A sliding mode active disturbance rejection control method for permanent magnet synchronous motor based on improved extended observer

Abstract

The present invention belongs to the field of permanent magnet synchronous motor self-disturbance rejection, and specifically discloses a sliding mode self-disturbance rejection control method for a permanent magnet synchronous motor with an improved extended observer, the steps of which include: S1: listing the mathematical equation of the actual electromagnetic torque according to the mathematical model of the permanent magnet synchronous motor; S2: discretizing the differential structure of the input signal to obtain the equation of the most tracking differentiator; S3: establishing a third-order ESO structure to obtain the expanded state observer function; S4: linearly combining the errors to obtain the nonlinear state error feedback control law; S5: obtaining the function form of the sliding mode controller to realize the sliding mode self-disturbance rejection control of the permanent magnet synchronous motor. The present invention overcomes the defects of the traditional fal function being discontinuous and non-bright, improves the convergence speed and observation capability of the extended state observer; and the system robustness and anti-disturbance capability are also improved.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor anti-disturbance control, and in particular relates to a permanent magnet synchronous motor sliding mode anti-disturbance control method with an improved extended observer. Background Art

[0002] Permanent magnet synchronous motors have been widely used in high-performance position / speed servo systems due to their high power density, simple and reliable structure. However, due to the strong nonlinearity of PMSM and the existence of unknown disturbances, traditional PID control is no longer applicable. In the prior art, based on the limitations of PID and the idea of ​​using errors to eliminate errors, active disturbance rejection control (ADRC) was proposed. This method does not rely on the precise mathematical model of the object, can directly estimate the disturbance based on the input and output signals, and perform feedforward compensation in the input, and has the characteristics of strong anti-interference and robustness. ADRC is improved from two levels: the introduction of other control methods to form a fusion algorithm and the improvement of its own algorithm.

[0003] Among them, the fusion algorithm has the problem of limited estimation ability for ADRC. In the prior art, a neural network anti-disturbance control method is proposed to improve this problem. This method has the advantages of reducing the error range of the object and higher anti-disturbance control, but the neural network will take the local minimum as the global minimum and increase the error. In order to solve the above problems, two solutions are adopted in the prior art. One is to introduce backstepping control. Although this solution reduces the number of adjustment parameters, the differential operation increases the difficulty of calculation; the other is to use fuzzy control and introduce variable domain. This solution improves the estimation ability of anti-disturbance, but due to the limitations of fuzzy control itself, it affects the accuracy of the system. In summary, there is a contradiction between accuracy and estimation ability in the fusion algorithm.

[0004] In the prior art, the optimization of the fal function is used to improve the algorithm itself. In the design of the automatic landing flight control law based on the self-disturbance rejection control method, in order to overcome the discontinuity of the fal function, the new Ifal proposed is smoother and more continuous, but the overall control effect does not change much. The new fal function proposed in the literature Improvement of self-disturbance rejection fal function and its application in quadrotor attitude control has a smaller system gain and better anti-disturbance performance when the error is large, but the continuity near the zero point of the function is not improved. Therefore, there is a great contradiction in the improvement of the fal function, and its anti-disturbance and continuity cannot maintain a better state at the same time.

[0005] Therefore, there is an urgent need to develop a permanent magnet synchronous motor sliding mode anti-disturbance control method that can solve the above problems. Summary of the invention

[0006] The present invention provides a sliding mode anti-disturbance control method for a permanent magnet synchronous motor with an improved extended observer, which is used to solve the problem that the anti-disturbance and continuity in the current permanent magnet synchronous motor cannot be kept in a relatively optimal state at the same time.

