PMSM sensorless control method based on adaptive enhanced extended state observer

Abstract

The invention discloses a PMSM (permanent magnet synchronous motor) sensorless control method based on an adaptive enhanced extended state observer, and the method comprises the steps: monitoring the state of a system in real time, and dynamically adjusting control parameters, so as to optimize the response performance and robustness of the system; a three-order adaptive cascade linear extended state observer is introduced to replace a traditional fixed-bandwidth orthogonal phase-locked loop, and the problem that the dynamic performance of the system is remarkably reduced under speed sudden change and motor disturbance is effectively solved. According to the control method, the speed, the phase and the total disturbance can be accurately estimated in real time, the dynamic response capability of the system is remarkably improved, and meanwhile, the sensitivity to noise is reduced by adjusting parameters of the observer in a self-adaptive mode; meanwhile, the design of a linear state error feedback control law is combined, the control structure is further simplified, the anti-interference capability of the system is enhanced, and the superiority and reliability of the method under the complex dynamic working condition are proved through Lyapunov stability analysis and experimental verification.

Description

Technical Field

[0001] The invention belongs to the technical field of motor control, and in particular relates to a PMSM sensorless control method based on an adaptive enhanced extended state observer. Background Art

[0002] In modern society, PMSM (permanent magnet synchronous motor) has been widely used in the fields of transportation and aerospace, especially as a core component in propulsion systems. PMSM has become the first choice for high-performance motor applications due to its compact structure, light weight, flexible design, and convenient installation.

[0003] Among the many control strategies of PMSM, FOC (vector control) is the most common method; however, the key to this method is to accurately obtain the position information of the motor rotor, which usually relies on mechanical position sensors such as encoders or resolvers. Although these sensors can provide high-precision position signals, they have certain limitations. First of all, the cost of sensors is high, and they are easily affected by vibration, temperature changes and electromagnetic interference in harsh environments, resulting in reduced reliability. For this reason, exploring sensorless control technology has become one of the research hotspots in the field of electric propulsion systems.

[0004] In sensorless control technology, the literature [Novak Z, Novak M. Adaptive PLL-based sensorless control for improved dynamics of high-speed PMSM. IEEE Trans Power Electron. 2022; 37(9): 10154-10165. doi: 10.1109 / TPEL.2022.3169708] designed an adaptive four-quadrant phase-locked loop (AQ-PLL), which can adjust the phase-locked loop (PLL) bandwidth in real time, thereby enhancing the rotor position tracking performance and eliminating phase delay. Similarly, in order to solve the harmonic problem of back EMF and improve the estimation accuracy, the literature [Malekipour A, Corne A, Garbuio L, Granjon P, Gerbaud L. Injectionless acoustic-noise-based PMSM sensorless control using RCPLL for improved estimationperformance. IEEE Trans Power Electron. 2024; 39(1): 225-235. doi: 10.1109 / TPEL.2023.3319824] proposed an improved PLL algorithm, which significantly improved the estimation performance. Its technical solution can be regarded as a type II control system based on a proportional integral (PI) controller and a loop filter, which means that the ability to accurately track the ramp signal may be lost.

[0005] Most applications require motor drive systems with fast response, which has led to the widespread use of extended state observers (ESOs) as speed estimation schemes in sensorless motor control. In the literature [Hou Q, Zuo Y, Sun J, Lee CHT, Wang Y, Ding S. Modified nonlinear active disturbance rejection control for PMSM speed regulation with frequency domain analysis. IEEE Trans Power Electron. 2023; 38(7): 8126-8134. doi: 10.1109 / TPEL.2023.3262519], a nonlinear extended state observer (NLESO) and finite time technology are used to solve the problem of significant noise in the high-bandwidth ESO of the traditional adaptive disturbance observer (ADRC), aiming to improve the immunity to disturbances and reduce the noise level. Based on this, the literature [Zuo Y, GeX, Zheng Y, Chen Y, Wang H, Woldegiorgis AT. An adaptive active disturbance rejection control strategy for speed-sensorless induction motor drives. IEEE Trans Transport Electrific. 2022; 8(3): 3336-3348. doi: 10.1109 / TTE.2022.3148412] introduced a position-speed loop in ADRC control, which uses a third-order adaptive ESO to estimate speed and phase, thereby improving the dynamic performance of the system.

