Composite rotating speed control method and system of ultra-low speed permanent magnet synchronous motor

Abstract

The invention belongs to the field of motor driving control, and discloses a composite rotating speed control method and system of an ultra-low speed permanent magnet synchronous motor, and the method comprises the steps: S1, collecting a rotor position signal and reference rotor position setting, and dynamically calculating the rotating speed through Kalman filtering; s2, inputting the rotating speed tracking error into a self-adaptive resonance controller, and realizing dynamic compensation of multi-frequency periodic disturbance through a closed-loop resonance frequency tracking mechanism; s3, on the basis of Kalman filter dynamic position calculation, the self-adaptive resonance output and the backstepping control output are synthesized into a composite control signal, and the composite control signal is subjected to SVPWM modulation to drive an inverter; and S4, repeating the steps S1 to S3, and realizing high-precision rotating speed tracking under an ultra-low speed working condition. The problem of coupling of position decoding errors, periodic disturbance and friction hysteresis under the ultra-low-speed working condition is solved, and high-precision control over the rotating speed is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor drive control, and particularly relates to a composite speed control method and system for an ultra-low speed permanent magnet synchronous motor. Background Art

[0002] Due to the requirement of ultra-high control precision, ultra-low speed permanent magnet synchronous motors (PMSMs) are widely used in fields such as astronomical telescopes, precision medical devices, aerospace, etc. The core problems of its speed control are as follows: the insufficient resolution of the position sensor makes the quantization error of the rotor angular position significant at ultra-low speeds, resulting in the amplification of speed decoding noise; the harmonic of the current and flux linkage sampling errors, the cogging torque, and the non-linear effects of the inverter increase the proportion of the disturbance amplitude at low speeds; at the same time, when the ultra-low speed motor commutes, due to the hysteresis of non-linear friction, there is a sudden change, resulting in inaccurate speed tracking.

[0003] Regarding the position calculation error, in the existing technical solutions, although a low-pass filter can filter out high-frequency noise, the effect of speed filtering needs to be improved. At the same time, the speed observer method based on the back electromotive force method is commonly used in high-speed sensorless control. In the case of low-speed and light-load working conditions, the accuracy of speed estimation is poor; regarding periodic disturbances, for example, repetitive control depends on a periodic model and cannot adapt to broadband disturbances; the quasi-resonant control is difficult to suppress unknown frequency harmonics due to the fixed resonant frequency, and the suppression performance drops suddenly when there is a parameter mismatch; the adaptive neural network depends on high computing power, and the control cost increases greatly; regarding friction disturbances, for example, the strategy based on the disturbance observer has high robustness, but ignores the dynamic characteristics of friction, and at the same time, a trade-off needs to be made between the control gain and stability. At the same time, the existing technical solutions mainly focus on the suppression of single disturbances. Although they have a certain ability to suppress single disturbances, there are still the following limitations in the ultra-low speed scenario: the coupling of multi-source disturbances such as position decoding noise, periodic disturbances, and friction hysteresis interaction, and it is difficult for a single suppression strategy to take into account global stability. Summary of the Invention

[0004] To solve the problems of speed decoding error caused by low-resolution position sensors and the influence of periodic disturbances and non-linear friction coupling on the speed control accuracy, the present invention provides a composite speed control method and system for an ultra-low speed permanent magnet synchronous motor, which dynamically calculates the rotor position based on a Kalman filter, suppresses periodic disturbances with an adaptive resonant controller, and compensates for the friction torque by backstepping control to achieve the collaborative suppression of multi-source disturbances.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A composite speed control method for an ultra-low speed permanent magnet synchronous motor, the method comprising:

[0007] S1: Collect the rotor position signal and the reference rotor position given, and dynamically calculate the speed through Kalman filtering;

[0008] S2: Input the rotational speed tracking error into the adaptive resonance controller, and achieve dynamic compensation for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonance frequency;

[0009] S3: On the basis of dynamic position calculation based on the Kalman filter, synthesize the adaptive resonance output and the backstepping control output into a composite control signal, and drive the inverter after SVPWM modulation;

[0010] S4: Repeat S1 - S3 to achieve high-precision rotational speed tracking under ultra-low speed conditions.

