Permanent magnet synchronous motor rotating speed stability control method based on propeller load

Abstract

The invention discloses a cascaded auto-disturbance rejection rotating speed stability control method with a quasi-resonance link based on propeller load, and the method comprises the following steps: S1, building a speed ring mathematical equation containing disturbance according to the basic structure and working principle of a surface-mounted permanent magnet synchronous motor; s2, according to aerodynamic characteristics of the propeller, establishing a mathematical model of tension and load torque of the propeller; s3, establishing a quasi-resonance cascade active-disturbance-rejection speed controller containing disturbance compensation according to the S1 and the S2, and performing stability analysis on a cascade expansion observer equation according to a Lyapunov stability theorem; and S4, a cascade active disturbance rejection control method with a quasi-resonance link is used to realize suppression of periodic and non-periodic disturbance of the rotating speed so as to realize high-performance speed control. According to the method, the motor and the propeller are integrally modeled, the influence of periodic disturbance and non-periodic disturbance on the rotating speed is considered at the same time, and the method has better dynamic performance and steady-state performance.

Description

Technical Field

[0001] The present invention relates to the technical field of control of permanent magnet synchronous motors, and in particular to a method for smoothly controlling the rotation speed of a permanent magnet synchronous motor under propeller load. Background Art

[0002] With the increasing demand for low-carbon and energy-saving, electric propulsion systems are widely used in the aviation field, especially in electric propulsion systems driven by permanent magnet synchronous motors (PMSM). PMSM is widely used due to its high power density, high torque output and wide speed range, especially in electric propulsion systems that combine surface-mounted permanent magnet synchronous motors (SPMSM) with propellers. Aircraft performance is closely related to propeller speed, so the impact of disturbances on system performance is particularly prominent, resulting in speed fluctuations and increased control difficulty. The speed of the PMSM system is affected by a variety of disturbances (such as load torque mutations, cogging torque, flux harmonics, inverter dead zone, etc.). These disturbances can be divided into periodic and non-periodic types, which affect the steady-state performance of the speed. In order to improve system performance and reduce speed fluctuations, researchers have proposed a variety of disturbance suppression schemes, especially in the suppression of non-periodic disturbances. Active disturbance rejection control is widely used, estimating non-periodic disturbances through extended state observers and attenuating them using feedforward compensation. However, the observation error of the extended state observer under periodic disturbances will lead to unsatisfactory control effects. For periodic disturbances, methods such as resonant control, iterative learning control and repetitive control can effectively suppress periodic speed fluctuations, but these methods can usually only target a single type of disturbance. In practical applications, the speed loop is affected by both non-periodic and periodic disturbances, and existing suppression schemes may cause system instability. Therefore, a control method is urgently needed to improve the accuracy and anti-disturbance performance of speed control.

[0003] To this end, a cascaded linear anti-disturbance control speed controller with a quasi-resonant link is proposed. This method estimates and compensates for non-periodic disturbances through a cascaded extended state observer, and embeds a quasi-resonant link to suppress periodic disturbances, thereby improving the accuracy and anti-disturbance performance of speed control. Summary of the invention

[0004] The present invention aims to address the speed control problem of permanent magnet synchronous motors and provide a method for smooth speed control of permanent magnet synchronous motors under propeller load. The method estimates and compensates for non-periodic disturbances through a cascaded expanded state observer, and embeds a quasi-resonant link to suppress periodic disturbances, so as to improve the accuracy of speed control and anti-disturbance performance, thereby providing a new technical solution for improving the speed control performance of permanent magnet synchronous motors.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A cascaded anti-disturbance speed stabilization control method with a quasi-resonant link under propeller load comprises the following steps:

[0007] S1. According to the motion equation of the surface-mounted permanent magnet synchronous motor without disturbance, a speed loop mathematical equation with disturbance is established;

[0008] S2. According to the aerodynamic characteristics of the propeller, a mathematical model of the propeller's thrust and load torque is established;

[0009] S3. According to S1 and S2, a quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation is established, and the stability analysis of the quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation is performed according to the Lyapunov stability theorem.

[0010] S4. According to the stability analysis results, a quasi-resonant cascaded anti-disturbance speed controller with disturbance compensation that meets the stability requirements is used to suppress periodic and non-periodic disturbances of the surface-mounted permanent magnet synchronous motor speed to achieve high-performance speed control.

[0011] Preferably, in step S1, the motion equation without disturbance is:

[0012]

[0013] Where: i d 、i q is the current in dq axis coordinates, L d and L q is the dq axis inductance component, ψ f and ω m are the flux linkage and mechanical angle respectively, p n is the number of motor pole pairs, T e is the electromagnetic torque, T L is the load torque, B is the damping coefficient, and J is the moment of inertia.