[0006] It should be noted that in most ESO-based schemes, high gains are usually selected to achieve fast convergence, but this approach may bring some problems, including increased sensitivity to noise and decreased steady-state performance. In addition, in sensorless control systems, another challenge is that the PI-type speed controller, especially the integral term in the PI controller, may have an adverse effect on dynamic performance. Summary of the invention

[0007] Aiming at the problem that the traditional fixed-bandwidth quadrature phase-locked loop (Q-PLL) cannot meet the dynamic requirements of the system under speed mutation or motor disturbance, the present invention provides a PMSM sensorless control method based on an adaptive enhanced extended state observer, which can effectively suppress the influence of disturbance on system performance and improve control accuracy and stability.

[0008] A PMSM sensorless control method based on an adaptive enhanced extended state observer comprises the following steps:

[0009] (1) Based on the working principle and characteristics of PMSM, the dynamic equation and first-order speed model of PMSM are established;

[0010] (2) Establish a third-order extended state observer mathematical model of PMSM based on the dynamic equation and the first-order speed model;

[0011] (3) Optimizing the mathematical model of the third-order extended state observer;

[0012] (4) The motor speed observation value is estimated using the optimized third-order extended state observer mathematical model Then, the d-axis stator current reference value i is calculated by combining the linear state error feedback control law. d * and q-axis stator current reference value i q * , thereby achieving high-precision control of the PMSM.

[0013] Furthermore, the expression of the kinetic equation is as follows:

[0014]

[0015] Where: e is the speed of PMSM, ψ f is the magnetic flux of PMSM, T e is the electromagnetic torque of PMSM, T L is the load torque of PMSM, B is the viscosity coefficient of PMSM, J is the moment of inertia of PMSM, n p is the number of pole pairs of PMSM, i q is the q-axis stator current of PMSM, and t represents time.

[0016] Furthermore, the expression of the first-order speed model is as follows:

[0017]

[0018] in: is the speed ω e The first derivative of, b = 3n p ψ f / 2J, a=1 / J, a1=B / J.

[0019] Furthermore, the expression of the mathematical model of the third-order extended state observer is as follows:

[0020]

[0021] Where: θ e is the rotor electrical angle of PMSM, is the rotor electrical angle θ e The first derivative of q * is the q-axis stator current reference value, f total is the total disturbance of the motor system including load torque disturbance, viscous friction disturbance and q-axis current disturbance.

[0022] Furthermore, in step (3), two cascaded third-order linear state extended observers LESO1 and LESO2 are designed to construct the total disturbance f total , use LESO1 to estimate the total disturbance of the system and use it as the known disturbance of LESO2, so that LESO2 only needs to focus on estimating the unknown disturbance.

[0023] Furthermore, the total disturbance of the motor system f total The expression is as follows:

[0024]

[0025] Where: z1 = s1 and is the measured value of the electrical angle of the PMSM rotor, i q is the q-axis stator current of PMSM, and are the rotor electrical angle observation values ​​estimated by LESO1 and LESO2, e1 and e2 correspond to the electrical angle errors of LESO1 and LESO2 respectively. and are the motor speed observations estimated by LESO1 and LESO2 respectively, and are the disturbances of the estimated outputs of LESO1 and LESO2 respectively, β1~β6 are the gain coefficients of the observer, and They are and The first derivative of and They are and The first derivative of and They are and The first derivative of .

[0026] Furthermore, the expressions of the gain coefficients β1 to β6 are as follows:

[0027]

[0028] Where: ω0 and ω1 are the first-order bandwidth and second-order bandwidth of LESO (Linear State Extended Observer), and ω0=3ω1.