[0011] Preferably, the method for dynamically calculating the rotational speed through Kalman filtering includes: constructing a rotational speed - acceleration state observation equation, and suppressing low-resolution sensor quantization noise through recursive prediction and update;

[0012] Among them, the constructed state observation equation of rotational speed - acceleration:

[0013]

[0014] In the formula, ω a is the rotational speed of the motor, ω b is the rotational speed fluctuation during the operation of the motor. In the formula, the acceleration a is determined by the rotational speed setting, Δt is the operation time of the motor, are the prior estimated values of the rotational speed and rotational speed fluctuation at time t respectively.

[0015] Preferably, the method for inputting the rotational speed tracking error into the adaptive resonance controller and achieving dynamic compensation for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonance frequency includes: designing a closed-loop frequency tracking mechanism on the basis of suppressing bandwidth covering 6, 8, and 18 times frequency harmonics, and dynamically adjusting the resonance controller frequency point to match the unknown periodic disturbance frequency;

[0016] Among them, the transfer function of the adaptive resonance controller is:

[0017]

[0018] In the formula, K 1 、K 2 are the resonance gains, ω c is the resonance bandwidth, ω 0 is the fixed resonance frequency, ω 1 is the adaptive resonance frequency of closed-loop regulation.

[0019] Preferably, based on the dynamic position solution of the Kalman filter, the method of synthesizing the adaptive resonance output and the backstepping control output into a composite control signal and driving the inverter after SVPWM modulation includes: designing a dual observer in combination with the LuGre friction model, and adaptively compensating the current component through the Lyapunov stability criterion.

[0020] The present invention also provides a composite speed control system for a super-low-speed permanent magnet synchronous motor, and the system is used to implement any one of the above methods. The system includes: a Kalman filter position solution module, an adaptive resonance controller module, a backstepping control module, and an iteration module;

[0021] The Kalman filter position solution module is used to collect the rotor position signal and the reference rotor position given, and dynamically calculate the speed through Kalman filtering;

[0022] The adaptive resonance controller module is used to input the speed tracking error into the adaptive resonance controller, and dynamically compensate for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonance frequency;

[0023] The backstepping control module is used to synthesize the adaptive resonance output and the backstepping control output into a composite control signal based on the dynamic position solution of the Kalman filter, and drive the inverter after SVPWM modulation;

[0024] The iteration module repeats the Kalman filter position solution module - backstepping control module to achieve high-precision speed tracking under super-low-speed conditions.

[0025] Preferably, the process of dynamically calculating the speed through Kalman filtering includes: constructing a speed-acceleration state observation equation, and suppressing the quantization noise of the low-resolution sensor through recursive prediction and update;

[0026] Among them, the constructed speed-acceleration state observation equation:

[0027]

[0028] In the formula, ω a is the speed of the motor, ω b is the speed fluctuation during the operation of the motor. In the formula, the acceleration a is determined by the speed given, Δt is the operation time of the motor, are the prior estimated values of the speed and speed fluctuation at time t, respectively.

[0029] Preferably, the process of inputting the speed tracking error into the adaptive resonance controller and dynamically compensating for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonance frequency includes: designing a closed-loop frequency tracking mechanism on the basis of suppressing the bandwidth covering 6, 8, and 18 times frequency harmonics, and dynamically adjusting the resonance controller frequency point to match the unknown periodic disturbance frequency;

[0030] Among them, the transfer function of the adaptive resonance controller is as follows:

[0031]

[0032] In the formula, K 1 , K 2 are the resonance gains, ω c is the resonance bandwidth, ω 0 is the fixed resonance frequency, ω 1 is the adaptive resonance frequency for closed-loop regulation.