[0014] Preferably, in step 1, a velocity loop mathematical equation containing disturbance is further established based on the motion equation without disturbance as follows:

[0015]

[0016] Where b is 1.5p n i q ψ f , f is the lumped disturbance.

[0017] Preferably, the lumped disturbance includes a non-periodic disturbance and a periodic disturbance, as follows:

[0018]

[0019] Among them, fap and f p They are non-periodic disturbance and periodic disturbance respectively. Among the periodic disturbances, the main one is ΔT caused by the current sampling error. 1 and ΔT 2 , are the first and second harmonics of the fundamental frequency of the speed. Non-periodic disturbances are mainly parameter perturbations, load changes, unknown disturbances d, etc. ap and f p The whole is regarded as a lumped disturbance f.

[0020] Preferably, the specific method of step S3 is:

[0021] S3-1. Designing a cascade expansion observer according to a mathematical equation of a velocity loop containing disturbances, wherein the cascade expansion observer comprises a first-stage expansion observer and a second-stage expansion observer;

[0022] S3-2, embedding a quasi-resonant link in the second-stage expansion observer;

[0023] S3-3, estimating non-periodic disturbances and periodic disturbances by embedding a cascade extended observer after a quasi-resonant link in a second-stage extended observer, and feed-forward compensating them to a linear state feedback link in a quasi-resonant cascade self-disturbance rejection speed controller with disturbance compensation, as a lumped disturbance compensation to the system;

[0024] S3-4. Perform stability analysis on the cascade expansion observer equation based on Lyapunov stability theorem.

[0025] The present invention has the following characteristics and beneficial effects:

[0026] By adopting the above technical scheme, when a permanent magnet synchronous motor is used to directly drive a propeller, the motor speed is easily affected by multiple source disturbances such as airflow disturbance, parameter perturbation, cogging torque, flux harmonics, inverter dead zone, current sampling error, etc., which will cause speed fluctuations. By improving the cascaded anti-disturbance control and embedding a quasi-resonant link in the cascaded expanded observer, the improved cascaded anti-disturbance speed controller can have a better suppression effect on both non-periodic and periodic disturbances, and obtain higher control performance. The stability of the improved cascaded expanded observer is analyzed by the Lyapunov stability theorem. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] 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, other drawings can be obtained based on these drawings without paying creative labor.

[0028] Figure 1 This is the connection diagram of the permanent magnet synchronous motor direct-drive propeller.

[0029] Figure 2 Block diagram for improved cascaded ADRC speed controller.

[0030] Figure 3 This is the block diagram of the permanent magnet synchronous motor speed stabilization control system under propeller load.

[0031] Figure 4 This is the traditional PI control 500rpm-750rpm speed step response diagram.

[0032] Figure 5 500rpm-750rpm speed step response diagram for improved cascaded auto-disturbance rejection speed control.

[0033] Figure 6 This is the steady-state error diagram of the traditional PI control at 750rpm.

[0034] Figure 7 The steady-state error diagram of 750rpm speed for improved cascaded ADRC speed control.

[0035] Figure 8 This is the sinusoidal response diagram of the traditional PI control speed.

[0036] Fig. 9 Speed ​​sinusoidal response diagram for improved cascaded ADRC speed control.

[0037] Fig.10 This is the FFT diagram of the traditional PI control 750rpm steady-state speed.

[0038] Fig.11 FFT diagram of 750rpm steady-state speed for improved cascaded ADRC speed control. DETAILED DESCRIPTION

[0039] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0040] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying 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 the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0041] 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 it can be indirectly connected 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 by specific circumstances.

[0042] The present invention provides a cascaded anti-disturbance speed stabilization control method with a quasi-resonant link under propeller load, which is specifically as follows:

[0043] S1. According to the non-disturbance motion equation of the surface-mounted permanent magnet synchronous motor, a speed loop mathematical equation with disturbance is established.

[0044] Specifically, the disturbance-free motion equation of the surface-mounted permanent magnet synchronous motor is:

[0045]

[0046] Where: i d 、i q is the current in dq axis coordinates, L d and L q is the dq axis inductance component, ψ f and ω m are the flux linkage and mechanical angle respectively, p n is the number of motor pole pairs, T e is the electromagnetic torque, T L is the load torque, B is the damping coefficient, and J is the moment of inertia.