[0029] Furthermore, in step (4), the d-axis stator current reference value i is calculated by the following formula: d * and q-axis stator current reference value i q * ;

[0030]

[0031] Where: u0 is the linear state error feedback control law.

[0032] Furthermore, the expression of the linear state error feedback control law u0 is as follows:

[0033]

[0034] Where: e * is the motor speed reference value, k p is the proportionality coefficient.

[0035] The present invention effectively solves the problem of significant degradation of the system's dynamic performance under speed mutation and motor disturbance by introducing a third-order adaptive cascaded linear extended state observer (ACLESO) to replace the traditional fixed-bandwidth orthogonal phase-locked loop. ACLESO can accurately estimate the speed, phase and total disturbance in real time, significantly improving the dynamic response capability of the system, while reducing the sensitivity to noise by adaptively adjusting the observer parameters. In addition, the present invention combines the design of the linear state error feedback control law (LSEFCL) to further simplify the control structure and enhance the anti-disturbance capability of the system. The superiority and reliability of the method under complex dynamic conditions are proved through Lyapunov stability analysis and experimental verification. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The block diagram of the PMSM sensorless control system based on the adaptive enhanced extended state observer of the present invention.

[0037] Figure 2 Schematic diagram of the basic principle of a traditional second-order phase-locked loop.

[0038] Figure 3 The dual LESO control block diagram designed for the present invention.

[0039] Figure 4 Bode plot of the traditional third-order LESO perturbation error.

[0040] Figure 5Bode plot of the three-stage cascaded LESO disturbance error.

[0041] Figure 6 The block diagram of the adaptive third-order cascade LESO control designed for the present invention.

[0042] Figure 7 The block diagram of the ADRC speed control based on LSEFCL designed for the present invention.

[0043] Figure 8 Schematic diagram of the comparison results of the rotation speed estimation performance of the ACLESO scheme of the present invention, Q-PLL and LESO schemes.

[0044] Fig. 9 It is a schematic diagram of the comparison results of the speed estimation performance of the ACLESO scheme of the present invention, Q-PLL and LESO schemes under speed instructions.

[0045] Fig.10 It is a schematic diagram of the comparison results of the rotation speed estimation errors of the ACLESO scheme of the present invention and the Q-PLL and LESO schemes.

[0046] Fig.11 Schematic diagram of the actual position, position estimation and error of Q-PLL during sudden speed change.

[0047] Fig.12 Schematic diagram of ACLESO's actual position, position estimation and its error during sudden speed change.

[0048] Fig.13 Schematic diagram of the comparison results of the speed estimation performance of three different schemes under sudden load changes.

[0049] Fig.14 Schematic diagram of the comparison results of speed estimation errors of three different schemes during sudden speed changes.

[0050] Fig.15 Schematic diagram of the actual position, position estimation and error of the Q-PLL under load changes.

[0051] Fig.16 Schematic diagram of the actual position, estimated position and error of LESO under load changes.

[0052] Fig.17 Schematic diagram of the actual position, estimated position and error of ACLESO under load changes.

[0053] Fig.18 Schematic diagram of the comparison results of the speed estimation performance of three different schemes under sudden load at rated speed. DETAILED DESCRIPTION

[0054] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0055] The present invention is based on the speed estimation scheme of the traditional phase-locked loop:

[0056]

[0057] Where: e α and e β are the back electromotive force of the α-axis and β-axis motors, ω e is the speed of the motor, ψ f is the magnetic flux of the motor, θ e is the electrical angle of the motor.

[0058] The expression of the magnetic flux of a permanent magnet in a stationary coordinate system is:

[0059]

[0060] in: and are the magnetic flux along the α-axis and the β-axis respectively.

