Repeated fractional-order active disturbance rejection control method and system for permanent magnet synchronous motor

Abstract

The present invention discloses a repetitive fractional-order auto-disturbance rejection control method and system for a permanent magnet synchronous motor, the method comprising: establishing a linear state equation for the speed loop of the permanent magnet synchronous motor; performing disturbance observation and speed tracking on the speed loop based on fractional-order auto-disturbance rejection control, and then compensating the speed loop input and substituting it into the linear state equation of the speed loop; introducing a new repetitive controller before the fractional-order auto-disturbance rejection control system to periodically reduce the system error, and the corrected speed loop is input into the fractional-order auto-disturbance rejection control system. The present application improves the extended state observer, adopts a smooth internal function, and combines fractional-order control to simplify the controller structure, and introduces repetitive control to periodically reduce the system error. While maintaining the dynamic performance of the original auto-disturbance rejection controller, the present invention simplifies the controller structure, reduces the error and jitter of the system response, and greatly improves the robustness and anti-disturbance capability of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and in particular to a repetitive fractional-order auto-disturbance rejection control method and system for a permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in electric vehicle drive systems in recent years due to their simple structure, fast response, and excellent stability. To address the PMSM's susceptibility to interference from nonlinear factors and parameter variations, numerous researchers at home and abroad have proposed control strategies, including PID control, adaptive control, and active disturbance rejection control.

[0003] Active disturbance rejection control (ADRC) has garnered significant attention in the motor control field in recent years due to its strong anti-interference capabilities. When applied to PMSMs, ADRC algorithms achieve transitions through a tracking differentiator module, observe the total disturbance using an extended state observer (ESO), and then pass the observed disturbance term to the error feedback loop, enabling real-time disturbance compensation.

[0004] The internal function of the traditional active disturbance rejection controller ADRC is:

[0005]

[0006] Where ε is the deviation; is a nonlinear factor; δ is the filter factor, sign() is the sign function, and |ε| represents the absolute value of ε. The fal function has the characteristics of small gain for large errors and large gain for small errors. Its nonlinear range is (-∞, -δ) and (δ, +∞), and its linear range is (-δ, δ). As shown in the above formula, it has two inflection points at -δ and δ.

[0007] In traditional ADRC controllers, the extended state observer and the state feedback error control rate both use the above-mentioned fal function as their basis. However, since the transition of this function at the inflection point is not smooth enough, there will be a chattering problem at the inflection point, causing the output of the control quantity of the ADRC to jitter, resulting in reduced control accuracy, large errors, and unsatisfactory anti-interference ability of the system.

[0008] On the other hand, while ADRC can compensate for the total disturbance of a PMSM, its structure is complex and involves numerous parameters. The appropriateness of these parameters directly impacts the ADRC's ability to estimate and compensate for the total disturbance. Even for experienced researchers, this process can be time-consuming, limiting the practicality of ADRC control systems and leading to poor system stability. Summary of the Invention

[0009] The embodiments of the present application provide a repetitive fractional-order auto-disturbance rejection control method for a permanent magnet synchronous motor, addressing the existing issues of chattering, large errors, and difficulty adjusting numerous parameters in the auto-disturbance rejection control of permanent magnet synchronous motors. By combining fractional-order control with auto-disturbance rejection control and introducing repetitive control to periodically reduce the system error of the fractional-order auto-disturbance rejection controller, the controller structure is simplified, the number of parameters to be adjusted is reduced, and smooth transitions are achieved at the inflection points of the function. Furthermore, while ensuring the dynamic performance of the system, the jitter and error of the system response can be reduced, significantly improving the robustness and anti-disturbance performance of the system.

[0010] In order to solve the above technical problems, in a first aspect, an embodiment of the present application provides a repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor, the method comprising:

[0011] S1: Establish the linear state equation of the permanent magnet synchronous motor PMSM speed loop;

[0012] S2: Based on the fractional-order active disturbance rejection control system, the PMSM speed loop is subjected to disturbance observation and speed tracking, and the input of the PMSM speed loop is compensated. The compensated input of the PMSM speed loop is substituted into the linear state equation of the PMSM speed loop.

[0013] S3: A new repetitive controller is introduced before the fractional-order active disturbance rejection control system to periodically reduce the system error. The new repetitive controller includes a repetitive control unit and a delay compensation unit arranged before the repetitive control unit. The speed loop given speed after being corrected by the new repetitive controller is input into the fractional-order active disturbance rejection control system.

[0014] Preferably, the step S1 specifically includes:

[0015] Taking PMSM as the controlled object, in the dq synchronous rotating coordinate system, the ideal mathematical model of PMSM is as follows:

[0016]

[0017] Among them, ω e ——rotor electrical angular velocity;

[0018] R s - armature resistance;

[0019] ψ d ,ψ q ——d-axis and q-axis magnetic flux;

[0020] L d ,L q ——d and q axis inductance;

[0021] u d ,u q ——d-axis and q-axis voltage;

[0022] i d ,i q ——d and q axis currents;

[0023] According to the equation of PMSM in the dq synchronous rotating coordinate system, the PMSM speed loop state equation can be obtained as follows:

[0024]

[0025] Where J is the rotor inertia, p is the number of motor pole pairs, T m is the load torque, B is the motor resistance coefficient; set the PMSM speed loop input u=i q , speed loop output Y = ω e , state variable X1=ω e , then the state equation of the speed loop can be written as:

[0026] X1′=f(X1)+W+bu (3)

[0027] Y=X1 (4)

[0028] In formula (3), W is the total external disturbance of the system, b is the q-axis current i in the PMSM dynamic equation q The coefficient of , combined with equation (2) and equation (4), can be obtained as follows:

[0029]

[0030]

[0031] Let f(X1) be expressed as the internal disturbance of the system, including the rotor moment of inertia J, load torque T m And the q-axis current i q The expanded state variable expression of the total disturbance can be set as:

[0032] X2=f(X1)+W (7)

[0033] Let X2′ = ξ, then the standard linear state equation of the speed loop can be obtained based on equations (4) and (5):

[0034] X1′=X2+bu (8)

[0035] X2′=ξ (9)

[0036] Y=X1 (10).

