SPMSM robust speed control method based on adaptive high-order expansion sliding mode observer

Abstract

The invention discloses an SPMSM robust speed control method based on an adaptive high-order expansion sliding-mode observer, and the method comprises the following steps: designing and building a third-order LESO system according to a motor mathematical model, and the third-order LESO system is used for outputting an estimated rotating speed actual value, an estimated acceleration and estimated total disturbance; combining a non-singular fast terminal sliding mode algorithm with a disturbance observer, and designing a non-singular fast terminal sliding mode disturbance observer which is used for observing an acceleration state variable of the motor; the acceleration state variable is input into the third-order LESO system and replaces the estimated acceleration, and a high-order expansion sliding mode observer is generated; and constructing an active-disturbance-rejection controller by using the high-order expansion sliding-mode observer, linear state error feedback and total disturbance compensation, and performing speed control on the motor by using the active-disturbance-rejection controller. According to the method, high-precision observation of disturbance can be realized under the conditions that only less interference information exists and the method is not sensitive to interference frequency change.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to an SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in aerospace, new energy vehicles, intelligent robotics, and other fields due to their advantages, such as low moment of inertia, wide speed regulation range, high operating efficiency, and high energy efficiency. Based on the installation location of the rotor permanent magnets, PMSMs can be divided into two categories: interior permanent magnet synchronous motors (IPMSMs) and surface mounted permanent magnet synchronous motors (SPMSMs). Compared to IPMSMs, SPMSMs typically adopt a vector control strategy with id = 0, which is more flexible and easier to achieve high-precision control. In the dual closed-loop control system of an SPMSM, the outer speed loop provides a reference signal for the inner current loop, which in turn determines the control performance and dynamic response speed of the entire drive system. Therefore, the design quality of the speed loop controller directly affects the overall performance of the SPMSM drive system. Traditional linear control methods, such as proportional-integral control, have been widely used in the speed loop. However, due to the prevalence of disturbances in SPMSM drive systems, such as friction torque, flux harmonics, and load variations, traditional PI controllers are limited in their ability to address these disturbances and are unable to effectively mitigate their negative impact on system performance.

[0003] To cope with external disturbances, methods such as sliding mode control, iterative learning control, quasi-proportional resonant control, and fuzzy control have been widely used in the speed control of permanent magnet synchronous motors. However, these control strategies are only applicable to certain types of disturbances because they produce large open-loop gains at specific frequencies. In addition to suppressing disturbances through control strategies, another way to improve speed control performance is based on disturbance and disturbance estimation methods, such as disturbance observers, sliding mode observers, and extended state observers. These methods can quickly suppress the impact of disturbances on the control system by observing the disturbance and compensating it in real time into the control signal. Among them, the composite control method using the extended state observer is usually called nonlinear active disturbance rejection control (NADRC).

[0004] Although linear active disturbance rejection control (LADRC) has made significant progress in addressing parameter tuning and theoretical analysis challenges, its torque estimation performance remains limited due to its inability to achieve asymptotic estimation of time-varying disturbances. Conventional LADRC (Latin American Dynamics Control) enhances the system's ability to estimate time-varying disturbances by using a linear extended state observer (LESO) with a large bandwidth. However, this approach is limited by the system's observer bandwidth, which in turn impacts performance. To address this, various novel extended state observer (ESO) structures have been proposed to reduce the estimation error of time-varying disturbances and improve system performance. For example, a quasi-proportional resonant controller (QRC) combined with a super-warped extended state observer (SWEDO) was proposed to successfully suppress motor speed fluctuations and optimize the stability and disturbance rejection capability of the motor drive system. The QRC replaces the linear state error feedback in the LADRC, effectively reducing the impact of AC disturbances on the system. However, the performance of the resonant controller is highly dependent on real-time, high-precision acquisition of the disturbance frequency. Another approach, based on a high-order extended state observer (HESO), has been proposed. By increasing the number of extended states, asymptotic convergence of higher-order terms in the disturbance polynomial form is achieved, thereby improving the estimation accuracy of time-varying disturbances. Compared to schemes that incorporate quasi-proportional resonant controllers, HESO is less sensitive to variations in disturbance frequency and its design relies less on disturbance information. However, HESO's weak noise suppression capability limits its estimation accuracy in practical applications.