[0061] The basic principle of traditional Q-PLL, taking the flux observer as an example, designs a phase-locked loop to extract the position information of the rotor flux phase encoding. The angle error calculation formula is:

[0062]

[0063] The angular error is processed through a PI loop to calculate the angular velocity, which is given by the following equation:

[0064] ω e =k p Δθ e +∫k i Δθ e

[0065] The basic principle of the traditional second-order phase-locked loop is as follows Figure 2 As shown in the figure, the scheme takes the estimated rotor flux as input. k p , k i They are the α-axis component and β-axis component of the rotor flux, the proportional gain, and the integral gain; finally, the electrical angle error obtained from the phase-locked loop can converge to 0. The advantage of the phase-locked loop is that it makes the estimation process of the rotor speed into a closed-loop form, avoiding differential operations.

[0066] Combining the above formula, the transfer function of the phase-locked loop can be determined:

[0067]

[0068] The phase error function of the phase-locked loop is:

[0069]

[0070] When the input frequency ramps, the Q-PLL solution calculates the steady-state phase error as:

[0071]

[0072] Where: n is the gain of the frequency ramp. As can be seen from the above formula, the Q-PLL scheme may lose the ability to make accurate estimates due to a sharp increase in frequency, which means that the traditional Q-PLL scheme may provide unsatisfactory accuracy during acceleration and deceleration (under these conditions, the frequency undergoes a ramp change).

[0073] In order to improve the dynamic performance of the permanent magnet synchronous motor drive system, the present invention proposes a linear extended state observer (LESO) scheme based on mechanical dynamics for the traditional phase-locked loop. The dynamics of the permanent magnet synchronous motor can be expressed as follows:

[0074]

[0075] Where: R s is the motor stator resistance, L d and L q They are the motor d-axis stator inductance, q-axis stator inductance, u d and u q are the d-axis stator voltage and the q-axis stator voltage respectively, i d is the d-axis stator current.

[0076] In order to more clearly understand the impact of system factors on the speed, the above formula is transformed:

[0077]

[0078] Where: b = 3n p ψ f / 2J, a=1 / J, a1=B / J; when considering the disturbance of motor parameter changes, the above formula is:

[0079]

[0080] Among them: Δb, Δa, Δa1 are the disturbance terms caused by parameter changes.

[0081] Then, we can get:

[0082]

[0083]

[0084] Where: f1 is the known and unknown disturbance part of the system, including load torque disturbance, viscous friction, and q-axis current disturbance.

[0085] LESO is able to observe all state variables (including extended states) by utilizing the input and output signals from the controlled system, so the mathematical model of the third-order LESO can be expressed as:

[0086]

[0087] Where: β1, β2, and β3 represent the gains of the third-order LESO.

[0088] The transfer function of phase error with respect to input phase can be derived as:

[0089]

[0090] When the input frequency ramps, the steady-state phase error of a third-order LESO can be determined by the following calculation:

[0091]

[0092] As can be seen from the above equation, the third-order LESO performs well in tracking the frequency ramp, and the steady-state phase error is zero. However, the traditional LESO method uses a fixed high gain for fast convergence, which may lead to increased sensitivity to noise and amplified motor vibration. In order to solve these problems and improve the ability to suppress disturbances, we use a cascaded third-order adaptive linear expansion state observer in the position loop.

[0093] Next, we derive the third-order adaptive cascade LESO described above, using one of the third-order ESOs to estimate the “total disturbance” of the system, and then record the estimated value as f 11 , as another "known disturbance" of the third-order ESO, this arrangement allows the latter to focus only on estimating the "unknown disturbance" in addition to the "known disturbance". Therefore, this method reduces the estimation burden and improves the accuracy of perturbation estimation, and then generalizes to the following formula:

[0094]

[0095] Where: z1 and z2 are the estimated electrical angles θ of 1-LESO respectively. e and the estimated speed ω e , is the estimated disturbance of 1-LESO, β1, β2 and β3 are the gains of 1-LESO. s1 and s2 are the estimated electrical angles θ of 2-LESO respectively. e and the estimated speed ω e , is the estimated disturbance of 2-LESO, β4, β5 and β6 are the gains of 2-LESO, and ftotal is the total perturbation; the specific control of the dual LESO is as follows Figure 3 shown.