[0037] Preferably, in step S2, the fractional-order active disturbance rejection control system includes a tracking differentiator TD, a novel extended state observer NESO, a fractional-order controller and a disturbance compensator;

[0038] The tracking differentiator TD tracks the actual speed of the PMSM and inputs the tracking result into the new extended state observer NESO;

[0039] The estimated value of the PMSM actual speed, the estimated value of the PMSM actual speed differential and the observed value of the total disturbance are obtained through the new extended state observer (NESO).

[0040] The estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into the fractional-order controller to obtain the speed input of the PMSM speed loop before compensation;

[0041] Inputting the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation into the disturbance compensator to obtain the speed input of the PMSM speed loop after compensation;

[0042] Substitute the compensated PMSM speed loop speed input into the standard linear state equation of the PMSM speed loop.

[0043] Preferably, the step S2 is specifically as follows:

[0044] The fractional-order active disturbance rejection control system includes a tracking differentiator TD, a novel extended state observer NESO, a fractional-order controller and a disturbance compensator;

[0045] The control rate of the tracking differentiator TD is as follows:

[0046]

[0047]

[0048] in, is the given speed; ω e is the actual speed tracking value of PMSM; e0 is the error between the actual speed tracking value of PMSM and the given speed; α0 is the first nonlinear factor; δ is the filter factor; T is the operation period; r represents the tracking speed of the tracking differentiator;

[0049] The speed ω tracked by the tracking differentiator TD e Input into the new extended state observer NESO, the control rate of the new extended state observer NESO is as follows:

[0050]

[0051]

[0052] Where z1 is ωe The estimated value of z2 is ω e The estimated value of the differential; z3 is the observed value of the total disturbance; α1 is the second nonlinear factor; β1, β2, β3, β4 are output correction factors;

[0053] The novel extended state observer (NESO) is used to obtain z1, z2, and z3, which are then input into the fractional-order controller. The control rate of the fractional-order controller is as follows:

[0054]

[0055] Among them, K p is the proportional coefficient; K i is the integral coefficient; K d is the differential coefficient; λ is the integral order; μ is the differential order;

[0056] The PMSM speed loop speed input u2 before compensation is obtained through the fractional-order controller, and u2 and z3 are input into the disturbance compensator. The control rate of the disturbance compensator is as follows:

[0057]

[0058] Where u is the speed input of the PMSM speed loop after compensation;

[0059] Substitute the compensated PMSM speed loop speed input u into the permanent magnet synchronous motor speed loop linear state equation (8).

[0060] Preferably, in step S3, the novel repetitive controller is used to convert the input speed signal w(z) to the output The closed-loop transfer function is:

[0061]

[0062]

[0063] C(z)=k r *z k S(z) (18)

[0064] Among them, G RC (z) is the closed-loop transfer function of the new repetitive controller; w(z) is the input speed signal; Q(z) and S(z) are two low-pass filters; C(z) is the compensation link; k p2 is the proportional control coefficient of the repetitive controller; k r is the gain coefficient of the repetitive control unit; k is a constant, k1 is the same as k, k2 is the leading phase angle θ based on k1; z -N is the periodic delay link; N is the number of sampling times of a fundamental wave period; is the phase module; z -t / 2 is the hysteresis module, and t is the step response time of the system.

[0065] In a second aspect, an embodiment of the present application provides a repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor, the system comprising:

[0066] A repetitive fractional-order active disturbance rejection controller is used to control and adjust the input of the speed loop of a permanent magnet linear synchronous motor (PMSM);

[0067] CLARKE conversion module, used to convert the three-phase winding output current i of PMSM a 、i b 、i c Through the CLARKE transformation of the stationary coordinate system, the output current i of the CLARKE transformation module is obtained α 、i β ;

[0068] PRKE conversion module, used to convert the output current i α 、i β Transform from the stationary coordinate system to the rotating coordinate system to obtain the PMSM quadrature axis q-axis output current i q and the direct axis d-axis output current i d ;

[0069] PI controller, used for the quadrature axis q axis output current i based on the output of the PRKE conversion module q and the direct axis d-axis output current i d The speed loop speed input of the repetitive fractional order ADRC is used to perform PI control and output the voltage value U of the torque current regulator of the PMSM. d * and the voltage value U of the excitation current regulator q * ;

[0070] PRKE inverter module, used to convert the voltage value U d * and the voltage value U of the excitation current regulator q * Inverter processing, converted into voltage U α * 、U β * ;

[0071] SVPWM space vector pulse width modulation module is used to convert the output voltage U α * 、U β* Perform space vector transformation and output PWM waveform for controlling PMSM inverter.