[0047] In this embodiment, i d=0 double closed-loop vector control method, the surface-mounted air gap magnetic field is uniform, the difference between the quadrature-axis inductance and the direct-axis inductance is very small, and the motor can be regarded as a hidden pole. Assuming that the three-phase stator winding of the motor is symmetrical, the waveform of the induced back electromotive force on the stator side is a standard sine wave when the motor rotates, and the core saturation is ignored, the surface-mounted permanent magnet synchronous motor is taken as an example.

[0048] Furthermore, the mathematical equation of the velocity loop with disturbance is further established based on the motion equation without disturbance:

[0049]

[0050] Among them, f is the lumped disturbance, which mainly includes non-periodic disturbance and periodic disturbance, as follows:

[0051]

[0052] Among them, f ap and f p They are non-periodic disturbance and periodic disturbance respectively. Among the periodic disturbances, the main one is ΔT caused by the current sampling error. 1 and ΔT 2 , are the first and second harmonics of the fundamental frequency of the speed. Non-periodic disturbances are mainly parameter perturbations, load changes, unknown disturbances d, etc. ap and f p The whole is regarded as a lumped disturbance f.

[0053] S2. According to the aerodynamic characteristics of the propeller, a mathematical model of the propeller's thrust and load torque is established;

[0054] Specifically, the principle of constructing the mathematical model is as follows:

[0055] During the takeoff process, the lift of the drone is provided by the pulling force generated by the rotation of the propeller. The motor and propeller are directly driven. Figure 1 When performing aerodynamic analysis on a propeller, the propeller blade element analysis is performed based on the application of airfoil theory. The torque and thrust generated when the propeller rotates are:

[0056]

[0057] Among them, C F and C M are the thrust coefficient and torque coefficient of the propeller, respectively. It should be noted that the thrust coefficient and torque coefficient of the propeller are mainly determined by the geometric parameters of the propeller (such as blade length, width, pitch), material properties, rotation speed and air flow speed; F is the thrust generated by the propeller; M is the torque generated by the propeller; N is the rotation speed of the propeller; D pis the diameter of the propeller; ρ is the air density. When the motor directly drives the propeller to provide power, the load torque of the motor is the torque generated by the propeller.

[0058] S3. According to S1 and S2, a quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation is established, and the stability of the quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation is analyzed according to the Lyapunov stability theorem.

[0059] Specifically, in this embodiment, according to the mechanical motion equation in S1, the actual speed of the system and the state variable x of the unknown disturbance are used. 1 =ω m , x 2 =f; Establish the state space expression of the system motion equation:

[0060]

[0061] Where b = 1.5p n ψ f .

[0062] According to the motion equation of the permanent magnet synchronous motor system, a cascade expansion observer with a quasi-resonant link is designed. The observer equation is as follows:

[0063]

[0064] In the formula, β 1 , β 2 , β 3 and β 4 represents the observer gain; z 11 and z 12 are the velocity observation value and disturbance observation value of the first-level expanded observer respectively; z 21 and z 22 are the velocity observation value and disturbance observation value of the second-level expanded observer respectively; e 11 and e 21 are the velocity observation errors of the first-level expanded observer and the second-level expanded observer, G QR (s) is a quasi-resonant controller, and its expression is:

[0065]

[0066] In the formula, ω 1 and ω 2 Two different resonant frequencies; ω c1 and ω c2 is the cutoff frequency; k r1 and k r2 is the resonance coefficient.

[0067] It should be noted that ω 1,ω 2 The choice of is related to the motor's fundamental frequency angular velocity, ω 1 =p n ω m ,ω 2 =2p n ω m ;ω c1 =0.015ω 1 ,ω c2 =0.015ω 2 , choose k reasonably r1 and k r2 size to ensure system stability.

[0068] In this embodiment, the linear state feedback link adopts a proportional link k p , which can simplify the system design, the controller output is:

[0069]

[0070] Where u is the output of the speed controller. The control block diagram of the entire speed control system is as follows: Figure 2 shown.

[0071] Observer gain β 1 , β 2 , β 3 and β 4 The bandwidth method can be used for setting as follows:

[0072]

[0073] The stability of the proposed method is proved by Lyapunov method. According to the system's equation of motion and observer equation, the error equation of the first-order extended observer can be obtained as:

[0074]

[0075] make According to the above formula, we can get:

[0076]

[0077] Write the above formula in matrix form:

[0078]

[0079] in, The two characteristic roots of the matrix Q are -1, which proves that Q satisfies Hurwitz stability. Therefore, there exists a unique positive definite matrix P such that:

[0080] Q T P+PQ=-I

[0081] in, I is the identity matrix

[0082] Choose the Lyapunov function as:

