonlinear bounded function that satisfies the Lebesgue measurability theorem, u represents the system input, and x is the nonlinear system input.

5. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: The extended hyperlocal model of the SPMSM speed loop is: Among them, α is the q-axis current gain that has yet to be determined, β is the speed gain that has yet to be determined, F is the uncertainty and unknown disturbance part of the system parameters, ξ(t) is the rate of change of F, i q is the q-axis stator current component.

6. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: The integral differential sliding surface is: Where x1 is the speed error, and c and m are both constants greater than 0.

7. The control method based on ESMDO and model-free adaptive sliding mode according to claim 6, characterized in that: Based on the integral differential sliding surface, the adaptive exponential reaching law is designed as follows: in, a>0, η is the adaptive factor, and k is any positive real number.

8. The control method based on ESMDO and model-free adaptive sliding mode according to claim 7, characterized in that: The model-free adaptive sliding mode control rate of the speed loop is: in, is the online estimation of F using the extended sliding mode disturbance observer, is the reference speed of the motor, ω e is the electrical angular velocity, and α is the q-axis current coefficient which has yet to be determined.

9. The control method based on ESMDO and model-free adaptive sliding mode according to claim 1, characterized in that: The disturbance observer model is: in, is the observed value of the rotational speed; is the observed value of the uncertain and unknown disturbance part of the system parameters; yes The rate of change of χ is the gain of the disturbance observer, u ESMDO is the observer sliding mode control law.

10. The control method based on ESMDO and model-free adaptive sliding mode according to claim 9, characterized in that: Based on the disturbance observer model and the SPMSM speed loop extended super-local model, the error equation is obtained as follows: Among them, e s is the speed observation error, e f is the observation error of F, The sliding surface of the selected observer is: The exponential reaching law of the selected observer is: Among them, ε ω is the switch gain to be designed; k ω is the coefficient of the exponential term to be designed; ε ω and k ω All greater than 0; According to the error equation and the observer exponential reaching law, the observer sliding mode control law u is obtained ESMDO For: u ESMDO =-ε ω sigmoid(es)-k ω e s -βe s .

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