[0072] Preferably, the repetitive fractional-order active disturbance rejection controller includes:

[0073] A fractional-order active disturbance rejection controller is used to perform disturbance observation and speed tracking on the PMSM speed loop, thereby compensating the input of the PMSM speed loop and inputting the compensated PMSM speed loop input into the PI controller;

[0074] a repetitive control unit connected to the fractional-order active disturbance rejection controller for periodically reducing system error interference;

[0075] A delay compensation unit is connected to the repetitive control unit and is used to periodically compensate for the response time difference between the repetitive control unit and the PI controller.

[0076] Preferably, the fractional-order active disturbance rejection controller includes a tracking differentiator, an extended state observer, a fractional-order controller and a disturbance compensator;

[0077] A tracking differentiator tracks the actual speed of the PMSM and inputs the tracking result into a novel extended state observer; an estimated value of the actual speed of the PMSM, an estimated value of the differential of the actual speed of the PMSM, and an observed value of the total disturbance are obtained through the novel extended state observer; the estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into a fractional-order controller to obtain a speed input of the PMSM speed loop before compensation; the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation are input into a disturbance compensator to obtain a speed input of the PMSM speed loop after compensation; and the speed input of the PMSM speed loop after compensation is input into the PI controller.

[0078] In a third aspect, an embodiment of the present application provides a repetitive fractional-order active disturbance rejection control device for a permanent magnet synchronous motor. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the following steps are implemented:

[0079] Establish the linear state equation of the permanent magnet synchronous motor PMSM speed loop;

[0080] Based on the fractional-order active disturbance rejection control system, the PMSM speed loop is subjected to disturbance observation and speed tracking, and then the input of the PMSM speed loop is compensated. The compensated input of the PMSM speed loop is substituted into the linear state equation of the PMSM speed loop.

[0081] A new repetitive controller is introduced before the fractional-order active disturbance rejection control system to periodically reduce the system error. The new repetitive controller includes a repetitive control unit and a delay compensation unit arranged before the repetitive control unit. The speed loop given speed after being corrected by the new repetitive controller is input into the fractional-order active disturbance rejection control system.

[0082] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps:

[0083] Establish the linear state equation of the permanent magnet synchronous motor PMSM speed loop;

[0084] Based on the fractional-order active disturbance rejection control system, the PMSM speed loop is subjected to disturbance observation and speed tracking, and then the input of the PMSM speed loop is compensated. The compensated input of the PMSM speed loop is substituted into the linear state equation of the PMSM speed loop.

[0085] A new repetitive controller is introduced before the fractional-order active disturbance rejection control system to periodically reduce the system error. The new repetitive controller includes a repetitive control unit and a delay compensation unit arranged before the repetitive control unit. The speed loop given speed after being corrected by the new repetitive controller is input into the fractional-order active disturbance rejection control system.

[0086] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0087] The present invention provides an innovative control method for a permanent magnet synchronous motor (PMSM). Based on the second-order ADRC model of the PMSM's velocity loop, the extended state observer (ESO) structure is improved, a smoother internal function is adopted, and fractional-order control is combined to simplify the controller structure. Finally, repetitive control is introduced to periodically reduce the system error of the fractional-order ADRC controller. While maintaining the dynamic performance of the original ADRC controller, the present invention simplifies the controller structure, reduces system response errors and jitter, and significantly improves the system's robustness and anti-disturbance capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 This is a flow chart of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor provided in the first embodiment of the present application;

[0089] Figure 2 This is a structural diagram of the novel fractional-order active disturbance rejection controller provided in Example 1 of the present application;

[0090] Figure 3 This is a structural diagram of the new extended state observer provided in Example 1 of the present application;

[0091] Figure 4 This is a structural diagram of the fractional-order controller provided in Example 1 of the present application;

[0092] Figure 5 This is a system structure diagram after a new repetitive controller is introduced before the new fractional-order controller provided in Example 1 of the present application;

[0093] Figure 6 A comparison diagram of the traditional FAL function and the new LTFL function provided in Example 1 of the present application (the horizontal axis x = ε, ε represents the error, i.e., the first of the three variables in the brackets of the LTFL function);

[0094] Figure 7 A comparison diagram of the disturbance observation waveforms of the traditional ESO and the new NESO provided in Example 1 of the present application (the vertical axis Torque represents the load torque);

[0095] Figure 8 This is a schematic diagram of the novel repetitive controller provided in Example 1 of the present application;

[0096] Figure 9 This is a schematic diagram of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor provided in the first embodiment of the present application;

[0097] Figure 10 This is a startup speed response diagram under three control methods in Example 1 of this application;

[0098] Figure 11 This is a speed change response diagram after load is added under the three control methods in Example 1 of this application;

[0099] Figure 12 This is a structural diagram of the repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor provided in the second embodiment of the present application;

[0100] Figure 13 This is a structural diagram of the repetitive fractional-order active disturbance rejection control device for a permanent magnet synchronous motor provided in Example 3 of the present application. DETAILED DESCRIPTION

[0101] The embodiments of the present application provide a repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor, thereby solving the problems of chattering, large errors, and difficulty in adjusting numerous parameters in the active disturbance rejection control of a permanent magnet synchronous motor in the prior art.