[0033] Preferably, on the basis of the dynamic position solution based on the Kalman filter, the process of synthesizing the adaptive resonance output and the backstepping control output into a composite control signal and driving the inverter through SVPWM modulation includes: designing a dual observer in combination with the LuGre friction model, and adaptively compensating the current component through the Lyapunov stability criterion.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] Based on the Kalman filter for dynamic rotor position solution, the adaptive resonance controller suppresses periodic disturbances, and the backstepping control compensates for the friction torque, realizing the collaborative suppression of multi-source disturbances. Compared with the traditional PI control and single disturbance rejection strategy, the proposed method significantly improves the position solution accuracy, periodic disturbance suppression ability and friction compensation effect. Experiments show that the rotational speed fluctuation suppression rate reaches more than 65%, and it can adapt to the full working conditions of 0-100% load, with excellent dynamic response and steady-state accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0037] Figure 1 It is a schematic diagram of the Kalman filter and backstepping-adaptive resonance control strategy in the embodiment of the present invention;

[0038] Figure 2 It is a schematic diagram of the structure of the adaptive resonance controller in the embodiment of the present invention;

[0039] Figure 3 It is a Nyquist diagram of different resonance frequencies in the embodiment of the present invention;

[0040] Figure 4 It is a schematic diagram of the backstepping control in the embodiment of the present invention. Detailed Embodiments

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0042] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Embodiment 1

[0044] Due to the large speed fluctuation and the difficulty in suppressing the influence of multi-source disturbances in the traditional ultra-low speed permanent magnet synchronous motor speed control method, in order to improve the accuracy of speed tracking, a composite speed control method for ultra-low speed permanent magnet synchronous motors is invented to solve the coupling problems of position decoding error, periodic disturbance, and friction hysteresis under ultra-low speed conditions and achieve high-precision speed control. Specifically:

[0045] As Figure 1 shown, the present invention provides a composite speed control method for ultra-low speed permanent magnet synchronous motors, and the method includes:

[0046] S1: Collect the rotor position signal and the reference rotor position given, dynamically calculate the speed through Kalman filtering, and suppress the quantization noise of the low-resolution sensor;

[0047] S2: Input the speed tracking error into the adaptive resonance controller, and realize the dynamic compensation of multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonance frequency;

[0048] S3: On the basis of the dynamic position calculation based on the Kalman filter, synthesize the adaptive resonance output and the backstepping control output into a composite control signal, and drive the inverter after SVPWM modulation;

[0049] S4: Repeat S1 - S3 to achieve high-precision speed tracking under ultra-low speed conditions.

[0050] In this embodiment, step 1: The dynamic position calculation method based on the Kalman filter is specifically to propose to construct a speed-acceleration state observation equation, and suppress the quantization noise of the low-resolution sensor through recursive prediction and update.

[0051] The Kalman filter is a state estimation method based on a recursive algorithm, which can achieve the optimal estimation of a dynamic system from a noisy observation sequence. Its core process includes two stages: prediction and update, corresponding to Equation (1) and Equation (2) respectively:

[0052]

[0053] The prediction stage is to calculate the prior estimate through the state equation and covariance The update stage is to use the observation value z t to correct the posterior estimate and covariance P t . Among them, K t is the Kalman gain, Q and R respectively represent the process noise and measurement noise covariance matrices, H is the observation matrix, A and B are the state transition matrices, u t is the system input variable, and I is the identity matrix.

[0054] For the problem of speed fluctuation of ultra-low speed permanent magnet motors, an extended state vector x = [ω a , ω b is defined T , where ω a is the speed of the motor, and ω b is the speed fluctuation during the operation of the motor. Combining the kinematic model of the motor, the state observation equation of speed-acceleration is established as follows:

[0055]

[0056] In the formula, Δt is the operation time of the motor, are the prior estimates of the speed and speed fluctuation at time t respectively, and the acceleration a is determined by the speed command. For example, when running at a constant speed n ref = 1 r / min, a = 0; when reciprocating n ref = sin(10t) r / min, a = 10cos10t. At the same time, the initial values of the process noise, measurement noise and covariance Q, R and P are calibrated through experiments 0 respectively as follows:

[0057]

[0058] In this embodiment, step 2: The periodic disturbance suppression strategy of the ultra-low speed motor based on the adaptive resonance controller is specifically to design a closed-loop frequency tracking mechanism on the basis of suppressing the 6th, 8th, and 18th harmonic frequencies, and dynamically adjust the resonance controller frequency point to match the unknown periodic disturbance frequency.