[0005] In summary, HESO still needs to be further explored in terms of its noise attenuation capability and the trade-off between signal convergence rate and estimation accuracy. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer, which can achieve high-precision observation of disturbances with only less interference information and insensitivity to changes in interference frequency.

[0007] In order to solve the above technical problems, the present invention provides a SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer, comprising the following steps:

[0008] A third-order LESO system is designed and established based on the motor mathematical model. The third-order LESO system is used to output the estimated actual speed value, estimated acceleration, and estimated total disturbance.

[0009] Combining the non-singular fast terminal sliding mode algorithm with the disturbance observer, a non-singular fast terminal sliding mode disturbance observer is designed and used to observe the acceleration state variables of the motor;

[0010] The acceleration state variable is input into the third-order LESO system and replaces the estimated acceleration to generate a high-order extended sliding mode observer;

[0011] An active disturbance rejection controller is constructed by combining a high-order extended sliding mode observer with linear state error feedback and total disturbance compensation, and the motor speed is controlled by the active disturbance rejection controller.

[0012] Furthermore, the state space of the third-order LESO system is expressed as follows:

[0013]

[0014] By configuring the poles, the observer feedback gain coefficient is configured at -ω0, where ω0 is the observer bandwidth; where l1=3ω0, x1=ω r ,ω r is the mechanical angular velocity of the dq axis coordinate system; x2 is the acceleration of the mechanical angular velocity; x3 = f, f is the total disturbance to be observed; u = i q ,i q is the stator current in the motor q coordinate system; y = x1; u is the output of the linear active disturbance rejection controller; J0 is the initial value of the motor's moment of inertia, ψ f is the permanent magnet flux, and P is the number of magnetic pole pairs of the motor.

[0015] Furthermore, the feedback gain coefficient is brought into the third-order LESO system to obtain:

[0016] Where z1, z2, and z3 are the output estimated actual speed value, estimated acceleration, and estimated total disturbance, respectively.

[0017] Furthermore, the design steps of the non-singular fast terminal sliding mode disturbance observer are as follows:

[0018] Design of non-singular fast terminal sliding surface based on sigmoid(x) function;

[0019] According to the equivalent sliding mode control principle, the equivalent term of the sliding mode control law is obtained, and then the switching control law is designed by controlling the system state on the sliding mode surface;

[0020] A non-singular fast terminal sliding mode disturbance observer is designed based on the non-singular fast terminal sliding mode surface and switching control law.

[0021] The motor is observed by a non-singular fast terminal sliding mode disturbance observer and the state variables are output.

[0022] Furthermore, the non-singular fast terminal sliding surface is:

[0023] α, β>0; 0<γ<1, e ω is the speed estimation error.

[0024] Furthermore, the switching control law is:

[0025] M=αe ω +β|e ω | γ sigmoid(e ω )+M n

[0026]

[0027] Among them, M n (0)=0; P is the parameter of control law design, k1,η,r,μ>0; 0<δ<1; 0<Q<1.

[0028] Furthermore, the non-singular fast terminal sliding mode disturbance observer is:

[0029] Where, ω r The estimated value of M is the switching control law; h is the derivative of the total disturbance f that needs to be observed, T e is the electromagnetic torque, and J is the moment of inertia.

[0030] Furthermore, the high-order extended sliding mode observer is:

[0031]

[0032] Beneficial effects of the present invention:

[0033] 1. This application uses HESO, which enables high-precision observation of disturbances with minimal interference information and insensitivity to changes in interference frequency. Furthermore, to further improve system performance and mitigate high-frequency chattering, a sliding mode algorithm is introduced within the HESO framework for variable observation, and a non-singular fast terminal sliding mode algorithm is employed to mitigate high-frequency chattering, making variable observation more accurate.