[0007] In order to solve the above technical problems, the technical solution of the present invention is: the permanent magnet synchronous motor sliding mode anti-disturbance control method of the improved extended observer comprises the following steps:

[0008] S1: According to the mathematical model of the permanent magnet synchronous motor, the electromagnetic torque in the mathematical model is simplified, and then the mathematical equation of the actual electromagnetic torque is listed in combination with the disturbance of the motor operation, as shown in Formula 1:

[0009]

[0010] Among them, T e is the electromagnetic torque, n p is the pole pair number, L md is the mutual inductance of the d-axis, i q is the q-axis component of the stator current, i df is the d-axis equivalent magnetizing current, μ is the total disturbance;

[0011] S2: Discretize the differential structure of the input signal to obtain the equation of the best tracking differentiator;

[0012] S3: Establish a third-order ESO structure, combine the electromagnetic torque mathematical equation of formula 1 and the permanent magnet synchronous motor state equation, and obtain the expanded state observer function in the form of formula 2:

[0013]

[0014] Among them, z1 represents speed estimation; z2 represents comprehensive disturbance estimation; z3 is the real-time estimation and online compensation of unknown disturbances in the total disturbance. β1, β2, β3 are ESO observer filter coefficients, and galn is the new function proposed in this paper;

[0015] S4: Using the non-singular terminal sliding surface function and reaching law, the errors are linearly combined to obtain the nonlinear state error feedback control law;

[0016] S5: Apply the equation of the most tracking differentiator of S2, the formal function of the extended state observer of S3 and the nonlinear state error feedback control law of S4 to the sliding mode controller, and obtain the functional form of the sliding mode controller to realize the sliding mode self-disturbance rejection control of the permanent magnet synchronous motor.

[0017] In a preferred embodiment of the present invention, the mathematical model of the permanent magnet synchronous motor in step S1 is based on an ideal state assumption and a control mode setting of id=0, and its form in the dq coordinate system is Formula 3-Formula 6:

[0018]

[0019] λ q =L q i q (4)

[0020] λ d =L d i d +L md i df (5)

[0021] ω e =n p ω r (6)

[0022] In the formula, i d 、i q are the d-axis and q-axis components of the stator current respectively; U d , U q are the d-axis and q-axis components of the stator voltage respectively; R s is the stator resistance; L d , L q are the stator d-axis and q-axis inductances respectively; ω e is the rotor electrical angular velocity; ω r is the rotor mechanical angular velocity; d , q is the stator flux of d and q axes; L md is the mutual inductance of the d-axis; i df is the d-axis equivalent magnetizing current; n p is the pole pair number.

[0023] In a preferred embodiment of the present invention, the motor torque in step S1 is simplified based on the equality of the stator flux of the d and q axes, and the simplified electromagnetic torque equation is Formula 7:

[0024]

[0025] In a preferred embodiment of the present invention, in step S2, the equation of the most tracking differentiator is equation 8:

[0026]

[0027] Among them, h is the integration step; r is the speed factor, whose value determines the tracking speed; h0 is the filter factor, and the function fhan(x1,x2,r,h) is the fastest control comprehensive function;

[0028] The algorithm of fhan(x1,x2,r,h) is formula 9:

[0029]

[0030] Among them, h is the integration step size; r is the speed factor.

[0031] In a preferred embodiment of the present invention, the state equation of the permanent magnet synchronous motor in step S3 is equation 10:

[0032]

[0033] Among them, ω * is the given speed, ω is the actual speed;

[0034] Combining the permanent magnet synchronous motor state equation 10 with the mathematical equation 1 of the actual electromagnetic torque, we get equation 11:

[0035]

[0036] in ω(t) is the interference;

[0037] Taking f(x1,x2,ω(t),t) as the state variable x3, the expression function of x3 is Equation 12:

[0038]

[0039] In a preferred embodiment of the present invention, the galn function in step S3 is in the form of equation 13,

[0040]

[0041] In a preferred embodiment of the present invention, the non-singular terminal sliding surface function in step S4 is Formula 14:

[0042]

[0043] Among them, h>g>0, α>0;

[0044] The reaching law is expressed as formula 15:

[0045]

[0046] in, k1>0,k2>0,a>1,0 <b<1,h> g>0.

[0047] In a preferred embodiment of the present invention, the function form of the sliding mode controller in step S5 is formula 16:

[0048]

[0049] Among them, k1, k2 and k3 are variable reaching law coefficients, n p is the pole pair number, J is the moment of inertia, is the permanent magnet flux, β>0, h>g>0.

