A composite quasi-resonant optimization-based active disturbance rejection controller and control method

Abstract

This invention is applicable to the field of motor control technology and provides an active disturbance rejection controller and control method based on composite quasi-resonant optimization. The active disturbance rejection controller improves on the traditional quasi-resonant controller by combining the hyperbolic tangent function with a resonant controller. The designed resonant controller is embedded in an ADRC controller to improve the ADRC controller's bandwidth at medium frequencies and enhance its ability to suppress multi-source disturbances. The stability of the controller is also analyzed. Finally, a permanent magnet synchronous motor drive system is constructed and the effectiveness of the proposed method is verified by comparison. Compared with a traditional proportional-integral controller, the control method of the present invention can reduce speed drop by 58% and reduce speed fluctuation to within 0.45%, thereby improving the control accuracy of the motor drive system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor control, and provides a composite quasi-resonance optimization-based active disturbance rejection controller and a control method. BACKGROUND

[0002] Permanent magnet synchronous linear motor (PMSLM) has been widely used in high-speed and high-precision linear servo occasions such as advanced robots, numerical control machine tools, 3D printing and semiconductor manufacturing due to its advantages of high precision, high dynamic response and simple structure. The permanent magnet synchronous motor for advanced robots has been significantly improved in driving capacity, control strategy optimization or precision, and has gradually replaced the traditional motor and been applied to various advanced robot application occasions including industrial robot arms, service robots, special operation robots, etc. In recent years, in the field of high-performance robot applications such as intelligent warehouse robots, surgical robots and underwater operation robots, high-precision, high-efficiency and high-quality requirements are put forward for the motor drive system of advanced robots. In the system of industrial robot arms, the robot usually needs to work under the condition of multi-joint cooperative motion and variable load, and the response speed and torque stability of the motor directly determine the operation precision and working efficiency of the robot; in the field of surgical robots, in the face of the demand for fine surgical operation, the drive of the surgical robot needs to have the ability to accurately control in a small action, especially when performing high-precision surgical operations, it is necessary to ensure the smooth operation of the robot to meet the safety and precision requirements of the operation; in the drive system of underwater operation robots, as the core component, the performance of the permanent magnet synchronous motor drive control directly determines the overall operation ability of the underwater operation robot.

[0003] In high-performance control occasions, strict requirements are put forward for motor speed regulation, specifically including strong resistance to speed (especially in low-speed high-torque operation state) and excellent low-speed stable operation ability. However, the permanent magnet synchronous motor based on the traditional control algorithm has exposed many problems when facing the task of low-speed high-torque driving; for example: the motor drive system is affected by multi-source disturbance; the equivalent load disturbance from the source will cause the speed to drop sharply when suddenly increasing; and when decreasing, the speed will quickly rise. At the same time, the equivalent torque disturbance from the multi-source disturbance mainly includes cogging torque, motor parameter change and unmodeled dynamics, etc. The equivalent torque disturbance often generates torque harmonics, which has a bad influence on the stability performance of the speed, especially at low speed, which will cause the speed to fluctuate periodically. Therefore, the control of the speed loop has time-varying and nonlinear characteristics, so it can be known that the traditional linear proportional integral control strategy is difficult to meet the strict standards of high-performance speed control, and needs to be improved. SUMMARY

[0004] The application aims to provide a self-disturbance control device and method based on composite quasi-resonance optimization to solve the problem of speed fluctuation caused by multi-source disturbance in traditional permanent magnet synchronous motor drive system.

[0005] In the first aspect, the application is implemented as a self-disturbance control device based on composite quasi-resonance optimization, which is configured to:

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

[0007]

[0008] wherein k r is an amplification coefficient, ω0 is a resonance frequency, ω c is a cutoff frequency, and s is a time domain variable;

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

[0010]

[0011]

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

[0013] The composite quasi-resonance controller is embedded in a preset active disturbance rejection controller to obtain a self-disturbance control device based on composite quasi-resonance optimization. The self-disturbance control device improves the conventional quasi-resonance controller, combines the hyperbolic tangent function with the resonance controller, and embeds the designed resonance controller in the ADRC (active disturbance rejection control) controller, which is an improved PID controller, to improve the bandwidth of the ADRC controller at medium frequency and enhance the suppression ability of the ADRC controller to multi-source disturbance.