[0102] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows:

[0103] Based on a second-order active disturbance rejection model for the permanent magnet synchronous motor speed loop, the extended state observer (ESO) structure is improved, employing a smoother internal function to achieve smooth transitions at the function's inflection points. Fractional-order control is also incorporated to simplify the controller structure, reducing the number of parameters to be adjusted. Finally, repetitive control is introduced to periodically reduce the system error within the fractional-order ADRC controller. This approach achieves the goal of simplifying the controller structure, reducing the number of parameters to be adjusted, and achieving smooth transitions at the function's inflection points. Furthermore, while maintaining the system's dynamic performance, it reduces jitter and errors in the system response, significantly improving the system's robustness and disturbance rejection.

[0104] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0105] Example 1

[0106] Figure 1 Flowchart of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor provided in this embodiment. The repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor includes the following steps:

[0107] Step S1: Establishing a linear state equation of the permanent magnet synchronous motor (PMSM) speed loop.

[0108] This embodiment uses a surface-mounted permanent magnet synchronous motor as the controlled object. In the dq synchronous rotating coordinate system, the ideal mathematical model of the PMSM is as follows:

[0109]

[0110] Among them, ω e ——rotor electrical angular velocity;

[0111] R s - armature resistance;

[0112] ψ d ,ψ q ——d-axis and q-axis magnetic flux;

[0113] L d ,L q ——d and q axis inductance;

[0114] u d ,u q ——d-axis and q-axis voltage;

[0115] i d ,i q ——d and q axis currents.

[0116] According to the equation of PMSM in the dq synchronous rotating coordinate system, the PMSM speed loop state equation can be obtained as follows:

[0117]

[0118] Where J is the rotor inertia, p is the number of motor pole pairs, T m is the load torque, B is the motor resistance coefficient. Set the PMSM speed loop input u=i q , speed loop output Y = ω e , state variable X1=ω e , then the state equation of the speed loop can be written as:

[0119] X1′=f(X1)+W+bu (3)

[0120] Y=X1 (4)

[0121] In formula (3), W is the total external disturbance of the system, b is the q-axis current i in the PMSM dynamic equation q The coefficient of , combined with equation (2) and equation (4), can be obtained as follows:

[0122]

[0123]

[0124] Let f(X1) be expressed as the internal disturbance of the system, including the rotor moment of inertia J, load torque T m And the q-axis current i q The expanded state variable expression of the total disturbance can be set as:

[0125] X2=f(X1)+W (7)

[0126] Let X2′ = ξ, then the standard linear state equation of the speed loop can be obtained based on equations (4) and (5):

[0127] X1′=X2+bu (8)

[0128] X2′=ξ (9)

[0129] Y=X1 (10)

[0130] Step S2: Based on the novel fractional-order active disturbance rejection controller (FO-ADRC), the PMSM speed loop is subjected to disturbance observation and speed tracking, and the input of the PMSM speed loop is compensated. The compensated input of the PMSM speed loop is substituted into the linear state equation of the PMSM speed loop.

[0131] Combine Figure 2The FO-ADRC includes a tracking differentiator (TD), a novel extended state observer (NESO), a fractional-order controller, and a disturbance compensator; the tracking differentiator (TD) tracks the actual speed of the PMSM and inputs the tracking result into the novel extended state observer (NESO); an estimated value of the actual speed of the PMSM, an estimated value of the differential of the actual speed of the PMSM, and an observed value of the total disturbance are obtained through the novel extended state observer (NESO); the estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into the fractional-order controller to obtain a speed input of the PMSM speed loop before compensation; the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation are input into the disturbance compensator to obtain a speed input of the PMSM speed loop after compensation; and the speed input of the PMSM speed loop after compensation is substituted into the standard linear state equation of the PMSM speed loop.

[0132] Specifically, the control rate of the tracking differentiator TD is as follows:

[0133]

[0134]

[0135] in, is the given speed; ω e is the actual speed tracking value of PMSM; e0 is the error between the actual speed tracking value of PMSM and the given speed; α0 is the first nonlinear factor; δ is the filter factor; T is the operation period; r represents the tracking speed of the tracking differentiator. The tracking differentiator is part of the active disturbance rejection controller and is used to adjust the given speed. A transition process is provided to reduce overshoot and oscillation without reducing response speed, thus obtaining better speed output.

[0136] Next, the speed ω tracked by the differentiator TD is tracked e Input into the new extended state observer NESO, Figure 3 The structure of the new extended state observer (NESO) is shown in FIG. The control rate of the new extended state observer (NESO) is as follows:

[0137]

[0138]

[0139] Where z1 is ω e The estimated value of z2 is ω e The estimated value of the differential; z3 is the observed value of the total disturbance; α1 is the second nonlinear factor; β1, β2, β3, β4 are output correction factors.

[0140] z1, z2, and z3 are obtained through the new extended state observer NESO, and z1 and z2 are input into the fractional-order controller. Figure 4 The structure of the fractional-order controller is shown. The control rate of the fractional-order controller is as follows:

[0141]

[0142] Among them, K p is the proportional coefficient; K i is the integral coefficient; K d is the differential coefficient; λ is the integration order; μ is the differential order.

[0143] The PMSM speed loop speed input u2 before compensation is obtained through the fractional-order controller, and u2 and z3 are input into the disturbance compensator. The control rate of the disturbance compensator is as follows:

[0144]

[0145] Wherein, u is the speed input of the PMSM speed loop after compensation.

[0146] Substitute the compensated PMSM speed loop speed input u into the permanent magnet synchronous motor speed loop linear state equation (8).