[0083] V(γ)=γ T Pγ

[0084] Then we have:

[0085]

[0086] Perturbation is a global Lipschitz with respect to x, that is, there exists a constant ζ such that For all x and z 1i Both have:

[0087]

[0088] When 0 ≥1, we can observe:

[0089] ω 0 -1 ||xz 1i ||=ω 0 -1 ||e 1i ||≤||γ||

[0090] Therefore, we can get the inequality:

[0091]

[0092] Where, ρ = ||PKζ|| 2 +1, combining the above two equations, we can get:

[0093]

[0094] When 0 >ρ, we can get And this method also applies to e 2i ,therefore:

[0095]

[0096] i,j=1,2. Based on the above analysis, it can be concluded that Lyapunov's asymptotic stability theorem holds, indicating that the cascade extended state observer is convergent.

[0097] S4. According to the stability analysis results, a quasi-resonant cascaded anti-disturbance speed controller with disturbance compensation that meets the stability requirements is used to suppress periodic and non-periodic disturbances of the surface-mounted permanent magnet synchronous motor speed to achieve high-performance speed control.

[0098] In this embodiment, the parameters of the motor and propeller are shown in Table 1:

[0099]

[0100] According to the technical solution provided in this embodiment, by Figure 3 It can be seen that the error between the reference speed and the feedback speed is input into the improved cascade anti-disturbance speed controller designed. First, the error passes through the designed linear state feedback link k p The improved cascade expansion observer consists of three parts: the first-stage expansion observer, the second-stage expansion observer, and the quasi-resonance link; the two observers mainly compensate for non-periodic disturbances, and the quasi-resonance link mainly compensates for periodic disturbances. The outputs of the three are used as the estimation of the lumped disturbance. The output of the linear state feedback is compensated and then used as the reference input of the current loop.

[0101] Compare this embodiment with traditional PI control:

[0102] from Figure 4 and Figure 5 It can be seen that in the step response of 0-750 rpm, the PI control speed has a speed overshoot of 55 rpm and reaches a steady state at 0.55 s; while the speed of this design has no overshoot and reaches a steady state at 0.33 s. This shows that this design has better dynamic performance.

[0103] from Figure 6 and Figure 7 , is the steady-state speed when the step response is 0-750 rpm. The steady-state error of the speed is about 5 rpm when PI is used for control, while the steady-state error of the speed of this design is within 2 rpm. This shows that this design has better steady-state performance.

[0104] from Figure 8 and Fig. 9 It can be seen that for the speed sinusoidal response, the PI controller has a maximum speed error of 16.3rpm; while the maximum speed error of the controller in this scheme is within 8.3rpm. This shows that this design has better tracking performance for the sinusoidal response.

[0105] from Fig.10 and Fig.11It can be seen that when the speed is at a steady state of 750rpm, the FFT analysis of the speed shows that when PI 1 is controlled, the one-fold fundamental frequency and the two-fold fundamental frequency of the speed account for the main components of the periodic disturbance of the speed. When PI is controlled, the first harmonic and the second harmonic account for 0.54% and 0.20% respectively, and the THD is 0.62%; while in this control scheme, the first harmonic and the second harmonic account for 0.13% and 0.16% respectively, and the THD is 0.19%. This shows that this design scheme has a certain inhibitory effect on periodic disturbances.

[0106] Based on the above simulation results, it can be seen that the cascaded self-disturbance rejection speed stabilization control method with a quasi-resonant link under propeller load provided in this embodiment has better dynamic performance and steady-state performance, and its tracking ability for sinusoidal speed is higher than that of traditional PI control, and its ability to suppress periodic disturbances is greatly improved compared to PI control.

[0107] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A method for controlling the speed of a permanent magnet synchronous motor under propeller load, characterized in that: The steps include: S1. According to the motion equation of the surface-mounted permanent magnet synchronous motor without disturbance, a speed loop mathematical equation with disturbance is established; S2. According to the aerodynamic characteristics of the propeller, a mathematical model of the propeller's thrust and load torque is established; S3. According to S1 and S2, a quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation is established, wherein the quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation includes a cascade linear expansion observer, a linear state feedback link, and a quasi-resonant link. According to the Lyapunov stability theorem, a stability analysis is performed on the quasi-resonant cascade auto-disturbance rejection speed controller with disturbance compensation. S4. According to the stability analysis results, a quasi-resonant cascaded anti-disturbance speed controller with disturbance compensation that meets the stability requirements is used to suppress periodic and non-periodic disturbances of the surface-mounted permanent magnet synchronous motor speed to achieve high-performance speed control.

