PMSM disturbance suppression method based on ESO and nonsingular fast terminal sliding mode control

Abstract

The invention belongs to the technical field of motor disturbance suppression, and particularly discloses a PMSM disturbance suppression method based on ESO and nonsingular fast terminal sliding mode control, and the method comprises the steps: S1, building an ideal mathematical model of a PMSM, and obtaining a mathematical model of disturbance caused by interference and uncertainty factors; s2, designing an extended state observer, performing disturbance estimation and feed-forward compensation on a mathematical model of disturbance caused by disturbance and uncertainty factors, and determining a gain coefficient of the extended state observer; s3, defining an error state of the system, and designing a sliding mode controller; and S4, in combination with the second-order extended state observer model and the sliding mode controller, obtaining a current output value of a current controller. According to the method, the problem of large fluctuation of a rotating speed ring is solved, the actual current of the motor is corrected by using the observed current for the current static difference generated when parameters such as inductance or flux linkage are mismatched, and the reference voltage of the motor is corrected by using the observed internal and external disturbance of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor disturbance suppression, and particularly relates to a PMSM disturbance suppression method based on ESO and nonsingular fast terminal sliding mode control. Background Technique

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in various mechatronic energy conversion systems due to their small size, excellent performance, simple structure, high efficiency, etc. As is well known, PI control technology is very popular because of its simple implementation. However, the PMSM system is a strongly nonlinear and coupled system, and nonlinear factors widely exist in the PMSM drive. The existence of factors such as inverter nonlinearity, flux linkage harmonics, and unbalanced phase impedance will affect the stable operation of the motor. In this case, it is difficult to simply use the PI control algorithm to cope with the operation of the motor in diverse and complex environments.

[0003] Therefore, scholars at home and abroad have carried out a large number of research on control technologies for disturbance suppression in the field of PMSM, and several nonlinear control methods have been proposed and implemented, such as active disturbance rejection control, predictive current control, internal model control, sliding mode control (SMC), and adaptive control methods.

[0004] Among the above several methods, SMC is considered to be one of the most effective methods for dealing with uncertain nonlinear systems because it is insensitive to uncertainties and disturbances. In order to further improve the effect of disturbance suppression, the sliding mode control method is often combined with an observer.

[0005] The prior art Li Z et al. proposed a nonsingular fast terminal sliding mode controller based on disturbance compensation in the article "Nonsingular fast terminal sliding mode control strategy for PMLSM based on disturbance compensation. (Journal of Electrical Engineering & Technology, 2024, 19(3): 1331 - 1342.)", and introduced the system state variables into the exponential reaching law, enabling the controller to adaptively adjust with the change of the system state. However, it can be seen from the experimental results that there is still room for improvement in the steady-state accuracy of the PMSM speed tracking control.

[0006] The prior art Gao X K proposed a backstepping nonsingular fast terminal sliding mode control in "Backstepping nonsingular fast terminal sliding mode control for manipulators driven by PMSM with measurement noise. (in: Proceedings of 2023 Chinese intelligent automation conference: 2023 Chinese intelligent automation conference (CIAC2023), October 2 - 5, 2023, Nanjing, China. 2023. 322 - 330.)", and a high - gain extended state observer was used to compensate for lumped disturbances and modeling errors. In view of the sensitivity of the high - gain extended state observer to measurement noise, an extended Kalman filter (EKF) was added to combine with it. However, the backstepping control design is complex. Its method requires step - by - step design and recursive calculation, and the stability of the system must be ensured at each step, which makes the design process complex and time - consuming.

[0007] Another prior art Li T et al. proposed a non - cascade fast nonsingular terminal sliding mode control of permanent magnet synchronous motor based on disturbance observers in "Non - Cascade fast nonsingular terminal sliding mode control of permanent magnet synchronous motor based on disturbance observers.