[0147] Step S3: To address the problem that FO-ADRC has limited effect on disturbance suppression of PMSM control system, a new repetitive controller is introduced before FO-ADRC to periodically reduce the system error, such as Figure 5 As shown in the figure, the new repetitive controller includes a repetitive control unit and a delay compensation unit. The input speed signal w(z) is corrected by the delay compensation unit and the repetitive control unit, and the corrected given speed is converted to As the input of the FO-ADRC system, the new repetitive controller converts the input speed signal w(z) to the output The closed-loop transfer function is:

[0148]

[0149]

[0150] C(z)=k r *z k S(z) (18)

[0151] Among them, G RC (z) is the closed-loop transfer function of the new repetitive controller; w(z) is the input speed signal; Q(z) and S(z) are two low-pass filters; C(z) is the compensation link; k p2 is the proportional control coefficient of the repetitive controller; k ris the gain coefficient of the repetitive control unit; k is a constant, k1 is the same as k, k2 is the leading phase angle θ based on k1; z -N is the periodic delay link, N is the number of sampling times of a fundamental wave period; is the phase module; z -t / 2 is the hysteresis module, and t is the step response time of the system.

[0152] The repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor provided in this embodiment adopts a novel fractional-order active disturbance rejection controller and a novel repetitive controller. The novel fractional-order active disturbance rejection controller mainly adopts a novel internal function design, a novel extended state observer design, and a fractional-order controller design with a disturbance compensator. The specific analysis is as follows:

[0153] (1) New internal function design

[0154] In the ADRC controller, both the extended state observer and the state feedback error control rate use the fal function as their basis. However, due to the smooth transition of this function at the inflection point, the output of the control variable of the ADRC will produce jitter, which reduces the control accuracy of the system and limits its application in some high-precision control applications. This embodiment replaces the traditional ADRC internal function fal function with the smoother ltfal function. The expression of the ltfal function is shown in Equation (14).

[0155] In order to compare the difference between the fal function and the ltfal function, the filter factor is set to 0.02 and the nonlinear factor is set to 0.25. The two functions are compared. The comparison chart is as follows Figure 6 As shown by Figure 6 It can be seen that the new function ltfal has better smoothness and can effectively weaken chattering.

[0156] (2) Design of a new extended state observer

[0157] To further improve the error tracking performance of the extended state observer (ESO) while reducing chattering, the total disturbance observation value of the extended state observer (NESO) is replaced by the time-proportional integral of the error instead of the time integral of the error. This results in a new extended state observer (NESO), whose control rate is shown in Equation 13. The new extended state observer (NESO) can increase the utilization of the error signal and improve the dynamic disturbance observation performance.

[0158] In order to verify the performance of the new extended state observer (NESO) in observing disturbances, simulation models of the second-order traditional extended state observer (ESO) and the second-order new extended state observer (NESO) were built. The bandwidth of the observer was designed to be 300, the parameters of the traditional extended state observer (ESO) were selected as [β1 β2 β3] = [300 90000 300], and the parameters of the new extended state observer (NESO) were selected as [β1 β2 β3 β4] = [300 90000 300 300]. The speed was set to 100 r / min, a load of 3 N·M was suddenly added at 0.2s, and the load was removed at 0.4s. The simulation results are shown in Figure 2. Figure 7 As shown in the simulation graph, it can be seen that the new extended state observer NESO observes disturbances faster than the traditional extended state observer ESO and has better stability, which is of great benefit to the system's disturbance compensation.

[0159] The error of the new extended state observer is analyzed theoretically below.

[0160] Assume a first-order nonlinear system:

[0161]

[0162] Among them, x1 is the state variable; f(x1) is the total disturbance, and the state variable x2 can be set to f(x1). u is the input signal, b is the q-axis current i in the PMSM dynamic equation q The coefficient of .

[0163] The expanded system of formula (19) is:

[0164]

[0165] The state observer of the system can be constructed from formula (20):

[0166]

[0167] Where z1 is the estimated value of the speed signal y; z2 is the differential of the speed signal y; z3 is the observed value of the total disturbance; b is the q-axis current i in the PMSM dynamic equation q The coefficient of e i (i=1,2) is the error between the estimated value of the speed signal y and the speed signal y; u is the input signal; β1, β2, β3 are the output correction factors; α i (i=1,2) is the nonlinear factor, δ is the filter factor. Since the function |s(t)| 2 <s0 is bounded (s0 is a constant), and let Where e1 = z1-y, e2 = z2-x2, and sign is the sign function. From this we can see that the error equation is:

[0168]

[0169] According to the known theorem, the (e1, e2) plane can be divided into 5 regions Based on this, we construct the discontinuous piecewise smooth Lyapunov positive definite function V i According to the multi-Lyapunov function theorem, it can be proved that the system (21) is stable, and the system error is ultimately limited by the region G0, where β i >s0(i=1,2), the minimum convergence error of the ESO state can be obtained as:

[0170]

[0171]

[0172] Therefore, when the system is stable, the actual speed observation error is |e1| < 1. This proves that the new extended state observer converges stably.

[0173] (3) Design of fractional-order controller with disturbance compensator

[0174] In order to further reduce the chattering problem caused by the original internal function, this embodiment uses a fractional order controller PI λ D μ Replace the state feedback error control law in the traditional active disturbance rejection controller. Compared with the integer order controller, PI λ D μ The controller has two adjustable parameters: integral order λ and differential order μ. λ D μ The transfer function of the controller is as follows:

[0175] G(s)=K p +K i s -λ +K d s μ (25)

[0176] Among them, K p is the proportionality coefficient, K i is the integral coefficient, K d is the differential coefficient, s is the Laplace operator, λ is the integration order, and μ is the differential order.