[0059] The transfer function of the traditional Quasi-Resonant (QR) controller is shown in Equation (5). Among them, K 1 is the resonance gain, ω c is the resonance bandwidth, ω 0 is the resonance frequency, and s is a complex variable representing the frequency in the Laplace transform domain.

[0060]

[0061] During the operation of the ultra-low speed motor, factors such as motor parameters and load changes exist, resulting in periodic disturbances with unknown torque and variable frequency. To address the above problems, a controller with adaptive resonant frequency adjustment is designed in this paper, and its structure is as follows Figure 2 shown. This controller takes the speed deviation e and the given value i of the current loop qref as inputs and outputs the compensation amount u. Specifically, based on the quasi-resonant controller, a dynamic adjustable unit for resonant frequency is connected in parallel, and the adaptive resonant frequency ω is generated through the PI regulation of the speed deviation and the compensation amount error 1 , realizing the closed-loop tracking of the resonant frequency.

[0062] From Figure 2 the open-loop transfer function of the adaptive resonant controller can be obtained as follows:

[0063]

[0064] Let the resonant gain K 1 =K 2 =200, the fixed resonant frequency ω 0 =5 rad / s, and the resonant bandwidth ω c =2 rad / s. Figure 3 The Nyquist curve of 1 shows that when ω 1 varies in the range of 5 - 20 rad / s, all the open-loop poles of the system are located in the left half-plane, and the curve does not cross the point (-1, j0). The stability of the proposed method is verified by the Nyquist stability criterion.

[0065] In this embodiment, step 3: The friction disturbance suppression strategy for the ultra-low speed permanent magnet motor based on backstepping control is specifically to design a double observer in combination with the LuGre friction model and adaptively compensate the current component through the Lyapunov stability criterion.

[0066] Considering that the LuGre friction model is a model that can comprehensively characterize the static and dynamic characteristics of friction force, the LuGre friction model is used for analysis and research, and its model is shown in Equation (7):

[0067]

[0068] where σ 0 is the bristle stiffness, σ 1 is the bristle damping, σ 2 is the viscous coefficient, z is the deformation amount, T f is the friction torque, T s is the static friction force, T cis the Coulomb friction, g(ω) is the function describing the friction characteristics, ω is the angular velocity, and ω s is the corner frequency.

[0069] Substituting Equation (7) into the motion equation of the motor gives:

[0070]

[0071] where J is the moment of inertia of the motor, is the derivative of the angular velocity, the control variable u is the given value compensated to the current loop, and the friction coefficient σ is defined for convenient operation 2 ’ = σ 1 + σ 2 . Establish the error e equation:

[0072]

[0073] where ω ref is the speed reference, is the derivative of the error, is the derivative of the speed reference. Substituting Equation (8) into the error equation gives:

[0074]

[0075] Design a dual observer to observe two items related to the state variable z:

[0076]

[0077] where z 0 , z 1 are state variables, is the derivative of the state variable, τ 0 , τ 1 is the observation error compensation amount.

[0078] Therefore, the given value u compensated to the current loop can be expressed as:

[0079]

[0080] where, is the estimated value of the stiffness of the whiskers, is the estimated value of the damping of the whiskers, is the estimated value of the viscosity coefficient;

[0081] Define the estimation error Substitute Equation (12) into Equation (10) and simplify to obtain the error:

[0082]

[0083] where, is the error value of the state variable; is the error value of the stiffness of the whiskers; is the error value of the damping of the whiskers; is the error value of the viscosity coefficient;

[0084] Construct the Lyapunov function:

[0085]

[0086] where k 2 , k 3 , k 4 are gains. According to the Lyapunov function stability principle, by combining Equation (11), Equation (13), and Equation (14), we can obtain:

[0087]

[0088] To satisfy the Lyapunov function stability and make the rotational speed error tend to zero, let:

[0089]

[0090] Then:

[0091]

[0092] Satisfy the Lyapunov asymptotic stability condition. Therefore, the backstepping control strategy is feasible in theoretical analysis. The schematic diagram of the backstepping control is as Figure 4 shown.