[0008] (Journal of Electrical Engineering & Technology, 2022, 17(2): 1061 - 1075.)", and a non - cascade fast nonsingular terminal sliding mode control algorithm based on disturbance observers was proposed. At the same time, a nonlinear disturbance observer and a dual disturbance observer were designed respectively to estimate the disturbances during the motion process. However, the influence of the current static error generated by the current loop on the system was ignored.

[0009] In summary, although the prior art effectively suppresses the influence of disturbances and uncertainty factors on PMSM, the current static error generated when the inductance and magnetic flux are mismatched in the current loop is often ignored. Summary of the Invention

[0010] The present invention provides a PMSM disturbance suppression method based on ESO and non - singular fast terminal sliding mode control to solve the problem of disturbances generated by the current static error when the inductance and magnetic flux of the permanent magnet synchronous motor are mismatched.

[0011] To solve the above technical problems, the technical solution of the present invention is as follows: For a PMSM disturbance suppression method based on ESO and nonsingular fast terminal sliding mode control, it includes the following steps:

[0012] S1: Establish an ideal mathematical model of the PMSM, and obtain a mathematical model of the disturbance caused by interference and uncertainty factors;

[0013] S2: Design an extended state observer to perform disturbance estimation and feedforward compensation on the mathematical model of the disturbance caused by interference and uncertainty factors, and determine the gain coefficient of the extended state observer in combination with the second-order extended state observer model;

[0014] S3: Define the error state of the system and design a sliding mode controller;

[0015] S4: Combine the second-order extended state observer model and the sliding mode controller to obtain the current output value of the current controller.

[0016] In a preferred embodiment of the present invention, in step S1, the mathematical model of the disturbance caused by interference and uncertainty factors is obtained through Equation 1:

[0017]

[0018] Wherein, ΔJ, ΔB, ΔR s , ΔL are all the errors between the actual value and the nominal value, U d , U q are the d-axis and q-axis voltages respectively, L is the inductance, i d , i q are the d-axis and q-axis currents respectively, ω is the actual rotational speed; p n is the number of pole pairs; is the permanent magnet rotor flux linkage, R s is the resistance, J is the moment of inertia, B is the damping coefficient, T L is the load torque, d i (i = 1, 2, 3) are the disturbances caused by interference and uncertainty factors, d1 is the disturbance in the rotational speed channel, d2 is the disturbance in the i q axis channel, and d3 is the disturbance in the i d axis channel.

[0019] In a preferred embodiment of the present invention, the ideal mathematical model is obtained through Equation 2:

[0020]

[0021] Wherein, L d , L qThe inductances on the d and q axes, d i (i = 1, 2, 3) are disturbances caused by interference and uncertainty factors. d1 is the disturbance of the speed channel, d2 is the disturbance of the q i-axis channel, and d3 is the disturbance of the d i-axis channel.

[0022] In a preferred embodiment of the present invention, in the step S2, the disturbance estimation and feedforward compensation for the mathematical model of the disturbance caused by interference and uncertainty factors are obtained through Equation 3:

[0023]

[0024] where a1 = -B / J, a2 = a3 = -R s / L, u1 = 0, u2 = u q , u3 = u d , r1 = 0, r2 = r3 = 1 / L, l3 = p n ωi q , z1 = ω, z2 = i q , z3 = i d .

[0025] In a preferred embodiment of the present invention, in the step S2, the extended state observer is obtained through Equation 4:

[0026]

[0027] where is the observation of the state, is the observation of the disturbance, and β i , β 0i are the gain coefficients of the ESO;

[0028] The gain coefficients of the extended state observer are obtained through Equation 5:

[0029]

[0030] where ω0 is the bandwidth of the linear extended state observer.

[0031] In a preferred embodiment of the present invention, in the step S3, the sliding mode controller is obtained through Equation 6:

[0032]

[0033] where s is the sliding mode surface, ε, c are constants and greater than 0.

[0034] In a preferred embodiment of the present invention, the selected sliding mode surface s is obtained by Equation 7:

[0035]

[0036] where sig σi (e i ) = sig(e i )| ei| σi , and λ1 > 0, λ2 > 0, 1 < σ2 < 2, σ1 > σ2.