[0177] In addition, a disturbance compensator is designed to compensate for the disturbance of the system. The control rate of the disturbance compensator is shown in formula (15).

[0178] (4) New repetitive controller

[0179] In traditional repetitive control, the response time between repetitive control and PI controller is not synchronized, which makes the repetitive control have poor error suppression effect and the operation of the control system is disturbed. In order to solve the cycle delay problem, this embodiment improves on the basis of traditional repetitive control. Its principle is as follows: Figure 8 shown.

[0180] A delay compensation unit is added after the input signal, which includes a phase module and hysteresis module z -t / 2 , where k1 is the same as the constant k in the compensation link C(z), k2 is the phase angle θ based on k1, and t is the step response time of the system. The forward channel is changed from being derived from the error signal to being derived from the input signal, and the PI controller in the forward channel is changed to a proportional controller k p , where k p Equal to the gain coefficient k of the repeated control in the compensation link C(z) r The reciprocal of .

[0181] The reliability of the repetitive fractional-order active disturbance rejection control method for the permanent magnet synchronous motor of this embodiment is analyzed below.

[0182] The principle diagram of the repetitive fractional-order active disturbance rejection control method for permanent magnet synchronous motor is as follows: Figure 9 As shown, the error function of the system is:

[0183] e(z)=R(z)H(z) (26)

[0184]

[0185]

[0186] Where, e(z) is the error function of the repetitive fractional-order active disturbance rejection controller, R(z) is the error gain after adding the new repetitive control, H(z) is the error function without adding the new repetitive control, G(z) is the error function of the fractional-order active disturbance rejection controller, d(z) is the error disturbance, u(z) is the system output, and k p is the proportional control coefficient, z -N is the periodic delay link, and N is the number of sampling times of a fundamental wave period. From the above formula, we can see that the parameter Q(z) in the controller should be reasonably designed so that 1-Q(z)z -N →0, thus making R(z)→0, which can make the system error close to zero.

[0187] In order to verify the effectiveness of the repetitive fractional-order active disturbance rejection control method for permanent magnet synchronous motors, a first-order speed control system model of PMSM was built in the Matlab / Simulink environment. Simulation and comparative experiments were carried out on three control methods: traditional active disturbance rejection control (ADRC), fractional-order active disturbance rejection control (FO-ADRC), and repetitive fractional-order active disturbance rejection control (RCFO-ADRC).

[0188] In the simulation experiment, the initial speed is set to 500r / min, and at 0.5s, a load of 0.2Nm is suddenly added to the motor. Figure 10 is the starting speed response under three control methods, Figure 11 The speed change response after adding load under the three control methods is shown in the simulation experiment. It can be seen that RCFO-ADRC can effectively speed up the system response speed, enhance the system robustness, and reduce the system steady-state error.

[0189] Example 2

[0190] Based on the same inventive concept as the repetitive fractional-order active disturbance rejection control method of the permanent magnet synchronous motor in the aforementioned embodiment 1, this embodiment provides a repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor, such as Figure 12 As shown, the system includes:

[0191] A repetitive fractional-order active disturbance rejection controller is used to control and adjust the input of the speed loop of a permanent magnet linear synchronous motor (PMSM);

[0192] CLARKE conversion module, used to convert the three-phase winding output current i of the permanent magnet linear synchronous motor PMSM a 、i b 、i c Through the CLARKE transformation of the stationary coordinate system, the output current i of the CLARKE transformation module is obtained α 、i β ;

[0193] PRKE conversion module, used to convert the output current i α 、i β Transform from the stationary coordinate system to the rotating coordinate system to obtain the PMSM quadrature axis q-axis output current i q and the direct axis d-axis output current i d ;

[0194] PI controller, used for the quadrature axis q axis output current i based on the output of the PRKE conversion module q and the direct axis d-axis output current i d The speed loop speed input of the repetitive fractional order ADRC is used to perform PI control and output the voltage value U of the torque current regulator of the PMSM.d * and the voltage value U of the excitation current regulator q * ;

[0195] PRKE inverter module, used to convert the voltage value U d * and the voltage value U of the excitation current regulator q * Inverter processing, converted into voltage U α * 、U β * ;

[0196] SVPWM space vector pulse width modulation module is used to convert the output voltage U α * 、U β * Perform space vector transformation and output PWM waveform for adjusting the permanent magnet linear synchronous motor inverter.

[0197] The SVPWM space vector pulse width modulation module is connected to the three-phase inverter and outputs a PWM waveform to the three-phase inverter; the three-phase inverter is connected to the permanent magnet linear synchronous motor and inputs a three-phase voltage to the permanent magnet linear synchronous motor to control its operation; the position and speed detection module is connected to the permanent magnet linear synchronous motor to detect the position and actual speed of the permanent magnet linear synchronous motor rotor, and input the actual speed into the repetitive fractional-order active disturbance rejection controller.

