A quasi-resonant discrete sliding mode speed regulation method for permanent magnet arc motor

Abstract

This invention relates to a quasi-resonant discrete sliding mode speed control method for permanent magnet arc motors. First, a discrete error model considering lumped disturbances is established based on the speed loop model of the permanent magnet arc motor. Second, one or more quasi-resonant control branches are constructed based on the characteristic frequencies of the disturbances dominated by the end torque, and the discrete outputs of each quasi-resonant branch are obtained. Then, the mechanical angular velocity error, the error integral term, and the outputs of the quasi-resonant branches are introduced into a discrete sliding surface to construct a quasi-resonant sliding surface considering periodic disturbances. Based on this, a speed control law composed of equivalent control terms and discrete super-helical switch control terms is designed, outputting the q-axis current and completing closed-loop control. This invention can selectively suppress the 55th, 110th, and 165th harmonics related to the end torque under low-speed conditions of the permanent magnet arc motor, reducing the speed ripple factor and total harmonic distortion, and improving the stability of the system's low-speed steady-state operation.

Description

Technical Field

[0001] This invention relates to a quasi-resonant discrete sliding mode speed control method for suppressing harmonic speed fluctuations in the edge torque characteristics of permanent magnet arc motors operating at low speeds, and specifically relates to the field of motor control technology. Background Technology

[0002] Permanent magnet arc motors offer advantages such as convenient segmented manufacturing, suitability for direct drive of large loads, and high torque output at low speeds, making them promising for applications in large telescopes, direct-drive turntables, and specialized servo systems. However, due to their discontinuous stator structure, permanent magnet arc motors are susceptible to positioning torque, especially end torque, at low speeds, leading to significant speed fluctuations and reducing the system's steady-state operation stability and control accuracy.

[0003] While existing PI control and conventional sliding mode control possess a certain degree of robustness, they lack the ability to selectively suppress periodic disturbances at specific frequencies dominated by edge torque, making it difficult to simultaneously achieve low-speed steady-state accuracy, disturbance suppression performance, and closed-loop robustness. Therefore, it is necessary to propose a speed regulation method that can maintain the disturbance rejection advantages of discrete sliding mode control while providing directional compensation for the characteristic harmonics of edge torque. Summary of the Invention

[0004] Technical Problem: To address the issues of large speed ripple caused by the periodic disturbance dominated by the end torque during low-speed operation of a permanent magnet arc motor, and the insufficient selective suppression capability of existing control methods for the characteristic harmonics of the end torque, this invention proposes a quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor.

[0005] Technical solution: The present invention provides a quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor, comprising the following steps:

[0006] Step S1: Define the mechanical angular velocity error based on the speed loop model of the permanent magnet arc motor, and establish a discrete error model that takes into account the lumped disturbance;

[0007] Step S2: For the periodic disturbance dominated by the end torque during the low-speed operation of the permanent magnet arc motor, construct one or more quasi-resonant control branches and obtain the discrete output of each quasi-resonant control branch.

[0008] Step S3: Introduce the mechanical angular velocity error, error integral term, and output of each quasi-resonant control branch into the sliding surface to construct a quasi-resonant discrete sliding surface that takes into account periodic disturbances.

[0009] Step S4: Based on the quasi-resonant discrete sliding mode surface, design a velocity control law consisting of an equivalent control term and a discrete super-helical switch control term to obtain the q-axis current command;

[0010] Step S5: The q-axis current is fed into the inner current loop and the inverter drive system to suppress the harmonic speed fluctuation of the end torque characteristic when the permanent magnet arc motor is running at low speed.