[0037] In a preferred embodiment of the present invention, in step S3, the error state of the system is defined by Equation 8:

[0038]

[0039] where ω ref is the given rotational speed, i d , i q are the d-axis and q-axis currents respectively, ω is the actual rotational speed, J is the moment of inertia, B is the damping coefficient, and d1 is the disturbance in the rotational speed channel.

[0040] In a preferred embodiment of the present invention, in step S4, the current output values of the current controller are obtained by Equation 9 and Equation 10:

[0041]

[0042] where U d , U q are the d-axis and q-axis voltages respectively; L is the inductance, i d , i q are the d-axis and q-axis currents respectively, ω is the actual rotational speed, is the permanent magnet rotor flux linkage, R is the resistance, and T s is the sampling time.

[0043] In a preferred embodiment of the present invention, the d-axis and q-axis currents i d , i q are obtained by Equation 11:

[0044]

[0045] The technical solution provided by the present invention has the following advantages compared with the prior art:

[0046] To suppress the influence of interference and uncertainty factors in a permanent magnet synchronous motor, the present invention proposes a nonsingular fast terminal sliding mode control based on an extended state observer. Using the ESO for the speed loop, i q and i dThree channels are used for observation and disturbance compensation, solving the problem of large fluctuations in the speed loop. At the same time, for the current static error generated when parameters such as inductance or magnetic flux are mismatched, the observed current is used to correct the actual current of the motor, and the observed internal and external disturbances of the system are used to correct the reference voltage of the motor. Through simulation, it is proved that the proposed new controller can quickly track the given curve and effectively suppress the fluctuations generated by speed and torque. Description of the Drawings

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0048] Figure 1 It is the control schematic diagram of a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control described in an embodiment of the present invention;

[0049] Figure 2 It is the speed waveform obtained under three controllers in a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control described in an embodiment of the present invention;

[0050] Figure 3 is Figure 2 the partial enlarged view of;

[0051] Figure 4 It is the electromagnetic torque under three controllers in a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control described in an embodiment of the present invention;

[0052] Figure 5 It is the partial enlarged view of the electromagnetic torque without adding load torque in a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control described in an embodiment of the present invention;

[0053] Figure 6 It is the partial enlarged view of the electromagnetic torque with adding load torque in a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control described in an embodiment of the present invention. Detailed Embodiments

[0054] For ease of understanding, the following describes a PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control in combination with embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0055] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation and positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0056] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0057] For the convenience of understanding the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. The preferred embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0058] S1: Establish an ideal mathematical model of the PMSM and obtain the mathematical model of the disturbance caused by interference and uncertainty factors.

[0059] Before constructing the d-q coordinate mathematical model of the PMSM, the following assumptions are made for the surface-mounted permanent magnet synchronous motor:

[0060] (1) Ignore the effects of magnetic saturation, hysteresis and eddy currents;

[0061] (2) The air-gap magnetic field generated by the stator and rotor windings is sinusoidally distributed;

[0062] (3) The stator three-phase winding is symmetrical, and the rotor is symmetrical about the direct axis and the quadrature axis.

[0063] Based on the above assumptions, the PMSM mathematical model is shown in Equation 2:

[0064]

[0065] Among them, U d 、U q are the d-axis and q-axis voltages respectively, L d 、Lq are the inductances on the d- and q-axes, and i d 、i q are the d- and q-axis currents respectively, ω is the actual rotational speed, and p n is the number of pole pairs, is the permanent magnet rotor flux linkage, R s is the resistance, J is the moment of inertia, B is the damping coefficient, and d i (i = 1, 2, 3) are the disturbances caused by interference and uncertainty factors. d1 is the disturbance in the speed channel, d2 is the disturbance in the i q axis channel, and d3 is the disturbance in the i d axis channel.