[0198] The repetitive fractional-order active disturbance rejection controller comprises:

[0199] A fractional-order active disturbance rejection controller (FO-ADRC) is used to perform disturbance observation and speed tracking on the PMSM speed loop, thereby compensating the input of the PMSM speed loop and inputting the compensated PMSM speed loop input into the PI controller;

[0200] A repetitive control unit is connected to the fractional-order active disturbance rejection controller FO-ADRC to periodically reduce system error disturbances;

[0201] The delay compensation unit is connected to the repetitive control unit and is used for periodically compensating the response time between the repetitive control unit and the PI controller.

[0202] Furthermore, the FO-ADRC includes a tracking differentiator (TD), a novel extended state observer (NESO), a fractional-order controller and a disturbance compensator; the tracking differentiator (TD) tracks the actual speed of the PMSM and inputs the tracking result into the novel extended state observer (NESO); an estimated value of the actual speed of the PMSM, an estimated value of the differential of the actual speed of the PMSM and an observed value of the total disturbance are obtained through the novel extended state observer (NESO); the estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into the fractional-order controller to obtain a speed input of the PMSM speed loop before compensation, the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation are input into the disturbance compensator to obtain a speed input of the PMSM speed loop after compensation; and the speed input of the PMSM speed loop after compensation is input into the PI controller.

[0203] The control rates of the tracking differentiator (TD), novel extended state observer (NESO), fractional-order controller, and disturbance compensator are the same as those described in Example 1. The control rates of the repetitive control unit and delay compensation unit are the same as those described in Example 1. The overall control principle and method of the repetitive fractional-order active disturbance rejection controller are the same as those described in Example 1. For the sake of brevity, they are not described in detail here.

[0204] Example 3

[0205] Based on the same inventive concept as the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor in the aforementioned embodiment, the present invention also provides a repetitive fractional-order active disturbance rejection control device for a permanent magnet synchronous motor, such as Figure 13 As shown, a computer program is stored on the device, and when the program is executed by the processor, the steps of the above-mentioned repeated fractional-order active disturbance rejection control method for the permanent magnet synchronous motor are implemented.

[0206] Among them, Figure 13 In the embodiment of the present invention, a bus architecture (represented by bus 300) is shown. Bus 300 may include any number of interconnected buses and bridges. Bus 300 links various circuits together, including one or more processors represented by processor 302 and memory represented by memory 304. Bus 300 may also link various other circuits together, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and are not described further herein. Bus interface 306 provides an interface between bus 300 and receiver 301 and transmitter 303. Receiver 301 and transmitter 303 may be the same component, namely a transceiver, which provides a means for communicating with various other devices over a transmission medium.

[0207] The processor 302 is responsible for managing the bus 300 and general processing, while the memory 304 may be used to store data used by the processor 302 when performing operations.

[0208] Example 4

[0209] Based on the same inventive concept as the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor in the aforementioned embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor are as described in the first embodiment.

[0210] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0211] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0212] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0213] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0214] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0215] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor, characterized in that: The method comprises: S1: Establish the linear state equation of the permanent magnet synchronous motor PMSM speed loop; S2: Based on the fractional-order active disturbance rejection control system, the PMSM speed loop is subjected to disturbance observation and speed tracking, and the input of the PMSM speed loop is compensated. The compensated input of the PMSM speed loop is substituted into the linear state equation of the PMSM speed loop. S3: Introducing a new repetitive controller before the fractional-order active disturbance rejection control system to periodically reduce the system error, the new repetitive controller comprising a repetitive control unit and a delay compensation unit provided before the repetitive control unit, and inputting a speed loop given speed after being corrected by the new repetitive controller into the fractional-order active disturbance rejection control system; The step S2 is specifically as follows: The fractional-order active disturbance rejection control system includes a tracking differentiator TD, a new extended state observer NESO, a fractional-order controller and a disturbance compensator; The control rate of the tracking differentiator TD is as follows: in, is the given speed; ω e is the actual speed tracking value of PMSM; e0 is the error between the actual speed tracking value of PMSM and the given speed; α0 is the first nonlinear factor; δ is the filter factor; T is the operation period; r represents the tracking speed of the tracking differentiator; The speed ω tracked by the tracking differentiator TD e Input into the new extended state observer NESO, the control rate of the new extended state observer NESO is as follows: Where z1 is ω e The estimated value of z2 is ω e The estimated value of the differential; z3 is the observed value of the total disturbance; α1 is the second nonlinear factor; β1, β2, β3, β4 are output correction factors; The novel extended state observer (NESO) is used to obtain z1, z2, and z3, which are then input into the fractional-order controller. The control rate of the fractional-order controller is as follows: Among them, K p is the proportional coefficient; K i is the integral coefficient; K d is the differential coefficient; λ is the integral order; μ is the differential order; The PMSM speed loop speed input u2 before compensation is obtained through the fractional-order controller, and u2 and z3 are input into the disturbance compensator. The control rate of the disturbance compensator is as follows: Where u is the speed input of the PMSM speed loop after compensation; Substitute the compensated PMSM speed loop speed input u into the PMSM speed loop linear state equation; In step S3, the novel repetitive controller converts the input speed signal w(z) to the output The closed-loop transfer function is: C(z)=k r *z k S(z) (18) Among them, G RC (z) is the closed-loop transfer function of the new repetitive controller; w(z) is the input speed signal; Q(z) and S(z) are two low-pass filters; C(z) is the compensation link; k p2 is the proportional control coefficient of the repetitive controller; k r is the gain coefficient of the repetitive control unit; k is a constant, k1 is the same as k, k2 is the leading phase angle θ based on k1; z -N is the periodic delay link; N is the number of sampling times of a fundamental wave period; is the phase module; z -t / 2 is the hysteresis module, and t is the step response time of the system.