[0050] In a preferred embodiment of the present invention, the disturbance compensation z3 of the system is introduced into equation 16, and finally the new active disturbance rejection control law is designed in the form of equation 17:

[0051]

[0052] Among them, k1, k2 and k3 are variable reaching law coefficients, n p is the pole pair number, J is the moment of inertia, is the permanent magnet flux, β>0, h>g>0.

[0053] The technical solution provided by the present invention has the following advantages over the prior art: In view of the load and uncertain disturbance problems existing in the permanent magnet synchronous motor control system, the present invention designs a sliding mode anti-disturbance control method based on an improved extended state observer. The discontinuous and non-bright characteristics of the traditional FAL function are replaced by the new GAL function, which improves the convergence speed and observation ability of the extended state observer. By introducing sliding mode control into the nonlinear control law, an anti-disturbance sliding mode control is formed, and the robustness and anti-disturbance ability of the system are improved at the same time. Through the simulation comparison of traditional anti-disturbance control and new composite anti-disturbance control, the applicability of the sliding mode anti-disturbance control method based on the improved extended state observer is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, drawings of other embodiments can be obtained based on these drawings without paying creative work.

[0055] Figure 1 It is a design flow chart of a sliding mode anti-disturbance control method for a permanent magnet synchronous motor with an improved extended observer described in one embodiment of the present invention;

[0056] Figure 2 It is an auto-disturbance rejection control structure diagram of a sliding mode auto-disturbance rejection control method for a permanent magnet synchronous motor using an improved extended observer described in one embodiment of the present invention;

[0057] Figure 3 It is a structural diagram of a second-order tracking differentiator of a sliding mode anti-disturbance control method for a permanent magnet synchronous motor using an improved extended observer described in one embodiment of the present invention;

[0058] Figure 4It is a structural diagram of an extended state observer of a sliding mode anti-disturbance control method for a permanent magnet synchronous motor with an improved extended observer described in one embodiment of the present invention;

[0059] Figure 5 It is a function curve comparison diagram of the fal function and the galn function of a permanent magnet synchronous motor sliding mode anti-disturbance control method of an improved extended observer described in one embodiment of the present invention;

[0060] Figure 6 It is a local enlarged comparison diagram of the function curves of the fal function and the galn function at point 0 of a permanent magnet synchronous motor sliding mode anti-disturbance control method of an improved extended observer described in one embodiment of the present invention;

[0061] Figure 7 It is a speed comparison diagram of a novel anti-disturbance sliding mode control and a traditional sliding mode control of a permanent magnet synchronous motor sliding mode anti-disturbance control method according to an improved extended observer described in one embodiment of the present invention. DETAILED DESCRIPTION

[0062] For ease of understanding, the following describes an improved extended observer permanent magnet synchronous motor sliding mode anti-disturbance control method in conjunction with embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0063] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation and positional relationship shown in the drawings, and are 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 cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0064] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected" and "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 a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0065] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thoroughly understood.

[0066] 1. Establish the mathematical model of permanent magnet synchronous motor

[0067] Assuming that the permanent magnet synchronous motor is in an ideal state, the present invention selects i d =0 control mode, so the dq coordinate system is selected for research. The model of permanent magnet synchronous motor in the dq coordinate system is:

[0068]

[0069] λ q =L q i q (1-2)

[0070] λ d =L d i d +L md i df (1-3)

[0071] ω e =n p ω r (1-4)

[0072] In the formula, i d 、i q are the d-axis and q-axis components of the stator current respectively; U d , U q are the d-axis and q-axis components of the stator voltage respectively; R s is the stator resistance; L d , L q are the stator d-axis and q-axis inductances respectively; ω e is the rotor electrical angular velocity; ω r is the rotor mechanical angular velocity; d , q is the stator flux of d and q axes; L md is the mutual inductance of the d-axis; i df is the d-axis equivalent magnetizing current; n p is the pole pair number.

[0073] The electromagnetic torque and mechanical torque equations of permanent magnet synchronous motor are:

[0074] T e =3n p [L md Idf i q +(L d -L q )i d i q ] / 2 (1-5)

[0075] T e =Jω r +T l (1-6)

[0076] Where, T e is the electromagnetic torque; T l is the load torque; B m is the friction coefficient; J is the moment of inertia.