[0014] In the second aspect, the application provides a self-disturbance control method based on composite quasi-resonance optimization, which is used for the self-disturbance control device and includes the following steps.

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

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

[0017] By the self-disturbance controller based on the composite quasi-resonance optimization, the reference signal is tracked without steady-state static error, and the periodic fluctuation of the rotating speed caused by the equivalent torque disturbance of the motor driving system is inhibited.

[0018] The self-disturbance control method based on the composite quasi-resonance optimization provided by the application firstly divides equivalent torque disturbance and equivalent load disturbance according to multi-source disturbance sources, respectively establishes disturbance models of the equivalent torque disturbance and the equivalent load disturbance, and constructs a dynamic model with multi-source disturbance according to the disturbance models, and deduces a state space equation of the ADRC controller. Secondly, the multi-source disturbance suppression capability of the ADRC controller is analyzed. Then, the traditional quasi-resonance controller is improved, the hyperbolic tangent function is combined with the resonance controller, the designed resonance controller is embedded into the ADRC controller, so that the bandwidth of the ADRC controller at the medium frequency is improved, the multi-source disturbance suppression capability of the ADRC controller is enhanced, and the stability of the controller is analyzed. Compared with the traditional proportional integral controller, the method can reduce the rotating speed drop by 58% and the rotating speed fluctuation to 0.45% within the rotating speed. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of the self-disturbance control method based on the composite quasi-resonance optimization provided by the embodiment of the application is shown in the figure.

[0020] Figure 2 A Bode diagram of the disturbance suppression of the self-disturbance controller system is shown in the figure.

[0021] Figure 3 A Bode diagram of the actual output of the disturbance of the self-disturbance controller system is shown in the figure.

[0022] Figure 4 A Bode diagram of the conventional quasi-resonance regulator is shown in the figure.

[0023] Figure 5 A function diagram of the hyperbolic tangent function is shown in the figure.

[0024] Figure 6 A Bode diagram of the composite quasi-resonance controller is shown in the figure.

[0025] Figure 7 A system block diagram of the self-disturbance controller based on the composite quasi-resonance optimization is shown in the figure.

[0026] Figure 8 A permanent magnet synchronous motor speed loop control system diagram using the self-disturbance controller based on the composite quasi-resonance optimization is shown in the figure.

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

[0028] Figure 9 is a waveform diagram of a speed loop running in a rated load mutation case based on a PI control;

[0029] Figure 10 is a waveform diagram of a speed loop running in a rated load mutation case controlled by a speed loop based on a composite quasi-resonant optimized active disturbance rejection controller;

[0030] Figure 11 is a speed waveform diagram based on an active disturbance rejection controller and a composite quasi-resonant optimized active disturbance rejection controller when the moment of inertia changes. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application, and are not used to limit the present application.

[0032] As shown in Figure 7 , Figure 8 In one embodiment, a composite quasi-resonant optimized active disturbance rejection controller is proposed, which is configured to:

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

[0034]

[0035] wherein k r is an amplification coefficient, ω0 is a resonant frequency, ω c is a cutoff frequency, and s is a time domain variable;

[0036] wherein the multi-source disturbance in the motor drive system is firstly classified and modeled, and is divided into equivalent torque disturbance and equivalent load disturbance according to the source, and a mathematical model thereof is established, and a motor motion equation containing multi-source disturbance is constructed;

[0037] The motor motion equation is rewritten as a state space equation, the multi-source disturbance in the motor drive system is expanded as a new state variable, and a new state space equation is constructed according to the new state variable;

[0038] A second-order extended state observer is constructed by using a new state space equation, i.e. 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 a hyperbolic tangent function to form a composite quasi-resonant controller, so that the composite quasi-resonant controller has identification performance for the size of the multi-source disturbance;

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

[0041]

[0042]

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

[0044] In order to ensure the practicability and stability of the embodiment, the composite quasi-resonant controller is embedded in a preset active anti-disturbance controller to obtain a self-anti-disturbance controller based on composite quasi-resonant optimization.

[0045] The preset active anti-disturbance controller is a conventional self-anti-disturbance controller. The self-anti-disturbance controller can effectively observe the equivalent load disturbance and perform feedforward compensation. The self-anti-disturbance controller in the embodiment realizes compensation for the equivalent torque disturbance of the system, thereby realizing high-performance control of the system. According to the division of multi-source disturbance sources into equivalent torque disturbance and equivalent load disturbance, the disturbance models of the two are established, and a dynamic model with multi-source disturbance is constructed accordingly, 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, thereby improving the bandwidth of the ADRC controller at medium frequency and enhancing the suppression ability of the ADRC controller to multi-source disturbance.