[0034] 2. The proposed speed controller effectively solves the trade-off between signal convergence rate and estimation accuracy, and at the same time shows significant advantages in anti-interference ability and disturbance estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the LADRC-based SPMSM vector control diagram of the present invention;

[0036] Figure 2 is a Bode plot of the disturbance estimate of the second-order LESO of the present invention;

[0037] Figure 3 is a Bode plot of the disturbance estimation error value of the second-order LESO of the present invention;

[0038] Figure 4is a Bode plot of the disturbance estimate of the third-order LESO of the present invention;

[0039] Figure 5 is a Bode plot of the disturbance estimation error value of the third-order LESO of the present invention;

[0040] Figure 6 is a Bode plot of the disturbance estimation value comparing the second-order LESO and the third-order LESO of the present invention;

[0041] Figure 7 is a Bode plot of the disturbance estimation error values comparing the second-order LESO and the third-order LESO of the present invention;

[0042] Figure 8 is a structural diagram of a high-order extended sliding mode observer of the present invention;

[0043] Figure 9 It is the improved speed controller of the present invention;

[0044] Figure 10 This is a comparison chart of the rotation speeds of the ILADRC and LADRC of the present invention;

[0045] Figure 11 This is a diagram of the dynamic experimental results of three controllers with step loads;

[0046] Figure 12 This is the dynamic experimental result diagram of the speed mutation of three controllers;

[0047] Figure 13 This is a graph showing the results of a dynamic acceleration experiment of a motor according to the present invention;

[0048] Figure 14 This is a diagram showing the results of a dynamic experiment on motor deceleration according to the present invention. DETAILED DESCRIPTION

[0049] 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.

[0050] Reference Figure 1 As shown, an embodiment of the SPMSM robust speed control method based on the adaptive high-order extended sliding mode observer of the present invention first needs to establish a mathematical model of the SPMSM motor:

[0051]

[0052] Where: u d ,u q are the stator voltages in the rotating dq coordinate system respectively; i d ,i q are the stator currents in the rotating dq coordinate system; Rs is the stator resistance; L d ,L q is the inductance component of the stator winding dq axis; ψ f is the permanent magnet flux; ω is the electrical angular velocity; ω r is the mechanical angular velocity of the dq axis coordinate system; P is the number of magnetic pole pairs of the motor; J is the moment of inertia; B is the friction factor; T e is the electromagnetic torque; T L is the load torque.

[0053] This application uses a first-order LADRC to control the SPMSM drive system without using a linear tracking differentiator, such as Figure 1 As shown. For a first-order system Select the system output y = x1 and the unknown disturbance x2 = f as state variables. In the SPMSM speed control, let the motor output speed x1 = ω r ,u=i q , and then combine the motor mathematical model (1) to construct the observation model of the extended state observer, and obtain the state space expression:

[0054]

[0055] in, J0 is the initial value of the motor's moment of inertia, x1=ω r , x2=f, y=x1.

[0056] According to the mathematical model of the motor and taking into account the uncertainty of the moment of inertia and viscous friction coefficient, formula (1) is transformed into:

[0057]

[0058] Where ΔJ is the deviation between the actual value and the initial value of the motor's moment of inertia, and f is the total disturbance that needs to be observed.

[0059] According to formula (3), the second-order LESO is designed as follows:

[0060]

[0061] where z1, z2, are the estimated values of x1, x2, and y respectively; l1 and l2 are the observer adjustment parameters.

[0062] Through pole configuration, the feedback gain coefficient of the observer is configured at -ω0, where ω0 is the observer bandwidth.

[0063] λ 2 +l1λ+l2=(λ+ω0) 2 (5)

[0064] According to formula (5), we can get l1=2ω0, Combining linear state error feedback and total disturbance compensation, the LADRC structure is obtained:

[0065]

[0066] Where u0 is the linear state error feedback output, u is the linear active disturbance rejection controller output, and f0 is the known disturbance.