[0066] In some practical cases, due to the long-term application of the motor, some parameters will change. For example, the values of J and B are uncertain, and parameters such as L, Rs, and will fluctuate with the operating time, thus affecting the operating efficiency of the motor. In addition, the load torque T L is usually unknown. Therefore, the disturbance d1 in the speed loop, the disturbance d2 in the current loop i q channel, and the disturbance d3 in the current loop i d channel are expressed as Equation 1:

[0067]

[0068] where, ΔJ, ΔB, ΔR s 、ΔL are all the errors between the actual values and the nominal values.

[0069] S2: Design an extended state observer to perform disturbance estimation and feedforward compensation on the mathematical model of the disturbance caused by interference and uncertainty factors. Combine the second-order extended state observer model to determine the gain coefficient of the extended state observer.

[0070] To weaken the influence of the lumped disturbance on the control performance, 3 ESOs are used to perform disturbance estimation and feedforward compensation on d i (i = 1, 2, 3) respectively.

[0071] Let the state variables be z1 = ω, z2 = i q , z3 = i d , Then simplify Equation 2 to obtain Equation 3:

[0072]

[0073] where: a1 = -B / J, a2 = a3 = -R s / L, u1 = 0, u2 = u q , u3 = u d, r1 = 0, r2 = r3 = 1 / L, l3 = p n ωi q 。

[0074] The second - order extended state observer model is as shown in Equation 4:

[0075]

[0076] Among them, is the observation of the state, is the observation of the disturbance, β i and β 0i are the gain coefficients of the ESO.

[0077] To ensure the system stability, Gao Zhiqiang et al. proposed to tune the parameters of the linear extended state observer. Let the bandwidth of the linear extended state observer be ω0, so the gain coefficient of the extended state observer is

[0078] Equation 5:

[0079]

[0080] S3: Define the error state of the system and design a sliding - mode controller.

[0081] The nonsingular fast terminal sliding - mode control combines the characteristics of sliding - mode control and fast terminal control, overcomes the problems of uncertainty, perturbation, and external interference existing in nonlinear systems, and ensures that the system converges to the desired state within a finite time. By designing a suitable sliding - mode surface and combining the technology of fast terminal control, the nonsingular fast terminal sliding - mode control can achieve fast tracking of the system state and has a certain robustness to parameter changes and external interference, thus improving the performance and stability of the control system.

[0082] Define the error state of the system as Equation 8:

[0083]

[0084] Among them, ω ref is the given rotational speed.

[0085] Combining Equations (3) and (5), we can obtain:

[0086]

[0087] For the following nonsingular fast terminal sliding - mode, when the system state x reaches the sliding - mode surface, the system state can converge to the origin within a finite time T1:

[0088]

[0089] where sig σi (x i ) = sig(x i )|x i | σi , and λ1 > 0, λ2 > 0, 1 < σ2 < 2, σ1 > σ2. Finite time T1:

[0090]

[0091] where F(·) is the Gaussian hypergeometric function.

[0092] Therefore, select the sliding surface, as in Equation 7:

[0093]

[0094] where sig σi (e i ) = sig(e i )|e i | σi , and λ1 > 0, λ2 > 0, 1 < σ2 < 2, σ1 > σ2.

[0095] Taking the derivative of s, we can obtain:

[0096]

[0097] Traditional reaching laws usually use a high gain to ensure that the system can quickly converge to the vicinity of the sliding surface. However, this high gain will introduce high-frequency oscillation components, resulting in the appearance of chattering. Therefore, to achieve the stable operation of the system, a saturation function is used instead of the sign function on the basis of the exponential reaching law to suppress the chattering of the sliding mode. So the reaching law is:

[0098]

[0099] where: ε, c are constants and greater than 0.

[0100] To achieve the control objective, design the equivalent control term u qeq and the non-linear control term u qn , and the system control law u q can be obtained:

[0101] u q = u qeq + u qn (17)

[0102]

[0103] To prove the stability of the controller, use the Lyapunov function Then we have:

[0104]

[0105] Thus, it can be seen that the designed nonsingular fast terminal sliding mode controller satisfies the above theory, proving its stability, and the time for the system error to converge to zero is finite.