[0011] in,

[0012] The specific steps of S1 are as follows:

[0013] The difference between the actual mechanical angular velocity and the target mechanical angular velocity is defined as the mechanical angular velocity error, and a velocity loop error model is established based on the d-axis and q-axis motion equations of the permanent magnet arc motor: , , ,

[0014] In the formula, and Let e(k) represent the actual mechanical angular velocity and the target mechanical angular velocity, respectively. Let e(k) represent the mechanical angular velocity error in the k-th control cycle, where k is the sequence of the controller cycle, d represents the lumped disturbance, T represents the control cycle, a represents the control gain, and u represents the control input. The lumped disturbance includes edge torque, cogging torque, parameter mismatch, and other unmodeled disturbances. Within a single control cycle, the lumped disturbance is approximated as a constant, and its rate of change is bounded.

[0015] The quasi-resonant control branch in step S2 has a continuous domain transfer function and a discrete domain transfer function, respectively: , , ,

[0016] In the formula, k r For the resonant gain, ω c For controller bandwidth, ω Q Let be the resonant frequency, s be a continuous domain variable, z be a discrete domain variable, T be the control period, and a1, a2 and b0, b1, b2 be the discretized quasi-resonant control coefficients, respectively. The continuous domain quasi-resonant controller is discretized using a bilinear transformation to obtain a discrete quasi-resonant control branch suitable for digital controller implementation.

[0017] In step S2, multiple quasi-resonant control branches are set up, and the output of each quasi-resonant control branch is r. i (k); When selecting 3 quasi-resonant control branches, the corresponding P is dominated by the end torque of the permanent magnet arc motor. n 2P n and 3P nFrequency doubling periodic disturbance; for an 18-slot 55-pole permanent magnet arc motor, the dominant disturbances are preferably the 55th, 110th and 165th characteristic harmonics.

[0018] In step S3, the quasi-resonant discrete sliding mode surface is composed of the mechanical angular velocity error, the error integral term, and the outputs of each quasi-resonant control branch, specifically represented as follows: ,

[0019] In the formula, s(k) is the sliding surface, I(k) is the integral term of the mechanical angular velocity error, c is the integral coefficient, and r i (k) represents the output of the i-th quasi-resonant control branch, e(k) represents the mechanical angular velocity error of the k-th control cycle, and k is the sequence of the controller cycle.

[0020] The resonant frequency of each quasi-resonant control branch is set according to the target mechanical angular velocity and the corresponding harmonic order, so that the quasi-resonant control branch maintains selective suppression capability against periodic disturbances of the characteristic frequency of the end torque. ,

[0021] In the formula, P represents the resonant frequency of the i-th quasi-resonant branch. n This indicates the number of pole pairs of the motor.

[0022] The speed control law in step S4 is composed of the equivalent control term u. eq and discrete superspiral switch control term u PDTSTC It consists of two parts: , in, , , , In the formula, Here, k is an intermediate variable, k is the sequence number of the controller cycle, and k1 and k2 are the discrete sliding mode control gains, respectively. To control the gain, b mn These are the discretized quasi-resonant control coefficients, i=1,2, j=1,2,3, m=0,2, n=1,2,3. For discrete sliding mode controller parameters, As intermediate control variables, the equivalent control term is used to offset the known modelable parts of the system, while the discrete superhelical switch control term is used to drive the sliding surface to converge and enhance the system robustness.

[0023] The controller parameters are tuned in a step-by-step manner: first, the resonant gain of each quasi-resonant control branch is set to zero, so that the controller degenerates into a discrete sliding mode speed regulation method without quasi-resonant control branches, and the integral coefficient, discrete superspiral gain and exponential parameters are tuned; then, each quasi-resonant control branch is gradually introduced, and the bandwidth parameter and resonant gain are tuned to take into account closed-loop stability, frequency selectivity and steady-state disturbance suppression capability.