[0096] according to Figure 3 The transfer function of the closed-loop system, the relationship between the input phase and the estimated phase can be expressed as:

[0097]

[0098] In the formula: a=β1β5+β3+β2β4+β6, b=β1β6+β4+β2β5, c=β2β6+β5.

[0099] From the above formula, the phase error transfer function can be obtained as:

[0100]

[0101] When the input frequency ramps, the steady-state phase error of the third-order adaptive cascade LESO is calculated as follows:

[0102]

[0103] For a conventional third-order LESO, the ratio of the estimated disturbance to the actual disturbance when performing Laplace transform is:

[0104]

[0105] The transfer function of the perturbation error can be obtained:

[0106]

[0107] The present invention proposes to use a three-stage cascaded ESO in the position loop instead of a traditional phase-locked loop. Through Laplace transform, the ratio of the estimated disturbance to the actual disturbance can be determined as:

[0108]

[0109] The transfer function of the three-stage cascaded LESO disturbance error is:

[0110]

[0111] Thus, the Bode plots of the conventional third-order LESO perturbation error and the third-order cascaded LESO perturbation error are derived respectively. Figure 4 and Figure 5 That is, the frequency response characteristics of these errors are shown.

[0112] according to Figure 4 and Figure 5From the observations shown, it is clear that increasing the bandwidth of the ESO leads to a higher disturbance estimation speed and a consistent reduction in the estimation error for both the conventional LADRC and the enhanced LADRC. When faced with perturbations of varying slopes, the conventional third-order ESO exhibits a steady-state error in the perturbation estimation, with smaller errors observed at high bandwidths; on the other hand, the enhanced third-order LESO achieves accurate perturbation estimation with zero steady-state error, significantly improving the accuracy of the perturbation estimation.

[0113] Based on the above analysis, it is clear that the LESO scheme requires high gain to achieve accurate observations, but this high gain may raise concerns about its noise sensitivity. To address this challenge, the present invention provides an enhanced adaptive self-turbulence controller scheme, and below we provide a comprehensive description of its unique characteristics and features.

[0114] The pole placement technique can be used for the gain design of 1-LESO as follows:

[0115]

[0116] The control gains of the 2-LESO use the same pole placement technique as the 1-LESO, as shown below:

[0117]

[0118] Where: ω0 and ω1 are the first-order and second-order bandwidths of the three-order cascaded ESO respectively.

[0119] Based on experience and practical considerations, a large number of parameter adjustments were made and it can be observed that ω0 = 3ω1 is satisfied between the two bandwidths. In this case, the use of cascaded ESOs has several advantages. Compared with conventional ESOs, it can not only estimate z2, s2 and the total disturbance f from the measured signal total , and enhances the observation of disturbances and suppresses the amplification of noise measurements.

[0120] Adaptive bandwidth is used to achieve a proper balance between fast convergence and robust noise suppression. The adaptive bandwidth design of the third-order ACLESO is summarized as follows:

[0121]

[0122] Where: 0min is the minimum value of ω0 bandwidth, k s is the adaptive gain, the control structure is as follows Figure 6 shown.

[0123] The state error feedback design of the traditional linear ADRC is as follows:

[0124]

[0125] Where: e * Indicates the speed command value, k p is the gain factor.

[0126] By compensating the overall disturbance, the control variable is obtained as follows:

[0127]

[0128] Where: u0 represents the output of the feedback error after the gain factor, represents the total disturbance of the system. Figure 6 It can be seen that speed control has only one parameter and will not cause the problem of parameter adjustment.

[0129] Theorem 1: The system disturbance and its derivatives estimated by the cascaded extended state observer are ultimately uniformly bounded.

[0130] Proof: The stability of the chosen cascade extended state observer will be demonstrated by the following proof.