[0067] Next, we use frequency domain analysis to analyze the limitations of the second-order LESO. Let the tracking errors of z1 and z2 be e1 and e2, respectively. The error expressions are as follows:

[0068]

[0069] According to formulas (6), (7) and (8), the LESO transfer function G based on the interference observation value can be obtained z1 (s) and the LESO transfer function G based on the disturbance estimation error e1 (s), as follows:

[0070]

[0071] According to formulas (9) and (10), several Bode diagrams of the second-order LESO based on the disturbance estimation value and the disturbance estimation error with increasing ω0 are obtained, as shown in Figure 2. Figure 2 and Figure 3 shown.

[0072] In order to expand the estimation range of LESO for DC disturbances without increasing the observer bandwidth ω0, so that the extended state observer can accurately estimate DC disturbances, a third-order LESO is established, and the state space expression is as follows:

[0073]

[0074] By configuring the poles, the observer feedback gain coefficient is configured at -ω0, where ω0 is the observer bandwidth; where l1=3ω0, x1=ω r ,ω r is the mechanical angular velocity of the dq axis coordinate system; x2 is the acceleration of the mechanical angular velocity; x3 = f, f is the total disturbance to be observed; u = i q ,i q is the stator current in the motor q coordinate system; y = x1; u is the output of the linear active disturbance rejection controller; J0 is the initial value of the motor's moment of inertia, ψ f is the permanent magnet flux, and P is the number of magnetic pole pairs of the motor.

[0075]

[0076] According to formula (12), we can get l1=3ω0,

[0077] Since ω0 is a real number greater than zero, the odd-order Hurwitz determinant of formula (12) is described as follows:

[0078] D1=a1=3ω0>0 (13)

[0079]

[0080] Where a0=1,a1=3ω0,

[0081] Combining Equations (13) and (14) with the Lienard-Chipard stability criterion, it can be concluded that the third-order LESO is stable.

[0082] Substituting the feedback gain coefficient into the third-order LESO, we get:

[0083]

[0084] Among them, z1, z2, z3 are the estimated values of state variables, that is, z1, z2, z3 are the output estimated actual speed value, estimated acceleration and estimated total disturbance respectively; l1, l2, l3 are observer adjustment parameters.

[0085] The bandwidth is tuned using the pole placement method to place the closed-loop poles of the observer at the same position -ω0. The transfer function based on the disturbance estimate and the disturbance estimation error is:

[0086] Transfer function G based on disturbance estimate z (s):

[0087]

[0088] Transfer function G based on disturbance estimation error value e (s):

[0089]

[0090] According to formula (16), the transfer function of the third-order LESO based on the disturbance estimate is G z2 (s):

[0091]

[0092] According to formula (17), the transfer function of the third-order LESO based on the disturbance estimation error value is G e2 (s):

[0093]

[0094] According to formulas (18) and (19), several Bode diagrams of the second-order LESO based on the disturbance estimation value and the disturbance estimation error with increasing ω0 are obtained, as shown in Figure 2. Figure 4 and Figure 5 As shown, combined with the previous second-order LESO transfer function based on disturbance estimation value and disturbance estimation error, the comparative Bode diagram is obtained, as shown in Figure 6 and Figure 7 shown.

[0095] pass Figures 2 to 7 As shown, as the second-order LESO increases in observer bandwidth, its bandwidth becomes wider, and its ability to suppress high-frequency interference decreases. Under the same observer bandwidth ω0, the third-order LESO has a wider range of DC disturbance estimation than the second-order LESO, and the system has stronger anti-interference capability. Furthermore, the third-order LESO avoids high-frequency oscillations caused by an increase in ω0. In the low-frequency range, the third-order LESO's observation error amplitude gain for DC disturbances is smaller than that of the second-order LESO, further demonstrating that the third-order LESO has stronger DC interference suppression capability than the second-order LESO. At the same time, the impact of phase lag on the system is reduced. Therefore, as the order and bandwidth increase, the higher-order LESO has better anti-interference capability than the lower-order LESO.