[0093] The control method of the present invention integrates the dynamic position solution of the Kalman filter, adaptive resonance, and backstepping control output, realizes the collaborative suppression of multi-source disturbances, and further improves the rotational speed control accuracy of the ultra-low speed motor.

[0094] The experimental verification results show that: when the ultra-low speed motor operates at a constant speed of 1 r / min, the present invention reduces the amplitude of the rotational speed decoding fluctuation from ±1 r / min to ±0.25 r / min; under the reciprocating motion of n ref = sin(10t) r / min, the amplitude of the tracking error is reduced by 65% compared with the single PI control; the rotational speed fluctuation suppression rate within the full load range is ≥65%, which is applicable to high-precision servo systems

[0095] Embodiment 2

[0096] The present invention also provides a composite rotational speed control system for an ultra-low speed permanent magnet synchronous motor. The system is used to implement the method described in any one of Embodiment 1. The system includes: a Kalman filter position solution module, an adaptive resonance controller module, a backstepping control module, and an iteration module;

[0097] The Kalman filter position calculation module is used to collect the rotor position signal and the reference rotor position setting, and dynamically calculate the rotational speed through Kalman filtering;

[0098] The adaptive resonant controller module is used to input the rotational speed tracking error into the adaptive resonant controller, and dynamically compensate for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonant frequency;

[0099] The backstepping control module is used to synthesize the adaptive resonant output and the backstepping control output into a composite control signal based on the dynamic position calculation of the Kalman filter, and drive the inverter after SVPWM modulation;

[0100] The iteration module repeats the Kalman filter position calculation module - backstepping control module to achieve high-precision rotational speed tracking under ultra-low speed conditions.

[0101] In this embodiment, the process of dynamically calculating the rotational speed through Kalman filtering includes: constructing a rotational speed - acceleration state observation equation, and suppressing the quantization noise of the low-resolution sensor through recursive prediction and update;

[0102] Among them, the constructed state observation equation of rotational speed - acceleration is:

[0103]

[0104] In the formula, ω a is the rotational speed of the motor, ω b is the rotational speed fluctuation during the operation of the motor. In the formula, the acceleration a is determined by the rotational speed setting, Δt is the operation time of the motor, are the prior estimated values of the rotational speed and rotational speed fluctuation at time t, respectively.

[0105] In this embodiment, the process of inputting the rotational speed tracking error into the adaptive resonant controller and dynamically compensating for multi-frequency periodic disturbances through the mechanism of closed-loop tracking of the resonant frequency includes: designing a closed-loop frequency tracking mechanism on the basis of suppressing the bandwidth covering the 6th, 8th, and 18th harmonic frequencies, and dynamically adjusting the resonant controller frequency point to match the unknown periodic disturbance frequency;

[0106] Among them, the transfer function of the adaptive resonant controller is:

[0107]

[0108] In the formula, K 1 、K 2 are the resonant gains, ω c is the resonant bandwidth, ω 0 is the fixed resonant frequency, ω 1 is the adaptive resonant frequency of closed-loop regulation.

[0109] In this embodiment, on the basis of dynamic position calculation based on the Kalman filter, the process of synthesizing the adaptive resonance output and the backstepping control output into a composite control signal and driving the inverter after SVPWM modulation includes: designing a dual observer in combination with the LuGre friction model, and adaptively compensating the current component through the Lyapunov stability criterion.

[0110] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A composite speed control method for an ultra-low speed permanent magnet synchronous motor, characterized in that: The method comprises: S1: Collect the rotor position signal and reference rotor position given, and dynamically calculate the speed through Kalman filtering; S2: Input the speed tracking error into the adaptive resonant controller, and realize dynamic compensation of multi-frequency periodic disturbances through the closed-loop tracking resonant frequency mechanism; S3: Based on the dynamic position solution based on the Kalman filter, the adaptive resonant output and the back-stepping control output are synthesized into a composite control signal, which is modulated by SVPWM to drive the inverter; S4: Repeat S1-S3 to achieve high-precision speed tracking under ultra-low speed conditions.

