Active-disturbance-rejection controller based on composite quasi-resonance optimization and control method

Abstract

The invention is suitable for the technical field of motor control, and provides an active-disturbance-rejection controller based on composite quasi-resonance optimization and a control method.According to the active-disturbance-rejection controller, a traditional quasi-resonance controller is improved, a hyperbolic tangent function is combined with a resonance controller, and the designed resonance controller is embedded into an ADRC controller; the bandwidth of the ADRC controller under the medium frequency is improved, the inhibition capability of the ADRC controller on multi-source disturbance is enhanced, and the stability of the controller is analyzed; and finally, building a permanent magnet synchronous motor driving system, and comparing and verifying the effectiveness of the method. Compared with a traditional proportional-integral controller, the control method has the advantages that the rotating speed drop can be reduced by 58%, the rotating speed fluctuation can be reduced to be within 0.45%, and the control precision of a motor driving system is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of motor control, and provides an auto-disturbance rejection controller and a control method based on composite quasi-resonance optimization. Background Art

[0002] Permanent magnet synchronous linear motors (PMSLM) have been widely used in high-speed, high-precision linear servo applications such as advanced robots, CNC machine tools, 3D printing and semiconductor manufacturing due to their advantages of high precision, high dynamic response and simple structure. Permanent magnet synchronous motors for advanced robots have been significantly improved in terms of driving capabilities, optimization of control strategies and accuracy. Therefore, they have gradually replaced traditional motors and have been used in various advanced robot applications including industrial robotic arms, service robots, special operation robots, etc. In recent years, in high-performance robot applications such as intelligent storage robots, surgical robots and underwater operation robots, high-precision, high-efficiency and high-quality requirements have been put forward for motor drive systems for advanced robots. In the system of industrial robotic arms, the robotic arms usually need to work under the conditions of coordinated motion of multiple joints and variable loads. The response speed and torque stability of the motor directly determine the operating accuracy and work efficiency of the robotic arms. In the field of surgical robots, in the face of delicate surgical operation requirements, the drive of the surgical robot needs to have the ability to accurately control tiny movements, especially when performing high-precision surgical operations, to ensure the smooth operation of the robot to meet the safety and precision requirements of the surgery. In the drive system of underwater working robots, as a core component, the quality of the permanent magnet synchronous motor drive control performance directly determines the overall operating capability of the underwater working robot.

[0003] In high-performance control situations, strict requirements are put forward for motor speed regulation, including strong resistance to speed (especially in low-speed and high-torque operation) and excellent low-speed stable operation capability. However, permanent magnet synchronous motors based on traditional control algorithms have exposed many problems when facing low-speed and high-torque drive tasks; for example, the motor drive system is affected by multi-source disturbances; the equivalent load disturbances from its source will cause the speed to drop sharply when it suddenly increases; and when it decreases, the speed will rise rapidly. At the same time, the equivalent torque disturbances from multi-source disturbances mainly include cogging torque, motor parameter changes, and unmodeled dynamics. Equivalent torque disturbances often generate torque harmonics, which have an adverse effect on the stability of the speed, especially when running at low speeds, causing periodic fluctuations in the speed. Therefore, the control of the speed loop has time-varying and nonlinear characteristics. It can be seen that the traditional linear proportional integral control strategy is difficult to meet the stringent standards of high-performance speed control and needs to be improved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide an auto-disturbance rejection controller and a control method based on composite quasi-resonance optimization to solve the problem of speed fluctuation caused by multi-source disturbances in traditional permanent magnet synchronous motor drive systems.