[0024] Beneficial effects: Compared with traditional PI control and discrete sliding mode speed regulation methods without quasi-resonant control branches, this invention maintains the robustness of discrete sliding mode control while introducing a quasi-resonant control branch to selectively compensate for periodic disturbances at the target frequency dominated by the end torque. This effectively reduces the speed ripple, characteristic harmonic amplitude, speed ripple factor, and total harmonic distortion of the permanent magnet arc motor at low speeds, thereby improving the stability and overall control performance of the system at low speed steady-state operation. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the quasi-resonant discrete sliding mode speed regulation system of the present invention;

[0027] Figure 2 This is a schematic diagram of the structure of a single quasi-resonant control branch of the present invention;

[0028] Figure 3 This is a schematic diagram of the sliding surface structure that takes into account periodic disturbances in this invention;

[0029] Figure 4 The figures show a comparison of simulation results of different control methods under steady-state conditions according to the present invention. Figure 4 (a) in the figure is the PI simulation waveform. Figure 4 (b) in the figure is the NR-PDTSTC simulation waveform. Figure 4 (c) in the figure is the PDTSTC simulation waveform. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] The present invention provides a quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor, such as... Figure 1 As shown, it includes the following steps:

[0032] For ease of explanation, in this embodiment, PDTSTC represents a speed controller applying the quasi-resonant discrete sliding mode speed control method described in this invention; NR-PDTSTC represents a discrete sliding mode speed controller without a quasi-resonant control branch; and PI represents a proportional-integral controller. NR indicates non-resonant operation.

[0033] like Figure 1 As shown, the quasi-resonant discrete sliding mode speed regulation method for permanent magnet arc motors with end torque characteristic harmonic suppression proposed in this invention includes the following steps.

[0034] S1. Establish a discrete error model for the speed loop of the permanent magnet arc motor.

[0035] The mechanical angular velocity error is defined, and an error model considering lumped disturbances is constructed based on the speed loop model of the permanent magnet arc motor. Considering that the main disturbance frequency of the permanent magnet arc motor is significantly lower than the control frequency when it is running at low speed, the lumped disturbance can be approximated as a constant value with a bounded rate of change within a single sampling period, thus obtaining a discrete error model suitable for digital controller implementation.

[0036] , , ,

[0037] S2. Design the quasi-resonant control branch.

[0038] A quasi-resonant control branch is designed to address the characteristic harmonics corresponding to the periodic disturbance dominated by the end torque of a permanent magnet arc motor. The quasi-resonant controller exhibits high gain near the target frequency, enabling directional amplification and compensation of the periodic components within the target frequency and its neighborhood. Its continuous-domain and discretized expressions are as follows: , , ,

[0039] In this embodiment, three quasi-resonant control branches are set to compensate for the 55th, 110th, and 165th characteristic harmonics, respectively. More generally, the number of quasi-resonant control branches can also be set according to the number of dominant periodic disturbance frequencies of the controlled object.

[0040] S3, constructing a discrete sliding surface with periodic perturbations.

[0041] Based on the discrete error model and the output of the quasi-resonant branches, the mechanical angular velocity error, the error integral term, and the output of each quasi-resonant branch are introduced into the sliding surface to obtain a discrete sliding surface that takes into account periodic disturbances: , In the formula, I(k) is the error integral term, and c is the integration coefficient. The resonant frequency of each quasi-resonant branch is set according to the target mechanical angular velocity, and their relationship is as follows: , S4. Design a discrete superspiral velocity control law based on a quasi-resonant branch.

[0042] The velocity control law consists of an equivalent control term and a discrete superspiral switch control term. The total control input can be written as: , , , , In the formula, the equivalent control term is used to cancel out known modelable terms, and the discrete superspiral switch control term is used to drive the sliding surface convergence and enhance the system's robustness to disturbances and parameter perturbations. Through the above design, the selective suppression capability of periodic disturbances dominated by edge torque can be improved while maintaining the speed and robustness of discrete superspiral control.

[0043] S5. Achieve closed-loop control of permanent magnet arc motor.