[0096] After the establishment of the third-order LESO is completed, it is necessary to design the adaptive disturbance differential compensation high-order extended sliding mode observer:

[0097] In a third-order LESO design, the estimated value z2 of the state variable x2 is obtained using formula (15) and fed back into the system via the linear state error. However, the third-order LESO observations produce high-frequency chattering, which reduces the observer's accuracy. This application combines a non-singular fast terminal sliding mode algorithm with a disturbance observer to observe the state variable Z4, differentially compensate the disturbance to the control system, and simultaneously reduce chattering. This is then combined with the HESO to obtain a higher-order extended sliding mode observer (HESMSO). This is combined with linear state error feedback and total disturbance compensation to construct a novel active disturbance rejection controller (ILADCR).

[0098] First, in order to achieve the observation of accurate output values, a new non-singular terminal sliding surface is proposed. Secondly, based on this sliding surface, the enhanced fractional reaching law and the exponential reaching law are innovatively combined, so that the sliding mode control has a faster convergence speed when facing system disturbances.

[0099] Consider the general case of a nonlinear system with single input and single output.

[0100] Design a non-singular fast terminal sliding surface:

[0101]

[0102] Among them, α, β>0; 0<γ<1; the sigmoid(x) function with smooth and continuous characteristics is expressed as:

[0103]

[0104] Among them, d is an adjustable parameter.

[0105] When the state variable of the sliding mode observation enters the sliding mode, it satisfies Right now

[0106]

[0107] From formula (23), we can see that when the error state is far away from the equilibrium point, the linear term dominates the state convergence rate, and when the error state approaches the equilibrium point, the nonlinear term Therefore, in the sliding stage, the non-singular fast terminal sliding surface can achieve global fast convergence, and its convergence speed is comparable to that of the traditional non-singular fast terminal sliding surface. There is no negative exponential state in , which prevents singular phenomena, and compared with the traditional non-singular terminal sliding surface, it does not require differential states.

[0108] Based on the equivalent sliding mode control principle, the equivalent term of the sliding mode control law is obtained. Then, by controlling the system state on the sliding mode surface, a switching control law is designed to achieve system switching near the sliding mode surface, realizing robust control against uncertainties and disturbances. The control law is as follows:

[0109] u′=-f(x)-β|x|γsigmoid(x)+u n (twenty four)

[0110]

[0111] Among them, u n (0) = 0; T > 0, k > 0, all are designed parameters, k1, η, r, μ > 0; 0 < δ < 1; 0 < Q < 1. By selecting appropriate parameters, the non-singular fast terminal sliding mode control can be made highly robust to system disturbances.

[0112] The dynamic equation of the motor can be converted into:

[0113]

[0114] The non-singular fast terminal sliding mode disturbance observer is designed as:

[0115]

[0116] Where, ω r is the estimated value of ; M is the designed control law; h is the derivative of the disturbance value f.

[0117] The system error state equation can be obtained according to formula (26) and formula (27):

[0118]

[0119] in, is the speed estimation error; e d is the estimated error value of the system disturbance.

[0120] In order to make the sliding mode control converge faster when facing system disturbances, the non-singular fast terminal sliding mode surface is redesigned as:

[0121]

[0122] According to formula (24) and formula (25), the switching control law is redesigned as:

[0123] M=αe ω +β|e ω | γ sigmoid(e ω )+M n (30)

[0124]

[0125] Among them, M n (0) = 0; P is the parameter for the switching control law design. The equivalent disturbance value derivative can be designed as:

[0126]

[0127] Among them, k2 is the parameter of the design disturbance value derivative.

[0128] Z4 is obtained by design, and Z4 is added to the third-order LESO to obtain the high-order extended sliding mode observer:

[0129]

[0130] According to formula (33), a high-order extended sliding mode observer structure is constructed as follows Figure 8 As shown, the improved speed controller is as follows Figure 9To analyze the improved performance of ILADRC compared with LADRC, a comparative test was conducted with the motor starting at 1000 r / min without load, applying a 5N load mutation at 0.2s, and a 10N load mutation at 0.4s. The results are shown in the figure. Figure 10 The parameters of the non-singular sliding mode algorithm are α=1, β=2, γ=0.6, Q=0.001, k1=0.65, r=0.5, μ=4, δ=0.6.