[0077] Due to λ d =λ q , the electromagnetic torque equation of the motor can be simplified as:

[0078]

[0079] Where μ = T l +d, d is the unmeasurable external disturbance, and μ is the total disturbance.

[0080] 2. Best tracking differentiator design

[0081] The structure of the active disturbance rejection control is as follows Figure 2 As shown, the tracking differentiator (TD) prevents the input from entering the jump signal, greatly reducing the problem of excessive overshoot of the system, so that the input signal can be quickly tracked and the differential of the signal can be obtained. Its structure is as follows Figure 3 As shown in the figure, v0 is the input signal of the system, v1 is the tracking of the input signal, and v2 is the extraction of the differential of the input signal. Discretization can obtain the equation:

[0082]

[0083] Among them, h is the integration step; r is the speed factor, whose value determines the tracking speed; h0 is the filter factor, which plays a filtering role. The function fhan(x1,x2,r,h) is the fastest control comprehensive function, and its algorithm is as follows:

[0084]

[0085] 3. Design of Extended State Observer

[0086] The extended state observer is a nonlinear combination method, the purpose of which is to observe the state of the system output and the internal and external disturbances. It does not rely on the model, nor does it need to directly measure the disturbance to obtain the estimated value. The third-order ESO structure is as follows: Figure 4As shown, the state equation of the designed permanent magnet synchronous motor is:

[0087]

[0088] Among them, ω * is the given speed, and ω is the actual speed.

[0089] Substituting into formula (1-8) we can get

[0090]

[0091] in ω(t) is the interference.

[0092] Let f(x1,x2,ω(t),t) be the state variable x3, then

[0093]

[0094] The designed improved extended observer is:

[0095]

[0096] Where z1 represents the speed estimation; z2 represents the comprehensive disturbance estimation; z3 is the real-time estimation and online compensation of the unknown disturbance f in the total disturbance. β1, β2, β3 are the ESO observer filter coefficients. δ is the linear interval length.

[0097] The form of the galn function is as follows:

[0098]

[0099] The galn function is symmetrical about the origin and can be differentiated everywhere. Its curve has good continuity, convergence, and smoothness. There are few parameters to be adjusted, and it strictly follows the principle of "small error, large gain, large error, small gain". The function itself has the characteristics of symmetry, continuity, smoothness, and convergence, which is suitable for the application of normal distribution function in engineering.

[0100] In the prior art, the fal function is generally used to design the dilated observer. The improved dilated observer is

[0101]

[0102] In the formula, z1 represents the speed estimation; z2 represents the comprehensive disturbance estimation; z3 is the real-time estimation and online compensation of the unknown disturbance f in the total disturbance. β1, β2, β3 are the ESO observer filter coefficients. δ is the linear interval length. The specific form of the fal(e1, δ) function is as follows:

[0103]

[0104] Through Matlab simulation software, draw the images of galn function and fal function, such as Figure 5 As shown in the figure, it can be clearly seen that the use of the fal function will have the following problems: 1. The continuity and smoothness of the function are not good enough, and it is easy to cause high-frequency jitter in the vicinity of the origin. 2. During the overall operation, there are many parameter adjustments, which increases the complexity of the calculation and the difficulty of the operation. In addition, the increase in parameters increases the impact of high gain on the observation effect. 3. Although it can improve the convergence speed and observation ability, it aggravates the instability of the system by increasing the error gain.

[0105] The galn function proposed in the present invention is infinitely differentiable and meets the selection conditions of nonlinear functions. Figure 5 It can be seen that when the error is large, the gain is very small, and the function Its error is between 0 and 1, and the gain is smaller. Figure 6 It can be seen that near the 0 point, both functions meet the conditions of small error and large gain, but the galn function is smoother. Therefore, the galn function is more continuous and smooth, and the gain is smaller under the premise of large error.