[0044] The speed control law output is used as the q-axis current reference, and together with the d-axis current reference, it is fed into the inner current loop. Preferably, the d-axis current reference is 0. The inner current loop uses a PI regulator to obtain the dq-axis voltage reference, which is then transformed to obtain the voltage reference in the two-phase stationary coordinate system. This voltage reference is then generated by space vector pulse width modulation to drive the three-phase inverter drive signal, thereby driving the permanent magnet arc motor to operate in closed loop.

[0045] Experimental results:

[0046] Figure 4 Simulation comparison results of PI, NR-PDTSTC, and the PDTSTC of this invention under steady-state conditions at a given speed of 10 rpm are presented. Figure 4 (a) is the PI simulation waveform. Figure 4 (b) shows the simulated waveform of NR-PDTSTC. Figure 4 (c) is the PDTSTC simulation waveform. Here, THD represents total harmonic distortion, which is used to characterize the overall proportion of harmonic components in the speed signal; SRF represents speed ripple factor, which is used to characterize the degree of fluctuation of the maximum and minimum steady-state speed relative to a given speed.

[0047] Specifically, under the PI control method, the amplitudes of the 55th, 110th, and 165th harmonics are 0.8152 rpm, 0.2042 rpm, and 0.2822 rpm, respectively, with THD and SRF of 10.73% and 32.30%, respectively; under the NR-PDTSTC control method, the amplitudes of the 55th, 110th, and 165th harmonics are 0.4874 rpm, 0.1624 rpm, and 0.1717 rpm, respectively, with THD and SRF of 6.61% and 19.74%, respectively; under the PDTSTC control method of this invention, the amplitudes of the 55th, 110th, and 165th harmonics are reduced to 0.0819 rpm, 0.0635 rpm, and 0.0600 rpm, respectively, with THD and SRF reduced to 1.92% and 8.76%, respectively.

[0048] It can be seen that the PI control method is significantly affected by the periodic disturbance dominated by the edge torque, resulting in large fluctuations in steady-state speed. Although the NR-PDTSTC can reduce some speed ripple by relying on discrete super-helical control, its selective suppression capability for disturbances at specific frequencies is still limited. This invention introduces a quasi-resonant branch in the discrete sliding surface, enabling the controller to perform directional compensation for the 55th, 110th, and 165th characteristic harmonics. Therefore, it achieves optimal results in terms of the amplitude of the three target harmonics, THD, and SRF.

[0049] It is evident that the method of the present invention can effectively suppress the characteristic harmonic speed fluctuations caused by the periodic disturbance dominated by the end torque during the low-speed operation of the permanent magnet arc motor, and significantly reduce the speed ripple factor and total harmonic distortion. This demonstrates that the method of the present invention has a significant effect on improving the stability and overall control performance of the permanent magnet arc motor in low-speed steady-state operation.

[0050] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor, characterized in that, Includes the following steps: Step S1: Define the mechanical angular velocity error based on the speed loop model of the permanent magnet arc motor, and establish a discrete error model that takes into account the lumped disturbance; Step S2: For the periodic disturbance dominated by the end torque during the low-speed operation of the permanent magnet arc motor, construct one or more quasi-resonant control branches and obtain the discrete output of each quasi-resonant control branch. Step S3: Introduce the mechanical angular velocity error, error integral term, and output of each quasi-resonant control branch into the sliding surface to construct a quasi-resonant discrete sliding surface that takes into account periodic disturbances. Step S4: Based on the quasi-resonant discrete sliding mode surface, design a velocity control law consisting of an equivalent control term and a discrete super-helical switch control term to obtain the q-axis current command; Step S5: The q-axis current is fed into the inner current loop and the inverter drive system to suppress the harmonic speed fluctuation of the end torque characteristic when the permanent magnet arc motor is running at low speed.