[0131] according to Figure 10 It can be seen that the maximum speed overshoot of the LADRC is 1115 rpm, while that of the ILADRC is only 1083 rpm. The stabilization time is 0.03 seconds for the LADRC and 0.012 seconds for the ILADRC, which is 40% of the LADRC's. Under two sudden load changes, the ILADRC reaches stability much faster than the LADRC, maintaining a speed fluctuation of ±0.1 rpm. Even under higher loads, the ILADRC demonstrates significantly better results than the LADRC.

[0132] To fully verify the control performance of the HESMSO proposed in this application, a HESMSO active disturbance rejection controller was used for research and verification on an experimental platform. The controller uses the STM32F407IGTb chip. Specific motor parameters are shown in Table 1.

[0133] Table 1 Permanent magnet synchronous motor parameters:

[0134]

[0135]

[0136] In order to objectively verify the control performance of the algorithm, three controller methods were selected, namely traditional active disturbance rejection control, high-order active disturbance rejection control and improved high-order active disturbance rejection control. Figure 11 In the figure, the speed and q-axis current are shown when the load is applied and removed under the condition of a constant speed of 1000 r / min, where (a) is the result of the LADRC controller, (b) is the result of the HLADRC (high-order linear active disturbance rejection controller) controller, and (c) is the result of the ILADRC controller. Figure 12 Figure 2 shows the speed waveform and q-axis current when the speed is predetermined to be 1000 r / min-1500 r / min after starting under no-load running conditions, where (a) is the result of the LADRC controller, (b) is the result of the HLADRC controller, and (c) is the result of the ILADRC controller.

[0137] The ILADRC parameters are α=1, β=2, γ=0.6, Q=0.001, k1=0.65, r=0.5, μ=4, δ=0.6.

[0138] from Figure 11 In the study, the conventional LADRC-controlled motor experienced a 1.3% speed overshoot when the load changed, with a 9-second settling time and a stable speed fluctuation of ±3 rpm. The HLADRC-controlled motor experienced a 1.8% speed overshoot when the load changed, with a 11-second settling time and a stable speed fluctuation of ±0.6 rpm. The ILADRC-controlled motor experienced a 4.2% speed overshoot when the load changed, with a 2-second settling time and a stable speed fluctuation of ±0.8 rpm.

[0139] from Figure 12 In the study, a motor controlled by traditional LADRC experienced an 8.2% speed overshoot during no-load speed changes, with a stabilization time of 9 seconds and a stable speed fluctuation amplitude of ±3 rpm. Under no-load control, HLADRC achieved no speed overshoot during speed changes, with a stabilization time of 18 seconds and a stable speed fluctuation amplitude of ±0.6 rpm. After no-load startup, a motor controlled by ILADRC experienced a 10.8% speed overshoot during speed changes, a stabilization time of 2.5 seconds, and a stable speed fluctuation amplitude of ±0.8 rpm.

[0140] To systematically evaluate the dynamic control performance of the ILADRC algorithm across the entire speed range, this study designed comparative experiments under bidirectional speed-variable conditions. Under no-load starting conditions, the robustness of the algorithm was verified through a combination of step-wise speed-variable operation and time-varying load disturbances. The specific experimental scheme is as follows: During the acceleration phase, the speed was set to a four-step ramp-up sequence of 100-1000-2000-2500 r / min. Dynamic load disturbances were applied at each speed, and the speed tracking waveform and q-axis current response were simultaneously monitored. During the deceleration phase, the speed was set to a four-step ramp-down sequence of 2500-2000-1000-100 r / min. Time-varying load disturbances were applied and removed during each ramp-down phase, and the speed regulation process and the real-time changes in the q-axis current were recorded.

[0141] The experimental results show that Figure 13 and Figure 14As shown in the full-speed range test of forward acceleration (100-2500 rpm) and reverse deceleration (2500-100 rpm), the ILADRC algorithm still demonstrated excellent interference rejection characteristics under the continuous application and removal of external disturbances. Within different speed ranges, the maximum amplitude of the system speed fluctuation was always controlled to less than 1% of the target value. The results show that the active disturbance rejection controller using the HESMSO can effectively improve the system stability and accuracy compared to the widely used LADRC controller, and has excellent dynamic performance and control accuracy.