[0131] Assume e ij =e i , where i or j = 1, 2, 3, the error equation for the third-order 1-LESO used to observe f1 can be derived as:

[0132]

[0133] Where: e 13 is the estimation error associated with the perturbation f1 and can be expressed as:

[0134]

[0135] because We can get:

[0136]

[0137] Where:

[0138] Since both eigenvalues ​​of H are -1, it follows that H is Hurwitz stable. Therefore, there exists a unique positive definite matrix P such that:

[0139] H T P+PH=-I

[0140] Where:

[0141] Take the Lyapunov function as V(γ)=γ T Pγ, then:

[0142]

[0143] Because h is a global Lipschitz function with respect to x, that is, there exists a constant ζ such that h ≤ ζ||xz 1i ||For all x,z 1i , the following relationship can be derived:

[0144]

[0145] When ω0 ≥ 1, we observe So the inequality is:

[0146]

[0147] Where: ρ = ||PKξ|| + 1.

[0148] Substituting the formula into the equation, we get:

[0149]

[0150] When ω0>ρ, we can get The same applies to e 2i , so we can conclude that:

[0151]

[0152] Where: i or j = 1, 2, 3.

[0153] Based on the above analysis, it can be concluded that the Lyapunov asymptotic stability theorem holds, indicating that the cascade extended state observer (CLESO) is convergent. In addition, when the system reaches a steady state, the right-hand side of the above equation converges to 0, so it can be inferred that:

[0154]

[0155] From the observation results, it can be seen that when the value of β3 is significantly greater than h, the steady-state error is small enough.

[0156] Finally, the final linear extended observer is used to achieve high-precision control of PMSM.

[0157] In this embodiment, the simulation motor parameters are shown in Table 1:

[0158] Table 1: Motor parameters

[0159]

[0160] The present invention is based on the sensorless control system of permanent magnet synchronous motor based on adaptive enhanced extended state observer. Figure 1 shown. Figure 7The basic framework of the adaptive cascade linear extended state observer is demonstrated, in which the input of the observer is the angle error. By observing and suppressing the disturbance, the robustness of the system can be qualitatively improved, and a certain filtering effect can be achieved.

[0161] By analyzing Figure 8 to Figure 12 The experimental results shown show that the proposed ACLESO scheme significantly improves the dynamic performance of the controller compared with the traditional PI and LESO control schemes when encountering speed command changes.

[0162] Figure 8 The performance of the ACLESO scheme of the present invention is compared with that of the conventional Q-PLL scheme and LESO scheme. It can be seen that when the speed suddenly changes from 400r / min to 800r / min, the Q-PLL and LESO control schemes show obvious ripples. In contrast, the ACLESO scheme reduces the ripples while improving the response speed.

[0163] Fig. 9 and Fig.10 A comparative analysis of acceleration and deceleration between LESO and ACLESO schemes under half-load condition is provided, and the results show that the ACLESO scheme can stably track the actual speed and is very fast during dynamic speed changes, returning to steady state within 0.1s. On the other hand, the LESO control scheme requires 0.15s to reach steady state. Fig.11 and Fig.12 The position estimation and position estimation error of the traditional Q-PLL and ACLESO during acceleration and deceleration under half-load conditions are given. It can be seen from the figure that at 800r / min, the position estimation errors obtained by both schemes are kept within 0.15rad. In the experimental test, ACLESO has no effect on the steady-state effect of the position sensorless controller. Fig.13 and Fig.14 The performance of the Q-PLL, LESO, and ACLESO schemes when the rated load suddenly increases are compared. Specifically, the ACLESO scheme outperforms the LESO scheme, with smaller errors and minimum ripples under a load change of 600 r / min (including the sudden increase of rated load and unloading).

[0164] Fig.15 , Fig.16 , Fig.17 A comparative analysis of position estimation and position estimation error of three schemes at 600rpm sudden loading and unloading is given. It can be seen from the figure that the estimation error of the conventional phase-locked loop is relatively large, while the estimation errors of ACLESO and LESO are kept within 0.1rad.