2. A method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 1, characterized in that: In step S1, the motion equation without disturbance is: Where: i d 、i q is the current in dq axis coordinates, L d and L q is the dq axis inductance component, ψ f and ω m are the flux linkage and mechanical angle respectively, p n is the number of motor pole pairs, T e is the electromagnetic torque, T L is the load torque, B is the damping coefficient, and J is the moment of inertia.

3. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 2 is characterized in that: In step 1, the mathematical equation of the velocity loop containing disturbance is further established based on the motion equation without disturbance: Where b is 1.5p n i q ψ f , f is the lumped disturbance.

4. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 3 is characterized in that: The lumped disturbance includes non-periodic disturbance and periodic disturbance, as follows: Among them, f ap and f p They are non-periodic disturbance and periodic disturbance respectively. Among the periodic disturbances, the main ones are ΔT1 and ΔT2 caused by the current sampling error, which are the first and second harmonics of the speed fundamental frequency. The non-periodic disturbances are mainly parameter perturbations, load changes, unknown disturbances d, etc. ap and f p The whole is regarded as a lumped disturbance f.

5. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 1 is characterized in that: In step S2, the mathematical model of the propeller's pulling force and load torque is expressed as follows: In the formula, C F and C M are the thrust coefficient and torque coefficient of the propeller respectively; N is the speed of the propeller; D p is the diameter of the propeller; ρ is the air density.

6. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 1 is characterized in that: When the surface-mounted permanent magnet synchronous motor directly drives the propeller to provide power, the load torque of the surface-mounted permanent magnet synchronous motor is the torque generated by the propeller.

7. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 1 is characterized in that: The specific method of step S3 is: S3-1. Designing a cascade expansion observer according to a mathematical equation of a velocity loop containing disturbances, wherein the cascade expansion observer comprises a first-stage expansion observer and a second-stage expansion observer; S3-2, embedding a quasi-resonant link in the second-stage expansion observer; S3-3, estimating non-periodic disturbances and periodic disturbances by embedding a cascade extended observer after a quasi-resonant link in a second-stage extended observer, and feed-forward compensating them to a linear state feedback link in a quasi-resonant cascade self-disturbance rejection speed controller with disturbance compensation, as a lumped disturbance compensation to the system; S3-4. According to the Lyapunov stability theorem, the stability analysis of the quasi-resonant cascade anti-disturbance speed controller with disturbance compensation is carried out.

8. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 1 is characterized in that: In step S3, a cascade expansion observer with a quasi-resonant link is designed, and the observer equation is as follows: Where β1, β2, β3 and β4 represent observer gains; 11 and z 12 are the velocity observation value and disturbance observation value of the first-level expanded observer respectively; z 21 and z 22 are the velocity observation value and disturbance observation value of the second-level expanded observer respectively; e 11 and e 21 are the velocity observation errors of the first-level expanded observer and the second-level expanded observer, G QR (s) is a quasi-resonant link, and s represents a differential operator.

9. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 8, characterized in that: The linear state feedback link expression is as follows: Where u is the output of the quasi-resonant cascaded anti-disturbance speed controller with disturbance compensation, ω m,ref is the reference speed, k p The proportion link adopted.

10. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 8, characterized in that: The quasi-resonance link is expressed as: Where ω1 and ω2 are two different resonant frequencies; ω c1 and ω c2 is the cutoff frequency; k r1 and k r2 is the resonance coefficient.

11. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 8, characterized in that: The stability analysis method: According to the system's perturbation-containing velocity loop mathematical equation and the cascade expanded observer equation, the error equation of the first-stage expanded observer is obtained as follows: when i=1,2, indicating that the first cascade extended state observer is convergent; Similarly, the error equation of the second-stage extended observer is obtained: when i=1,2, indicating that the second cascade extended state observer is convergent; Combining the first cascade extended state observer and the second cascade extended state observer, when i=1,2,j=1,2, that is, the cascade expansion observer equation is convergent, which conforms to Lyapunov's asymptotic stability theorem.

12. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 8, characterized in that: In step S4, the parameters of the quasi-resonant cascaded anti-disturbance speed controller with disturbance compensation using the bandwidth method are adjusted, wherein the cascaded expansion observer gains β1, β2, β3 and β4 can be adjusted as follows:

13. The method for controlling the speed of a permanent magnet synchronous motor under propeller load according to claim 10, characterized in that: The parameters of the quasi-resonant link are set as follows: The selection of ω1 and ω2 is related to the fundamental frequency angular velocity of the motor, ω1 = p n ω m ,ω2=2p n ω m ;ω c1 =0.015ω1,ω2=2p n ω m .

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