[0142] This application is based on a motor speed controller of a high-order extended sliding mode observer with adaptive disturbance differential compensation, especially when there are external disturbances in the system, which improves the anti-disturbance performance of the observer and better observation. The high-order extended state observer is verified to be superior to the traditional extended state observer through frequency domain analysis. The proposed high-order extended sliding mode state observer performs disturbance differential compensation on the framework of the third-order extended state observer, and then by integrating the new non-singular sliding mode observation algorithm into the extended state observer, this controller effectively solves the problems of anti-disturbance ability and disturbance estimation accuracy. In addition, for the system stability under the coupling of speed step mutation and load disturbance, it can effectively test the dynamic adjustment quality of the control strategy under complex working conditions, and provide a quantitative basis for evaluating its reliability in the actual application of electric drive systems.

[0143] 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 SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer, characterized in that: The following steps are involved: A third-order LESO system is designed and established based on the motor mathematical model. The third-order LESO system is used to output the estimated actual speed value, estimated acceleration, and estimated total disturbance. Combining the non-singular fast terminal sliding mode algorithm with the disturbance observer, a non-singular fast terminal sliding mode disturbance observer is designed and used to observe the acceleration state variables of the motor; The acceleration state variable is input into the third-order LESO system and replaces the estimated acceleration to generate a high-order extended sliding mode observer; An active disturbance rejection controller is constructed by combining a high-order extended sliding mode observer with linear state error feedback and total disturbance compensation, and the motor speed is controlled by the active disturbance rejection controller.

2. The SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer according to claim 1, characterized in that: The state space expression of the third-order LESO system is as follows: By configuring the poles, the observer feedback gain coefficient is configured at -ω0, where ω0 is the observer bandwidth; x1=ω r ,ω r is the mechanical angular velocity of the dq axis coordinate system; x2 is the acceleration of the mechanical angular velocity; x3 = f, f is the total disturbance to be observed; u = i q ,i q is the stator current in the motor q coordinate system; y = x1; u is the output of the linear active disturbance rejection controller; J0 is the initial value of the motor's moment of inertia, ψ f is the permanent magnet flux, and P is the number of magnetic pole pairs of the motor.

3. The SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer according to claim 2, characterized in that: Substituting the feedback gain coefficient into the third-order LESO system, we get: Where z1, z2, and z3 are the output estimated actual speed value, estimated acceleration, and estimated total disturbance, respectively.

4. The SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer according to claim 1, characterized in that: The design steps of the non-singular fast terminal sliding mode disturbance observer are as follows: Design of non-singular fast terminal sliding surface based on sigmoid(x) function; According to the equivalent sliding mode control principle, the equivalent term of the sliding mode control law is obtained, and then the switching control law is designed by controlling the system state on the sliding mode surface; A non-singular fast terminal sliding mode disturbance observer is designed based on the non-singular fast terminal sliding mode surface and switching control law. The motor is observed by a non-singular fast terminal sliding mode disturbance observer and the state variables are output.

5. The SPMSM robust speed control method based on adaptive high-order extended sliding mode observer according to claim 1, characterized in that: The non-singular fast terminal sliding surface is: α, β>0; 0<γ<1, e ω is the speed estimation error.

6. The SPMSM robust speed control method based on adaptive high-order extended sliding mode observer according to claim 5, characterized in that: The switching control law is: M=αe ω +β|e ω | γ sigmoid(e ω )+M n Among them, M n (0)=0; P is the parameter of control law design, k1,η,r,μ>0; 0<δ<1; 0<Q<1.

7. The SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer according to claim 6, characterized in that: The non-singular fast terminal sliding mode disturbance observer is: Where, ω r The estimated value of M is the switching control law; h is the derivative of the total disturbance f that needs to be observed, T e is the electromagnetic torque, and J is the moment of inertia.

8. The SPMSM robust speed control method based on an adaptive high-order extended sliding mode observer according to claim 1, characterized in that: The high-order extended sliding mode observer is:

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