2. The method according to claim 1, characterized in that: The method of dynamically solving the speed through Kalman filtering includes: constructing the speed-acceleration state observation equation, suppressing the low-resolution sensor quantization noise through recursive prediction and updating; Among them, the constructed speed-acceleration state observation equation is: In the formula, ω a is the motor speed, ω b is the speed fluctuation during the motor operation process, where acceleration a is determined by the given speed, Δt is the motor operation time, are the prior estimates of the speed and speed fluctuation at time t respectively.

3. The method according to claim 1, characterized in that The method of inputting the speed tracking error into the adaptive resonant controller and realizing dynamic compensation of multi-frequency periodic disturbances through a closed-loop tracking resonant frequency mechanism includes: designing a closed-loop frequency tracking mechanism based on the suppression bandwidth covering 6, 8, and 18 times harmonics, and dynamically adjusting the frequency point of the resonant controller to match the unknown periodic disturbance frequency; Among them, the transfer function of the adaptive resonant controller is: Where K1 and K2 are the resonant gains, ω c is the resonance bandwidth, ω0 is the fixed resonance frequency, and ω1 is the adaptive resonance frequency of closed-loop regulation.

4. The method according to claim 1, characterized in that: Based on the dynamic position solution of Kalman filter, the method of synthesizing the composite control signal by the adaptive resonant output and the backstepping control output and driving the inverter after SVPWM modulation includes: designing a dual observer in combination with the LuGre friction model, and adaptively compensating the current component through the Lyapunov stability criterion.

5. A composite speed control system for an ultra-low speed permanent magnet synchronous motor, the system being used to implement the method according to any one of claims 1 to 4, characterized in that: The system comprises: a Kalman filter position solving module, an adaptive resonance controller module, a back-stepping control module and an iteration module; The Kalman filter position calculation module is used to collect the rotor position signal and reference the rotor position setting, and dynamically calculate the rotation speed through Kalman filtering; The adaptive resonant controller module is used to input the speed tracking error into the adaptive resonant controller, and realize dynamic compensation of multi-frequency periodic disturbances through a closed-loop tracking resonant frequency mechanism; The back-thrust control module is used to synthesize a composite control signal from the adaptive resonance output and the back-thrust control output based on the dynamic position solution of the Kalman filter, and drive the inverter after SVPWM modulation; The iterative module repeats the Kalman filter position solution module-backward control module to achieve high-precision speed tracking under ultra-low speed conditions.

6. The system according to claim 5, characterized in that The process of dynamically solving the speed through Kalman filtering includes: constructing the speed-acceleration state observation equation and suppressing the low-resolution sensor quantization noise through recursive prediction and updating; Among them, the constructed speed-acceleration state observation equation is: In the formula, ω a is the motor speed, ω b is the speed fluctuation during the motor operation process, where acceleration a is determined by the given speed, Δt is the motor operation time, are the prior estimates of the speed and speed fluctuation at time t respectively.

7. The system according to claim 5, characterized in that The process of inputting the speed tracking error into the adaptive resonant controller and realizing dynamic compensation of multi-frequency periodic disturbances through the closed-loop tracking resonant frequency mechanism includes: designing a closed-loop frequency tracking mechanism based on the suppression bandwidth covering 6, 8, and 18 times harmonics, and dynamically adjusting the frequency point of the resonant controller to match the unknown periodic disturbance frequency; Among them, the transfer function of the adaptive resonant controller is: Where K1 and K2 are the resonant gains, ω c is the resonance bandwidth, ω0 is the fixed resonance frequency, and ω1 is the adaptive resonance frequency of closed-loop regulation.

8. The system according to claim 5, characterized in that Based on the dynamic position solution of Kalman filter, the adaptive resonant output and the backstepping control output are synthesized into a composite control signal. The process of driving the inverter after SVPWM modulation includes: designing a dual observer in combination with the LuGre friction model, and adaptively compensating the current component through the Lyapunov stability criterion.

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