[0005] In a first aspect, the present invention is implemented as follows: an active disturbance rejection controller based on composite quasi-resonance optimization, wherein the active disturbance rejection controller is configured as follows:

[0006] A quasi-resonant regulator is selected, and the transfer function of the quasi-resonant regulator is as follows:

[0007]

[0008] Among them, k r is the amplification factor, ω0 is the resonant frequency, ω c is the cut-off frequency, s is the time domain variable;

[0009] The transfer function of the quasi-resonant regulator is combined with the hyperbolic tangent function to form a composite quasi-resonant controller. The transfer function of the composite quasi-resonant controller is as follows:

[0010]

[0011]

[0012] in, tanh(u) is the hyperbolic tangent function, u=e1 is the error between the estimated value and the actual value, γ is the control parameter of f(u), and p is the uncompensated control quantity;

[0013] The composite quasi-resonant controller is embedded in a preset active disturbance rejection controller to obtain an active disturbance rejection controller based on composite quasi-resonant optimization. The active disturbance rejection controller improves the traditional quasi-resonant controller by combining the hyperbolic tangent function with the resonant controller and embedding the designed resonant controller into an ADRC (active disturbance rejection control) controller (an improved PID controller) to improve the bandwidth of the ADRC controller at medium frequencies and enhance its ability to suppress multi-source disturbances.

[0014] In a second aspect, the present invention provides an active disturbance rejection control method based on composite quasi-resonance optimization, which is used in the active disturbance rejection controller, and the method comprises:

[0015] The motor motion equation is rewritten into a state space equation, the total disturbance in the motor drive system is expanded into a new state variable, and a new state space equation is constructed based on the new state variable;

[0016] An extended state observer is constructed using the new state space equation, and a total disturbance observed by the extended state observer is used for feedforward compensation;

[0017] Through the anti-disturbance controller based on composite quasi-resonant optimization, the reference signal is tracked without steady-state static error, and the periodic fluctuation of the speed caused by the total disturbance of the equivalent torque of the motor drive system is suppressed.

[0018] The present invention provides an anti-disturbance control method based on composite quasi-resonant optimization. First, the multi-source disturbance is divided into equivalent torque disturbance and equivalent load disturbance according to the source, and the disturbance models of the two are established respectively. Based on this, a dynamic model with multi-source disturbance is constructed to derive the state space equation of the ADRC controller. Secondly, the ability of the ADRC controller to suppress multi-source disturbances is analyzed; then, the traditional quasi-resonant controller is improved by combining the hyperbolic tangent function with the resonant controller, and the designed resonant controller is embedded in the ADRC controller to improve the bandwidth of the ADRC controller at medium frequency, enhance its ability to suppress multi-source disturbances, and analyze the stability of the controller. Compared with the traditional proportional-integral controller, the method of the present invention can reduce the speed drop by 58% and reduce the speed fluctuation to within 0.45% of the revolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of an auto-disturbance rejection control method based on composite quasi-resonance optimization provided by an embodiment of the present invention;

[0020] Figure 2 Bode plot of disturbance rejection of the ADRC system;

[0021] Figure 3 Bode diagram of the system disturbance of the ADRC versus the actual output;

[0022] Figure 4 is the Bode plot of a conventional quasi-resonant regulator;

[0023] Figure 5 is the function graph of the hyperbolic tangent function;

[0024] Figure 6 is the Bode diagram of the composite quasi-resonant controller;

[0025] Figure 7 The system block diagram of the active disturbance rejection controller based on composite quasi-resonant optimization;

[0026] Figure 8 This is a diagram of the speed loop control system of a permanent magnet synchronous motor using an auto-disturbance rejection controller based on composite quasi-resonant optimization;

[0027] Figure 8 Where: ω is the given speed of the motor, ω * is the first-order derivative of ω, u d represents the motor d-axis voltage, u q represents the motor d-axis voltage, θ represents the motor position angle, represents the d-axis reference current, represents the q-axis reference current, i d represents the d-axis current, i q represents d-axis current, PhI represents three-phase inverter, encoder represents encoder; MTPA represents maximum torque current ratio, PMSM represents permanent magnet synchronous motor, and SVPWM represents space vector pulse width modulation;

[0028] Fig. 9 This is the waveform diagram of the speed loop based on PI control running under the condition of rated load mutation;

[0029] Fig.10 This is a waveform diagram of the speed loop controlled by the active disturbance rejection controller based on composite quasi-resonance optimization running under the condition of rated load mutation;