[0106] 4. Nonlinear state error feedback law

[0107] The state error feedback control law linearly combines the errors of the system. According to the regulation principle of "small error, large gain; large error, small gain", the tracking signal and differential signal of the second-order fastest tracker are reasonably nonlinearly combined with the deviation value of the output state vector of the extended state observer. The sliding mode control is a nonlinear control method that is currently recognized by everyone because of its strong robustness, insensitivity to changes in internal system parameters and external load disturbances, and invariance to unmodeled dynamics. It has been introduced into the anti-disturbance control and has been well applied.

[0108] The present invention selects a non-singular terminal sliding surface:

[0109]

[0110] Where h>g>0,α>0.

[0111] The reaching law is selected:

[0112]

[0113] in k1>0,k2>0,a>1,0 <b<1,h> g, p>q, and p and q are positive odd numbers.

[0114] 5. Design of sliding mode controller

[0115] The present invention combines classical control with modern control. In order to make up for the fundamental defects of PID, a nonlinear tracking differentiator is designed to solve the problem of differential method, an extended observer with anti-disturbance function is designed to solve the disturbance estimation problem, and a new nonlinear combination structure is designed to find a suitable combination method. The limitations of PID are broken through in these three aspects.

[0116] The improved equation of the most tracking differentiator, the formal function of the extended state observer and the nonlinear state error feedback law are applied to the sliding mode controller to obtain the functional form of the sliding mode controller. The form of the sliding mode controller designed in this way is:

[0117]

[0118] Finally, the disturbance compensation z3 of the system is introduced to obtain the self-disturbance rejection nonlinear control law in the form of formula 5-2:

[0119]

[0120] Among them, k1, k2 and k3 are variable reaching law coefficients, n p is the pole pair number, J is the moment of inertia, is the permanent magnet flux, β>0, h>g>0.

[0121] 6. Simulation and result analysis

[0122] 6.1 Simulation parameters and method settings

[0123] In order to verify the correctness of the anti-disturbance sliding mode control algorithm of the present invention, a permanent magnet synchronous motor simulation structure is built in simulink. The specific parameters of the motor are: stator resistance R = 2.46Ω; d and q axis inductance L d =L q =6.35mH; permanent magnet flux Moment of inertia J = 1.02 gm 2 ; Viscous friction coefficient B = 0.0001; pole pair number P = 4; rated speed 3000r / min, inverter switching frequency is 15kHz.

[0124] The current loop of the present invention adopts PI control, and the speed loop adopts an anti-disturbance sliding mode controller. The simulation selects non-singular terminal sliding mode control for comparison.

[0125] 6.2 Analysis of simulation results

[0126] Given a motor speed of 1000r / min, and a sudden load is applied at 0.01s, the speed response simulation waveform of the PMSM is shown in the figure.

[0127] Depend on Figure 7It can be seen that the motor speed can reach a stable state very quickly, but the motor speed overshoot under traditional ADRC control is obviously large. The speed overshoot under the control of the new composite ADRC controller is very small. When the load is suddenly added at 0.2s, the new sliding mode anti-disturbance controller returns to the given speed value more quickly than the traditional sliding mode control. Therefore, the new composite control has a better disturbance suppression effect.

[0128] Aiming at the load and uncertain disturbance problems in the permanent magnet synchronous motor control system, a sliding mode anti-disturbance control method based on an improved extended state observer is designed. The discontinuous and non-bright characteristics of the traditional FAL function are replaced by the new GAL function, which improves the convergence speed and observation ability of the extended state observer. By introducing sliding mode control into the nonlinear control law, an anti-disturbance sliding mode control is formed, and the robustness and anti-disturbance ability of the system are improved at the same time. Through the simulation comparison of traditional anti-disturbance control and new composite anti-disturbance control, the applicability of the sliding mode anti-disturbance control method based on the improved extended state observer is obtained.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, a person skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some or all of the technical features can be replaced by equivalents, 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 embodiments of the present invention.