2. The method for quasi-resonant discrete sliding mode speed regulation of a permanent magnet arc motor according to claim 1, characterized in that, The specific steps of S1 are as follows: The difference between the actual mechanical angular velocity and the target mechanical angular velocity is defined as the mechanical angular velocity error, and a velocity loop error model is established based on the d-axis and q-axis motion equations of the permanent magnet arc motor: ， ， ， In the formula, and Let e(k) represent the actual mechanical angular velocity and the target mechanical angular velocity, respectively. Let e(k) represent the mechanical angular velocity error in the k-th control cycle, where k is the sequence of the controller cycle, d represents the lumped disturbance, T represents the control cycle, a represents the control gain, and u represents the control input. The lumped disturbance includes edge torque, cogging torque, parameter mismatch, and other unmodeled disturbances. Within a single control cycle, the lumped disturbance is approximated as a constant, and its rate of change is bounded.

3. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 1, characterized in that, The quasi-resonant control branch in step S2 has a continuous domain transfer function and a discrete domain transfer function, respectively: ， ， ， In the formula, k r For the resonant gain, ω c For controller bandwidth, ω Q Let be the resonant frequency, s be a continuous domain variable, z be a discrete domain variable, T be the control period, and a1, a2 and b0, b1, b2 be the discretized quasi-resonant control coefficients, respectively. The continuous domain quasi-resonant controller is discretized using a bilinear transformation to obtain a discrete quasi-resonant control branch suitable for digital controller implementation.

4. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 1, characterized in that, In step S2, multiple quasi-resonant control branches are set up, and the output of each quasi-resonant control branch is r. i (k); When selecting 3 quasi-resonant control branches, the corresponding P is dominated by the end torque of the permanent magnet arc motor. n 2P n and 3P n Frequency doubling periodic disturbance; for an 18-slot 55-pole permanent magnet arc motor, the dominant disturbances are preferably the 55th, 110th and 165th characteristic harmonics.

5. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 1, characterized in that, In step S3, the quasi-resonant discrete sliding mode surface is composed of the mechanical angular velocity error, the error integral term, and the outputs of each quasi-resonant control branch, specifically represented as follows: ， In the formula, s(k) is the sliding surface, I(k) is the integral term of the mechanical angular velocity error, c is the integral coefficient, and r i (k) represents the output of the i-th quasi-resonant control branch, e(k) represents the mechanical angular velocity error of the k-th control cycle, and k is the sequence of the controller cycle.

6. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 5, characterized in that, The resonant frequency of each quasi-resonant control branch is set according to the target mechanical angular velocity and the corresponding harmonic order, so that the quasi-resonant control branch maintains selective suppression capability against periodic disturbances of the characteristic frequency of the end torque. ， In the formula, P represents the resonant frequency of the i-th quasi-resonant branch. n This indicates the number of pole pairs of the motor.

7. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 6, characterized in that, The speed control law in step S4 is composed of the equivalent control term u. eq and discrete superspiral switch control term u PDTSTC Two parts composition: ， in, ， ， ， In the formula, Here, k is an intermediate variable, k is the sequence number of the controller cycle, and k1 and k2 are the discrete sliding mode control gains, respectively. To control the gain, b mn These are the discretized quasi-resonant control coefficients, i=1,2, j=1,2,3, m=0,2, n=1,2,3. For discrete sliding mode controller parameters, As intermediate control variables, the equivalent control term is used to offset the known modelable parts of the system, while the discrete superhelical switch control term is used to drive the sliding surface to converge and enhance the system robustness.

8. The quasi-resonant discrete sliding mode speed regulation method for a permanent magnet arc motor according to claim 7, characterized in that, The controller parameters are tuned in a step-by-step manner: first, the resonant gain of each quasi-resonant control branch is set to zero, so that the controller degenerates into a discrete sliding mode speed regulation method without quasi-resonant control branches, and the integral coefficient, discrete superspiral gain and exponential parameters are tuned; then, each quasi-resonant control branch is gradually introduced, and the bandwidth parameter and resonant gain are tuned to take into account closed-loop stability, frequency selectivity and steady-state disturbance suppression capability.

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