[0030] Fig.11 The speed waveforms of the active disturbance rejection controller and the active disturbance rejection controller based on composite quasi-resonant optimization when the moment of inertia changes. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0032] like Figure 7 , Figure 8 As shown, in one embodiment, an active disturbance rejection controller based on composite quasi-resonance optimization is proposed, and the active disturbance rejection controller is configured as follows:

[0033] A quasi-resonant regulator is selected, and the transfer function of the quasi-resonant regulator is as follows:

[0034]

[0035] Among them, k r is the amplification factor, ω0 is the resonant frequency, ω c is the cut-off frequency, s is the time domain variable;

[0036] Among them, the multi-source disturbances in the motor drive system are first classified and modeled, divided into equivalent torque disturbances and equivalent load disturbances according to their sources, and their mathematical models are established to construct the motor motion equations containing multi-source disturbances;

[0037] Rewrite the motor motion equation into a state space equation, expand the multi-source disturbance in the motor drive system into a new state variable, and construct a new state space equation based on the new state variable;

[0038] The second-order extended state observer is constructed by using the new state space equation, thus obtaining the quasi-resonant regulator; the total disturbance d observed by the extended state observer is used for feedforward compensation.

[0039] The transfer function of the quasi-resonant regulator is combined with the hyperbolic tangent function to form a composite quasi-resonant controller, which can make the composite quasi-resonant controller have the ability to identify the size of multi-source disturbances;

[0040] Among them, the transfer function of the composite quasi-resonant controller is as follows:

[0041]

[0042]

[0043] Where tanh(u) is the hyperbolic tangent function, u=e1 is the error between the estimated value and the actual value, γ is the control parameter of f(u), and p is the uncompensated control quantity;

[0044] In order to ensure the practicality and stability of this embodiment, the composite quasi-resonant controller is embedded in a preset active disturbance rejection controller to obtain an active disturbance rejection controller based on composite quasi-resonant optimization;

[0045] Among them, the preset active disturbance rejection controller is a conventional active disturbance rejection controller. The active disturbance rejection controller can effectively observe the equivalent load disturbance and perform feedforward compensation; the active disturbance rejection controller in this embodiment realizes the compensation of the system equivalent torque disturbance, thereby realizing high-performance control of the system. According to the source of multi-source disturbance, it is divided into equivalent torque disturbance and equivalent load disturbance, and the disturbance models of the two are established respectively. Based on this, a dynamic model with multi-source disturbance is constructed, and the state space equation of the ADRC controller is derived; the ability of the ADRC controller to suppress multi-source disturbance is analyzed, and then the traditional quasi-resonant controller is improved, the hyperbolic tangent function is combined with the resonant controller, and the designed resonant controller is embedded in the ADRC controller, which improves the bandwidth of the ADRC controller at medium frequency and enhances its ability to suppress multi-source disturbance.

[0046] In this embodiment, in the ADRC, the extended state observer is the core unit. It can obtain the sum of all disturbances of the system (i.e., the motor drive system) except the control quantity in an approximate manner. Therefore, the disturbance affecting the controlled output can be synthesized into a state quantity, which can be called the "extended state" of the system. By integrating this part of the disturbance into the control quantity in a certain form and inputting it into the system, the influence of the disturbance on the system can be eliminated. The basic principle is as follows:

[0047] For a first-order system state equation:

[0048]

[0049] In this expression, x1 represents the state variable of the system, d represents the uncertainty of the system other than the control input, u is the control input of the system, b is the control gain, and y is the output of the system.

[0050] Let x2 = y, then the state equation of the system can be written as:

[0051]

[0052] In this expression, x2 represents the expanded state variable of the system.

[0053] According to the above formula, the corresponding extended state observer is constructed for the first-order system; that is

[0054]

[0055] In this expression: p1, p2 are the gains of the extended state observer, z1, z2 are the estimated values ​​of the state variables x1, x2 respectively. p is the proportionality coefficient.