Claims

1. A sliding mode anti-disturbance control method for a permanent magnet synchronous motor based on an improved extended observer, characterized in that: The following steps are involved: S1: According to the mathematical model of the permanent magnet synchronous motor, the electromagnetic torque in the mathematical model is simplified, and then the mathematical equation of the actual electromagnetic torque is listed in combination with the disturbance of the motor operation, as shown in Formula 1: Among them, T e is the electromagnetic torque, n p is the pole pair number, L md is the mutual inductance of the d-axis, i q is the q-axis component of the stator current, i df is the d-axis equivalent magnetizing current, μ is the total disturbance; S2: Discretize the differential structure of the input signal to obtain the equation of the best tracking differentiator; In step S2, the differential structure is discretized by equation 8 to obtain the equation of the most tracking differentiator: Among them, h is the integration step; r is the speed factor, whose value determines the tracking speed; h0 is the filter factor, and the function fhan(x1,x2,r,h) is the fastest control comprehensive function; The algorithm of fhan(x1,x2,r,h) is formula 9: Where, h is the integration step; r is the speed factor; S3: Establish a third-order ESO structure, combine the electromagnetic torque mathematical equation of formula 1 and the permanent magnet synchronous motor state equation, and obtain the expanded state observer function in the form of formula 2: Among them, z1 represents speed estimation; z2 represents comprehensive disturbance estimation; z3 is the real-time estimation and online compensation of unknown disturbances in the total disturbance; β1, β2, β3 are ESO observer filter coefficients, and galn is a nonlinear function; The state equation of the permanent magnet synchronous motor in step S3 is equation 10: Among them, ω * is the given speed, ω is the actual speed; Combining the permanent magnet synchronous motor state equation 10 with the mathematical equation 1 of the actual electromagnetic torque, we get equation 11: in ω(t) is the interference; Taking f(x1,x2,ω(t),t) as the state variable x3, the expression function of x3 is Equation 12: The galn function in step S3 is in the form of equation 13: Where a is a non-zero constant; S4: Using the non-singular terminal sliding surface function and reaching law, the errors are linearly combined to obtain the nonlinear state error feedback control law; The non-singular terminal sliding surface function in step S4 is formula 14: Among them, h>g>0, α>0; The reaching law is expressed as formula 15: in, S5: Apply the equation of the most tracking differentiator of S2, the formal function of the extended state observer of S3, and the nonlinear state error feedback control law of S4 to the sliding mode controller, and obtain the functional form of the sliding mode controller to realize the sliding mode self-disturbance rejection control of the permanent magnet synchronous motor; The function form of the sliding mode controller in step S5 is as follows: Among them, k1, k2 and k3 are variable reaching law coefficients, n p is the pole pair number, J is the moment of inertia, is the permanent magnet flux, β>0, h>g>0.

2. The method for sliding mode auto-disturbance rejection control of a permanent magnet synchronous motor with an improved extended observer according to claim 1, characterized in that: The mathematical model of the permanent magnet synchronous motor in step S1 is based on the ideal state assumption and i d =0 control mode setting, its form in the dq coordinate system is formula 3-formula 6: l q =L q I q (4) λ d =L d and d +L md and df (5) oh e =n p oh r (6) In the formula, i d 、i q are the d-axis and q-axis components of the stator current respectively; U d , U q are the d-axis and q-axis components of the stator voltage respectively; R s is the stator resistance; L d , L q are the stator d-axis and q-axis inductances respectively; ω e is the rotor electrical angular velocity; ω r is the rotor mechanical angular velocity; d , q is the stator flux of d and q axes; L md is the mutual inductance of the d-axis; i df is the d-axis equivalent magnetizing current; n p is the pole pair number.

3. The sliding mode auto-disturbance rejection control method for a permanent magnet synchronous motor with an improved extended observer according to claim 2, characterized in that: In step S1, the motor torque is simplified based on the equality of the stator flux of the d and q axes, and the simplified electromagnetic torque equation is equation 7:

4. The sliding mode active disturbance rejection control method for a permanent magnet synchronous motor with an improved extended observer according to claim 1 is characterized in that: Introducing the system disturbance compensation z3 in Equation 16, the new active disturbance rejection control law is in the form of Equation 17: Among them, k1, k2 and k3 are variable reaching law coefficients, n p is the pole pair number, J is the moment of inertia, is the permanent magnet flux, β>0, h>g>0.

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