[0106] S4: Combine the second-order extended state observer model and the sliding mode controller to obtain the current output value of the current controller.

[0107] Deadbeat current predictive control is a control method used to replace the traditional current loop PI controller. Deadbeat current predictive control describes the dynamic characteristics of the motor by establishing a mathematical model of the motor and predicts the future current value of the motor based on this model. By comparing with the actual current, the control system can accurately adjust the control output to achieve precise control of the motor current. This method not only eliminates the difficulty of parameter tuning in traditional control methods but also can be adjusted adaptively according to changes in motor parameters, improving control accuracy and stability.

[0108] Process Equation (2). Since the time Ts is very short, using first-order Euler forward discretization, we can obtain:

[0109]

[0110] Written in matrix equation form, we can get:

[0111]

[0112] Define the variables in Equation (11) as follows: Let I(k) = [i d (k) i q (k)] T , F(k) = [u d (k) u q (k)] T , so Equation (11) is rewritten as:

[0113] I(k + 1) = CI(k) + DF(k) - E (21)

[0114] where

[0115] If the actual output current of the system is to track the reference current without deadbeat, then I(k + 1) = I * (k), where I * (k) = [i q * (k) iq * (k)] T , that is, the given current value on the d-q axis. Thus, the control output value of the deadbeat current controller is:

[0116] F(k) = [I * (k) - CI(k) + E]D -1 (22)

[0117] That is, written in a specific form as:

[0118]

[0119] To verify the practicability and effectiveness of the algorithm proposed in the present invention, simulation verification is carried out in Matlab / Simulink. The parameters used for the permanent magnet synchronous motor are shown in Table 1, and the PMSM control schematic diagram is as Figure 1 shown.

[0120] Table 1 PMSM parameters

[0121]

[0122] Starting without load at t = 0, the given speed is 1000 r / min. At t = 0.3 s, the load torque suddenly changes to 10 N·m. To verify the effectiveness of the controller, the traditional PI control, the ordinary sliding mode control and the method improved in the present invention are compared. The results are as Figure 2 shown, and the partial enlarged view is as Figure 3 shown.

[0123] From Figure 2 it can be seen that in the speed loop of the permanent magnet synchronous motor, the system response time under the new controller is 0.026 s, and there is almost no overshoot. The system response time under the PI controller is 0.121 s, and the system response time under the SMC controller is 0.074 s. Compared with the PI controller, the response time of the new controller is increased by 78.5%, and compared with the SMC controller, the response time is increased by 18.91%. At 0.3 s, a load torque of 10 N·m is added, and the new controller can obviously recover to stability in a shorter time.

[0124] From Figure 3 it can be seen that the fluctuation of the speed controlled by the non-singular fast terminal sliding mode adopted in the present invention is between ±0.1, while the fluctuation of the speed of the traditional PI controller is between ±2, and the fluctuation of the speed of the SMC controller is between ±1. Therefore, this controller can effectively weaken the chattering phenomenon and improve the steady-state accuracy.

[0125] While the new controller can suppress the speed fluctuation, it can also achieve a better suppression effect on the fluctuation of the electromagnetic torque. AsFigures 3 to 5 as shown

[0126] From Figures 3 through 5 It can be seen that before the load disturbance is added, the fluctuation of the electromagnetic torque of the new controller is about ±0.3, while the fluctuation of the electromagnetic torque of the PI and SMC controllers is about ±0.6. After the load torque is added at 0.3 s, the fluctuation of the electromagnetic torque of the new controller still remains at about ±0.3, while the fluctuation of the electromagnetic torque of the PI controller is about ±1.05, and the fluctuation of the electromagnetic torque of the SMC controller is about ±0.65. Thus, it can be proved that the new controller can well suppress the electromagnetic torque fluctuation that appears.