2. The repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor according to claim 1, wherein: The step S1 specifically includes: Taking PMSM as the controlled object, in the dq synchronous rotating coordinate system, the ideal mathematical model of PMSM is as follows: Among them, ω e ——rotor electrical angular velocity; R s - armature resistance; ψ d ,ψ q ——d-axis and q-axis magnetic flux; L d ,L q ——d and q axis inductance; u d ,u q ——d-axis and q-axis voltage; i d ,i q ——d-axis and q-axis currents; According to the equation of PMSM in the dq synchronous rotating coordinate system, the PMSM speed loop state equation can be obtained as follows: Where J is the rotor inertia, p is the number of motor pole pairs, T m is the load torque, B is the motor resistance coefficient; set the PMSM speed loop input u=i q , speed loop output Y = ω e , state variable X1=ω e , then the state equation of the speed loop can be written as: X1′=f(X1)+W+bu (3) Y=X1 (4) In formula (3), W is the total external disturbance of the system, b is the q-axis current i in the PMSM dynamic equation q The coefficient of , combined with equation (2) and equation (4), can be obtained as follows: Let f(X1) be expressed as the internal disturbance of the system, including the rotor moment of inertia J, load torque T m And the q-axis current i q The expanded state variable expression of the total disturbance can be set as: X2=f(X1)+W (7) Let X2′ = ξ, then the standard linear state equation of the speed loop can be obtained based on equations (4) and (5): X1′=X2+bu (8) X2′=ξ (9) Y=X1 (10).

3. The repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor according to claim 2, wherein: In step S2, the fractional-order active disturbance rejection control system includes a tracking differentiator TD, a novel extended state observer NESO, a fractional-order controller and a disturbance compensator; The tracking differentiator TD tracks the actual speed of the PMSM and inputs the tracking result into the new extended state observer NESO; The estimated value of the PMSM actual speed, the estimated value of the PMSM actual speed differential and the observed value of the total disturbance are obtained through the new extended state observer (NESO). The estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into the fractional-order controller to obtain the speed input of the PMSM speed loop before compensation; Inputting the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation into the disturbance compensator to obtain the speed input of the PMSM speed loop after compensation; Substitute the compensated PMSM speed loop speed input into the standard linear state equation of the PMSM speed loop.

4. A repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor, characterized in that: The system comprises: A repetitive fractional-order active disturbance rejection controller, using the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor according to any one of claims 1 to 3, for controlling and adjusting the input of a speed loop of a permanent magnet linear synchronous motor (PMSM); CLARKE conversion module, used to convert the three-phase winding output current i of PMSM a 、i b 、i c Through the CLARKE transformation of the stationary coordinate system, the output current i of the CLARKE transformation module is obtained α 、i β ; PRKE conversion module, used to convert the output current i α 、i β Transform from the stationary coordinate system to the rotating coordinate system to obtain the PMSM quadrature axis q-axis output current i q and the direct axis d-axis output current i d ; PI controller, used for the quadrature axis q axis output current i based on the output of the PRKE conversion module q and the direct axis d-axis output current i d The speed loop speed input of the repetitive fractional order ADRC is used to perform PI control and output the voltage value U of the torque current regulator of the PMSM. d * and the voltage value U of the excitation current regulator q * ; PRKE inverter module, used to convert the voltage value U d * and the voltage value U of the excitation current regulator q * Inverter processing, converted into voltage U α * 、U β * ; SVPWM space vector pulse width modulation module is used to convert the output voltage U α * 、U β * Perform space vector transformation and output PWM waveform for controlling PMSM inverter.

5. The repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor according to claim 4, characterized in that: The repetitive fractional-order active disturbance rejection controller comprises: A fractional-order active disturbance rejection controller is used to perform disturbance observation and speed tracking on the PMSM speed loop, thereby compensating the input of the PMSM speed loop and inputting the compensated PMSM speed loop input into the PI controller; a repetitive control unit connected to the fractional-order active disturbance rejection controller for periodically reducing system error interference; A delay compensation unit is connected to the repetitive control unit and is used to periodically compensate for the response time difference between the repetitive control unit and the PI controller.

6. The repetitive fractional-order active disturbance rejection control system for a permanent magnet synchronous motor according to claim 5, characterized in that: The fractional-order active disturbance rejection controller includes a tracking differentiator, an extended state observer, a fractional-order controller and a disturbance compensator; The tracking differentiator tracks the actual speed of the PMSM and inputs the tracking result into a new extended state observer; an estimated value of the actual speed of the PMSM, an estimated value of the differential of the actual speed of the PMSM, and an observed value of the total disturbance are obtained through the new extended state observer; the estimated value of the actual speed of the PMSM and the estimated value of the differential of the actual speed of the PMSM are input into a fractional-order controller to obtain a speed input of the PMSM speed loop before compensation; the observed value of the total disturbance and the speed input of the PMSM speed loop before compensation are input into a disturbance compensator to obtain a speed input of the PMSM speed loop after compensation; The compensated PMSM speed loop speed input is input into the PI controller.

7. A repetitive fractional-order active disturbance rejection control device for a permanent magnet synchronous motor, the device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor according to any one of claims 1 to 3 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the repetitive fractional-order active disturbance rejection control method for a permanent magnet synchronous motor as claimed in any one of claims 1 to 3 are implemented.

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