[0056] In the active disturbance rejection controller, three quasi-resonant regulators are connected in parallel in the integral part of the active disturbance rejection controller, and then the obtained parallel structure is connected in parallel with its integral part to obtain a modified active disturbance rejection controller; the active disturbance rejection controller can realize non-steady-state static error control. When the speed is in a steady state, a large gain can be obtained, which can compensate for the equivalent torque disturbance caused by the internal disturbance of the motor drive system, thereby effectively suppressing the speed fluctuation caused by the internal disturbance.

[0057] In another embodiment, Figure 1 As shown, a self-disturbance rejection control method based on composite quasi-resonant optimization is provided, which is used for a self-disturbance rejection controller and can be applied to the speed loop of a motor drive system. Next, the use of this method in the speed loop of a motor drive system will be introduced in detail.

[0058] The method of this embodiment may specifically include the following steps S101 to S103;

[0059] S101: rewriting the motor motion equation into a state space equation, expanding the total disturbance in the motor drive system into a new state variable, and constructing a new state space equation according to the new state variable;

[0060] Among them, the motor motion equation satisfies:

[0061]

[0062]

[0063] Where ω is the speed of the motor, is the first-order derivative of ω, J is the moment of inertia of the motor, T e is the electromagnetic torque, T L is the load torque of the motor, p n is the number of pole pairs of the motor, B is the viscosity coefficient of the motor, L d and L q is the d-axis and q-axis stator inductance, i d and i q are the d-axis and q-axis stator currents respectively, ψ is the permanent magnet flux linkage;

[0064] The motor current equation is expressed as follows:

[0065]

[0066] Among them, u d and u q are the d-axis and q-axis stator voltages, L d and L q is the d-axis and q-axis stator inductance, i d and i q are the d-axis and q-axis stator currents respectively; R s is the stator resistance, ω e is the rotor electrical angular velocity, ψ is the permanent magnet flux.

[0067] Convert the motor motion equations into the state space equation form:

[0068]

[0069] Where d is the total disturbance in the motor drive system; b0 is the control gain, which is also the actual moment of inertia of the motor;

[0070] The new state variable obtained by expanding the total disturbance in the motor drive system is set to x2, and the expression of the new state space equation is as follows:

[0071]

[0072] Among them, x1 is the state variable of the motor drive system, y is the output of the motor drive system, x2 is the new state variable expanded from the total disturbance in the motor drive system; b is the new control gain.

[0073] S102: constructing an extended state observer using the new state space equation, and performing feedforward compensation using the total disturbance observed by the extended state observer;

[0074] The equation of the extended state observer satisfies:

[0075]

[0076] Among them, p1 and p2 are the gains of the extended state observer, e is the error between z1 and x1, z1 and z2 are the estimated values ​​of the state variables x1 and x2 respectively, and k p is the proportionality coefficient.

[0077] S103: A self-disturbance rejection controller based on composite quasi-resonance optimization is used to realize a reference signal without steady-state static error tracking, thereby suppressing the periodic fluctuation of the speed caused by the total disturbance of the equivalent torque of the motor drive system.

[0078] In step S103, the frequency domain of the active disturbance rejection controller based on the composite quasi-resonance optimization satisfies:

[0079]

[0080] Among them, ω 1th ,ω 2th and ω 6th are the resonant frequencies of the three composite quasi-resonant controllers, ω 1th =ω e ,ω 2th =2ω e and ω 6th =6ω e They are used to compensate the 1st equivalent torque disturbance harmonic, the 2nd equivalent torque disturbance harmonic, and the 6th equivalent torque disturbance harmonic respectively; X1(s) and X2(s) are the Laplace transforms of x1 and x2; D a (s) and D p (s) represent the Laplace transform of the estimated values ​​of the equivalent load disturbance and the equivalent torque disturbance, respectively; T e is the electromagnetic torque; G QRC (s) is the Laplace transform of the composite resonant controller; E1(s) is the estimated error relative to the actual value; f(u) is the control function, p is the uncompensated control variable, and u is the error between the estimated value and the actual value.