[0127] In summary, in order to suppress the influence of interference and uncertainty factors in the permanent magnet synchronous motor, the present invention proposes a nonsingular fast terminal sliding mode control based on an extended state observer. The ESO is used to observe and compensate the disturbance in the speed loop, i q and i d three channels, solving the problem of large fluctuations generated in the speed loop. At the same time, for the current static error generated when parameters such as inductance or magnetic flux are mismatched, the observed current is used to correct the actual current of the motor, and the observed internal and external disturbances of the system are used to correct the reference voltage of the motor. Through simulation, it is proved that the proposed new controller can quickly track the given curve and effectively suppress the fluctuations generated by the speed and torque.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control, characterized in that: The following steps are involved: S1: Establish an ideal mathematical model of PMSM and obtain the mathematical model of disturbances caused by interference and uncertainty factors; S2: Design an extended state observer to perform disturbance estimation and feedforward compensation on the mathematical model of disturbances caused by interference and uncertainty factors, and determine the gain coefficient of the extended state observer in combination with the second-order extended state observer model; S3: Define the error state of the system and design a sliding mode controller; S4: Combining the second-order extended state observer model and the sliding mode controller, obtaining a current output value of a current controller.

2. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 1 is characterized in that: In step S1, the mathematical model of the disturbance caused by interference and uncertainty factors is obtained by formula 1: in, ΔJ, ΔB, ΔR s , ΔL are the errors between the actual value and the nominal value, U d , U q are d and q axis voltages respectively, L is the inductance, i d 、i q are d and q axis currents respectively, ω is the actual speed; p n is the pole pair number; is the permanent magnet rotor flux, R s is the resistance, J is the moment of inertia, B is the damping coefficient, T L is the load torque, d i (i=1, 2, 3) is the disturbance caused by interference and uncertainty factors, d1 is the disturbance of the speed channel, d2 is i q The disturbance of the axis channel, d3 is i d Disturbance of the axis channel.

3. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 2 is characterized in that: The ideal mathematical model is obtained by formula 2: Among them, L d , L q is the inductance on the d and q axes, d i (i=1, 2, 3) is the disturbance caused by interference and uncertainty factors, d1 is the disturbance of the speed channel, d2 is i q The disturbance of the axis channel, d3 is i d Disturbance of the axis channel.

4. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 1 is characterized in that: In step S2, the The mathematical model of the disturbance for disturbance estimation and feedforward compensation is obtained by Equation 3: Among them, a1=-B / J, a2=a3=-R s / L, u1 = 0, u2 = u q ,u3=u d ,r1=0,r2=r3=1 / L, l3=p n ωi q , z1=ω, z2=i q , z3=i d .

5. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 4 is characterized in that: In step S2, the extended state observer is obtained by equation 4: in, is an observation of the state, is the observation of the disturbance, β i , β 0i is the gain coefficient of ESO, The gain coefficient of the extended state observer is obtained by equation 5: Where ω0 is the bandwidth of the linear extended state observer.

6. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 1 is characterized in that: In step S3, the sliding mode controller is obtained by equation 6: Where s is the sliding surface, ε,c is a constant and greater than 0.

7. A PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 6, characterized in that: The selected sliding surface s is obtained by formula 7: Among them, sig σi (e i )=sig(e i )|e i | σi , and λ1>0, λ2>0, 1<σ2<2, σ1>σ2.

8. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 1 is characterized in that: In step S3, the error state of the system is defined by equation 8: in, ω ref is the given speed, i d 、i q are d and q axis currents respectively, ω is the actual speed, J is the moment of inertia, B is the damping coefficient, and d1 is the disturbance of the speed channel.

9. The PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 1 is characterized in that: In step S4, the current output value of the current controller is calculated by equation 9. And formula 10 to obtain: Among them, U d , U q are d and q axis voltages respectively; L is inductance, i d 、i q are d and q axis currents respectively, ω is the actual speed, is the permanent magnet rotor flux, R is the resistance, T s is the sampling time.

10. A PMSM disturbance suppression method based on ESO and non-singular fast terminal sliding mode control according to claim 9, characterized in that: d,q axis current i d 、i q By formula 11, we can obtain:

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