[0165] Fig.18The comparative analysis results of three schemes when a quarter of the rated load is suddenly applied at the rated speed are given. The results show that the ACLESO of the present invention has a good anti-stability effect when the rated speed is 1600rpm.

[0166] The above results show that the ACLESO scheme of the present invention has system dynamic characteristics comparable to those of the LESO scheme and has good noise suppression capability.

[0167] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A PMSM sensorless control method based on an adaptive enhanced extended state observer comprises the following steps: (1) Based on the working principle and characteristics of PMSM, the dynamic equation and first-order speed model of PMSM are established; (2) Establish a third-order extended state observer mathematical model of PMSM based on the dynamic equation and the first-order speed model; (3) Optimizing the mathematical model of the third-order extended state observer; (4) The motor speed observation value is estimated using the optimized third-order extended state observer mathematical model Then, the d-axis stator current reference value i is calculated by combining the linear state error feedback control law. d * and q-axis stator current reference value i q * , thereby achieving high-precision control of the PMSM.

2. The PMSM sensorless control method according to claim 1, characterized in that: The expression of the kinetic equation is as follows: Where: e is the speed of PMSM, ψ f is the magnetic flux of PMSM, T e is the electromagnetic torque of PMSM, T L is the load torque of PMSM, B is the viscosity coefficient of PMSM, J is the moment of inertia of PMSM, n p is the number of pole pairs of PMSM, i q is the q-axis stator current of PMSM, and t represents time.

3. The PMSM sensorless control method according to claim 2, characterized in that: The expression of the first-order speed model is as follows: in: is the speed ω e The first derivative of, b = 3n p ψ f / 2J, a=1 / J, a1=B / J.

4. The PMSM sensorless control method according to claim 3, characterized in that: The expression of the mathematical model of the third-order extended state observer is as follows: Where: θ e is the rotor electrical angle of the PMSM, is the rotor electrical angle θ e The first derivative of q * is the q-axis stator current reference value, f total is the total disturbance of the motor system including load torque disturbance, viscous friction disturbance and q-axis current disturbance.

5. The PMSM sensorless control method according to claim 4, characterized in that: In step (3), two cascaded third-order linear state extended observers LESO1 and LESO2 are designed to construct the total disturbance f total , use LESO1 to estimate the total disturbance of the system and use it as the known disturbance of LESO2, so that LESO2 only needs to focus on estimating the unknown disturbance.

6. The PMSM sensorless control method according to claim 5, characterized in that: The total disturbance of the motor system f total The expression is as follows: Where: z1 = s1 and is the measured value of the electrical angle of the PMSM rotor, i q is the q-axis stator current of PMSM, and are the rotor electrical angle observation values ​​estimated by LESO1 and LESO2, e1 and e2 correspond to the electrical angle errors of LESO1 and LESO2 respectively. and are the motor speed observations estimated by LESO1 and LESO2 respectively, and are the disturbances of the estimated outputs of LESO1 and LESO2 respectively, β1~β6 are the gain coefficients of the observer, and They are and The first derivative of and They are and The first derivative of and They are and The first derivative of .

7. The PMSM sensorless control method according to claim 6, characterized in that: The expressions of the gain coefficients β1 to β6 are as follows: Where: ω0 and ω1 are the first-order bandwidth and second-order bandwidth of LESO (Linear State Extended Observer), and ω0=3ω1.

8. The PMSM sensorless control method according to claim 4, characterized in that: In step (4), the d-axis stator current reference value i is calculated by the following formula: d * and q-axis stator current reference value i q * ; Where: u0 is the linear state error feedback control law.

9. The PMSM sensorless control method according to claim 8, characterized in that: The expression of the linear state error feedback control law u0 is as follows: Where: e * is the motor speed reference value, k p is the proportionality coefficient.

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