[0081] In this embodiment, the following expression can be obtained according to formulas (11) and (12):

[0082]

[0083] In this expression: * is the reference signal.

[0084] According to formulas (9) and (10), the transfer function between the estimated disturbance z and the actual disturbance d can be obtained:

[0085]

[0086] According to formulas (12) and (13), the transfer function between the actual output ω and the actual disturbance d can be obtained:

[0087]

[0088] Equation (15) reveals that the estimated total disturbance is the integral of the error between the estimated output and the actual output. Equation (16) shows that the extended state observer is similar to a low-pass filter, and its Bode diagram is as follows: Figure 2 As shown, the Bode diagram of formula (17) is as follows Figure 3 As shown; it can be seen from the figure that the active disturbance rejection controller can achieve control without steady-state error.

[0089] Although the active disturbance rejection controller effectively suppresses equivalent torque disturbance, sinusoidal disturbances are common in motion systems. In order to effectively suppress such disturbances, this embodiment introduces a composite quasi-resonant regulator into the active disturbance rejection controller;

[0090] In this embodiment, compared with the composite quasi-resonant regulator of this embodiment, the Bode diagram of the conventional quasi-resonant regulator is as follows: Figure 4 Compared with the traditional resonant regulator, the quasi-resonant regulator has a larger resonant bandwidth and a larger gain near the resonant frequency, thereby ensuring the stability of the system. Although the quasi-resonant regulator can accurately track the sinusoidal signal, its dynamic performance is poor and it cannot adjust the suppression performance according to the size of the multi-source disturbance. By combining it with the hyperbolic tangent function, a composite quasi-resonant controller is formed; the hyperbolic tangent function can be referred to Figure 5 ; Figure 6 This is the Bode diagram of the composite quasi-resonant controller. It can be found that the controller has a larger bandwidth when the disturbance is large, and at the same time, it has a larger gain at the resonant frequency when the disturbance is small, which can achieve more accurate suppression of multi-source disturbances.

[0091] In this embodiment, the extended state observer constructed in step S102 satisfies:

[0092]

[0093] Among them, p1 and p2 are the gains of the extended state observer, z1 and z2 are the estimated values ​​of the state variables x1 and x2 respectively; e is the error value between z1 and x1, k p is the proportionality coefficient.

[0094] In this embodiment, this embodiment is compared with a conventional proportional-integral controller; specifically, Fig. 9 This is the waveform of the speed loop based on proportional integral controller control (PI control) under the condition of rated torque mutation. Fig. 9It can be found that in the case of a sudden change in rated torque, the maximum drop speed is 36rpm; in the steady state, the peak-to-peak value of the periodic speed fluctuation caused by the motor drive system is 13.5rpm. This shows that the speed fluctuation is caused by multiple sources of disturbance, and also shows that the speed fluctuation is more serious when the motor runs at low speed and high torque. Fig.10 The waveform diagram of the speed loop controlled by the composite quasi-resonant optimized anti-disturbance controller under rated load mutation, under rated torque mutation, the speed fluctuation is reduced, which shows that the method of the present invention can effectively suppress multi-source disturbances in the motor system at the same time. Based on the speed loop of the proportional-integral controller and the optimized anti-disturbance controller, the speed drop dropped by 11.8rpm, and the speed fluctuation was reduced to 4.5rpm. Fig.11 The speed waveforms based on the auto-disturbance rejection controller and the auto-disturbance rejection controller based on composite quasi-resonance optimization when the moment of inertia changes are shown. It can be found that the control method of this embodiment is equivalent to the auto-disturbance rejection controller. It has better robustness when the moment of inertia changes and stronger suppression performance for multi-source disturbances. Therefore, compared with the traditional auto-disturbance rejection controller, the method of this embodiment can achieve better suppression performance for multi-source disturbances in the motor system.