[0046] In the self-anti-disturbance controller, 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 amount in an approximate manner. Therefore, the disturbances affecting the controlled output can be combined into a state variable, which can be referred to as the "extended state" of the system. By incorporating this part of the disturbance into the control amount 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 the expression, x1 represents the state variable of the system, d indicates the uncertain quantity of the system except 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, and the state equation of the system can be written as:

[0051]

[0052] In the expression, x2 represents the extended 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 the expression, 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, and k in the control rate is a proportional coefficient. p

[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 the integral part to obtain a modified active disturbance rejection controller; the active disturbance rejection controller can realize no steady-state static error control. When the speed is in a steady state, a larger gain can be obtained, and the gain 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, as shown in Figure 1 a composite quasi-resonant optimization-based active disturbance rejection control method is provided for an active disturbance rejection controller, which can be applied to a motor drive system speed loop; the use of the method in the motor drive system speed loop will be described in detail.

[0058] The method of the embodiment can specifically include the following steps S101-S103.

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

[0060] The motor motion equation satisfies:

[0061]

[0062]

[0063] ​where ω is the speed of the motor, is the first derivative of ω, J is the moment of inertia of the motor, 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 viscous coefficient of the motor, L d and L q are the d-axis and q-axis stator inductances, i d and i q are the d-axis and q-axis stator currents, respectively, and ψ is the permanent magnet flux linkage;

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

[0065]

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

[0067] The motor motion equation is converted into the form of state space equation and

[0068]

[0069] where d is the total disturbance in the motor drive system, and 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 as x2, and the expression of the new state space equation is as follows:

[0071]

[0072] where 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 obtained by expanding the total disturbance in the motor drive system, and b is the new control gain.

[0073] S102: An extended state observer is constructed using the new state space equation, and the total disturbance observed by the extended state observer is used for feedforward compensation;

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

[0075]

[0076] wherein p1, p2 are gains of the extended state observer, e is an error value between z1 and x1, z1, z2 are estimated values of state variables x1, x2 respectively, k p is a proportional coefficient.

[0077] S103: Realize no steady-state static error tracking reference signal by the active disturbance rejection controller based on the composite quasi-resonance optimization, and suppress the periodic fluctuation of the rotation speed caused by the equivalent torque total disturbance 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] wherein ω 1th , ω 2th and ω 6th are resonance frequencies of the three composite quasi-resonance controllers respectively, ω 1th = ω e , ω 2th = 2ω e and ω 6th = 6ω e are respectively used for compensating 1st order equivalent torque disturbance harmonic, 2nd order equivalent torque disturbance harmonic and 6th order equivalent torque disturbance harmonic; X1(s) and X2(s) are Laplace transforms of x1 and x2; D a (s) and D p (s) respectively represent Laplace transforms of estimated values of the equivalent load disturbance and the equivalent torque disturbance; T e is an electromagnetic torque; G QRC (s) is a Laplace transform of the composite resonance controller; E1(s) is an estimation error with an actual value; f(u) is a control function, p is an uncompensated control quantity, and u is an error between an estimated value and an actual value.

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

[0082]

[0083] In the expression, ω * is a 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 the formulas (12) and (13), the transfer function between the actual output ω and the actual disturbance d can be obtained:

[0087]

[0088] The formula (15) discloses that the estimated total disturbance is the integral of the error between the estimated output and the actual output. The formula (16) shows that the extended state observer is similar to a low-pass filter, and the Bode diagram thereof is as shown in Figure 2 The Bode diagram of the formula (17) is as shown in Figure 3 It can be seen from the figures that the active disturbance rejection controller can achieve the control without steady-state error.