[0095] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0096] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An active disturbance rejection controller based on composite quasi-resonant optimization, characterized in that: The ADRC is configured as: A quasi-resonant regulator is selected, and the transfer function of the quasi-resonant regulator is as follows: Among them, k r is the amplification factor, ω0 is the resonant frequency, ω c is the cut-off frequency, s is the time domain variable; The transfer function of the quasi-resonant regulator is combined with the hyperbolic tangent function to form a composite quasi-resonant controller. The transfer function of the composite quasi-resonant controller is as follows: Where tanh(u) is the hyperbolic tangent function, u=e1 is the error between the estimated value and the actual value, γ is the control parameter of f(u), and p is the uncompensated control quantity; The composite quasi-resonant controller is embedded in a preset active disturbance rejection controller to obtain an active disturbance rejection controller based on composite quasi-resonant optimization.

2. The active disturbance rejection controller according to claim 1, characterized in that: In the active disturbance rejection controller, three quasi-resonant regulators are connected in parallel in the integral part of the active disturbance rejection controller, and then the obtained parallel structure is connected in parallel with the integral part thereof to obtain a modified active disturbance rejection controller.

3. An auto-disturbance rejection control method based on composite quasi-resonance optimization, used in the auto-disturbance rejection controller according to claim 1 or 2, characterized in that: The method comprises: The motor motion equation is rewritten into a state space equation, the total disturbance in the motor drive system is expanded into a new state variable, and a new state space equation is constructed based on the new state variable; An extended state observer is constructed using the new state space equation, and a total disturbance observed by the extended state observer is used for feedforward compensation; Through the anti-disturbance controller based on composite quasi-resonant optimization, the reference signal is tracked without steady-state static error, and the periodic fluctuation of the speed caused by the total disturbance of the equivalent torque of the motor drive system is suppressed.

4. The method according to claim 3, characterized in that The motor motion equation satisfies: Where ω is the speed of the motor, is the first-order derivative of ω, J is the moment of inertia of the motor, T e is the electromagnetic torque, T L is the load torque of the motor, p n is the number of pole pairs of the motor, B is the viscosity coefficient of the motor, L d and L q is the d-axis and q-axis stator inductance, i d and i q are the d-axis and q-axis stator currents respectively, ψ is the permanent magnet flux linkage; Convert the motor motion equations into the state space equation form: Among them, d is the total disturbance in the motor drive system; b0 is the control gain, which is also the actual rotational inertia of the motor.

5. The method according to claim 4, characterized in that The new state variable obtained by expanding the total disturbance in the motor drive system is set to x2, and the expression of the new state space equation is as follows: Among them, x1 is the state variable of the motor drive system, y is the output of the motor drive system, x2 is the new state variable expanded from the total disturbance in the motor drive system; b is the new control gain.

6. The method according to claim 5, characterized in that The extended state observer satisfies: Among them, p1 and p2 are the gains of the extended state observer, z1 and z2 are the estimated values ​​of the state variables x1 and x2 respectively, e is the error between z1 and x1, and k p is the proportionality coefficient.

7. The method according to claim 6, characterized in that The frequency domain of the active disturbance rejection controller based on composite quasi-resonance optimization is as follows: Among them, ω 1th ,ω 2th and ω 6th are the resonant frequencies of the three composite quasi-resonant controllers, ω 1th =ω e ,ω 2th =2ω e and ω 6th =6ω e They are used to compensate the 1st equivalent torque disturbance harmonic, the 2nd equivalent torque disturbance harmonic, and the 6th equivalent torque disturbance harmonic respectively; X1(s) and X2(s) are the Laplace transforms of x1 and x2; D a (s) and D p (s) represent the Laplace transform of the estimated values ​​of the equivalent load disturbance and the equivalent torque disturbance, respectively; T e is the electromagnetic torque; G QRC (s) is the Laplace transform of the composite resonant controller; E1(s) is the estimated error relative to the actual value; f(u) is the control function, p is the uncompensated control variable, and u is the error between the estimated value and the actual value.

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