[0089] Although the active disturbance rejection controller effectively suppresses the equivalent torque disturbance, the sinusoidal disturbance is common in the motion system. In order to effectively suppress such disturbance, the compound quasi-resonant regulator is introduced into the active disturbance rejection controller in the embodiment;

[0090] In the embodiment, the Bode diagram of the conventional quasi-resonant regulator is as shown in Figure 4 Compared with the conventional quasi-resonant regulator, the quasi-resonant regulator has an increased resonant bandwidth and has a greater gain near the resonant frequency, thereby ensuring the stability of the system. Although the quasi-resonant regulator can accurately track the sinusoidal signal, it has poor dynamic performance and cannot adjust the suppression performance according to the size of the multi-source disturbance. The compound quasi-resonant controller is composed by combining the quasi-resonant regulator with the hyperbolic tangent function. The hyperbolic tangent function can be referred to Figure 5 ; Figure 6 The Bode diagram of the compound quasi-resonant controller is as shown in the figure. It can be found that the controller has a greater bandwidth when the disturbance is large, and has a greater gain at the resonant frequency when the disturbance is small, so that the multi-source disturbance can be more accurately suppressed.

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

[0092]

[0093] Wherein, 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, and k p is the proportional coefficient.

[0094] In the embodiment, the embodiment and the conventional proportional integral controller are compared. Specifically, Figure 9 is the waveform diagram of the speed loop based on the proportional integral controller control (PI control) under the condition of the sudden change of the rated torque. From Figure 9It can be found that the maximum drop speed is 36 rpm in the case of rated torque mutation, and the peak-to-peak value of periodic speed fluctuation caused by the internal motor drive system is 13.5 rpm in the steady state. This shows that the speed fluctuation is caused by multiple source disturbances, and also shows that the speed fluctuation is more serious when the motor operates at low speed and large torque. Figure 10 The waveform diagram of the speed loop controlled by the composite quasi-resonance optimization-based active disturbance rejection controller under the condition of rated load mutation shows that the speed fluctuation is reduced in the case of rated torque mutation, which shows that the method of the application can effectively suppress multiple source disturbances in the motor system. The speed drop of the speed loop based on the proportional integral controller and the optimized active disturbance rejection controller is reduced by 11.8 rpm, and the speed fluctuation is reduced to 4.5 rpm. Figure 11 The speed waveform diagram based on the active disturbance rejection controller and the composite quasi-resonance optimization-based active disturbance rejection controller when the moment of inertia changes shows that the control method of the embodiment has better robustness to the change of the moment of inertia and stronger suppression performance to multiple source disturbances compared with the active disturbance rejection controller. Therefore, compared with the traditional active disturbance rejection controller, the method of the embodiment can achieve better suppression performance to multiple source disturbances in the motor system.

[0095] It should be understood that although each step in the flowchart of each embodiment of the application is displayed in sequence according to the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless otherwise specified herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, at least part of the steps in each embodiment can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least part of other steps or sub-steps or stages of other steps.

[0096] The above-described embodiments only express several embodiments of the application, and the description is more specific and detailed, but it should not be understood as limiting the scope of the patent of the application. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the application, a number of modifications and improvements can be made, which are within the scope of protection of the application. Therefore, the protection scope of the patent of the application should be subject to the appended claims.

[0097] The above-described only the preferred embodiments of the application, and not to limit the application, any modification, equivalent replacement and improvement made within the spirit and principles of the application, should be included in the protection scope of the application.

Claims

1. An active disturbance rejection control method based on composite quasi-resonance optimization, for an active disturbance rejection controller based on composite quasi-resonance optimization, wherein the active disturbance rejection controller is configured as follows: A quasi-resonant regulator is selected, and the transfer function of the quasi-resonant regulator is as follows: in, k r is the amplification factor, ω0 is the resonant frequency, ω c is the cutoff 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 variable; 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; Characterized in that the method comprises: Rewrite the motor motion equation into a state-space equation, expand the total disturbance in the motor drive system into a new state variable, and construct a new state-space equation 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 auto-disturbance rejection controller based on composite quasi-resonant optimization, the reference signal is tracked without steady-state error, and the periodic fluctuation of the speed caused by the total disturbance of the equivalent torque of the motor drive system is suppressed.

2. The method according to claim 1, characterized in that The motor motion equation satisfies: Where ω is the motor speed, 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, and ψ is the permanent magnet flux linkage; Convert the motor motion equations into the state space equation form: 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.

3. The method according to claim 2, 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: Where 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, and b is the new control gain.

4. The method according to claim 3, 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 proportional coefficient.

5. The method according to claim 4, characterized in that The frequency domain of the active disturbance rejection controller based on composite quasi-resonant 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 for 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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