An Active Disturbance Rejection Control Method Based on Optimization of High-Pass Filter Linear Feedback Controller

Abstract

The present invention relates to the field of motor control technology, specifically, an anti-disturbance control method based on high-pass filter linear feedback controller optimization, comprising the following steps: S1, based on the motor motion equation, a state space equation is obtained, the total disturbance in the motor drive system is expanded into a new state variable, and a new state space equation is constructed according to the new state variable; S2, an extended state observer is constructed by the new state space equation, and the speed feedback value and total disturbance observed by the observer are used to perform feedforward compensation using the total disturbance; S3, a high-pass filter and a linear feedback controller are designed to realize speed reference signal tracking, and suppress the periodic fluctuation of speed caused by the internal disturbance of the motor drive system. The present invention retains the characteristic of fewer setting parameters of the linear ESO, reduces speed fluctuation, reduces the harmonic content in the speed when the motor is running at low speed, enables the system to take into account both tracking performance and anti-disturbance performance, and can reduce the speed fluctuation range and harmonic content at the same time.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to an auto-disturbance rejection control method based on high-pass filtering linear feedback controller optimization. Background Art

[0002] Permanent magnet synchronous motors have the advantages of simple structure, low operating loss, and high power density. They are widely used and continuously developed in the field of low-speed servo. When running at low speed, the nonlinear factors such as friction, cogging torque, load torque fluctuation, and feedback element error of the permanent magnet synchronous motor itself have a more obvious influence, causing the motor to jitter when climbing, which seriously affects the control performance of the system. Therefore, when the permanent magnet synchronous motor runs at low speed, speed stability and control accuracy become important indicators of the low-speed servo system.

[0003] There are a large number of periodic disturbances in the motor control system, such as cogging torque, flux harmonics, voltage calibration error, etc. The disturbance frequency that the extended state observer can observe increases with the increase of bandwidth. However, increasing the bandwidth will introduce noise and reduce the stability of the system. Compared with the high-speed operation of the motor, the noise introduced by the bandwidth of the extended state observer has a greater impact on the speed fluctuation when the motor is running at a low speed, and the stability of the system is also lower. Summary of the invention

[0004] In order to solve the deficiencies mentioned in the above background technology, the object of the present invention is to provide an auto-disturbance rejection control method based on high-pass filtering linear feedback controller optimization.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] An active disturbance rejection control method based on high-pass filter linear feedback controller optimization, the active disturbance rejection control method comprising the following steps:

[0007] S1. Based on the motor motion equation, the state space equation is obtained, the total disturbance in the motor drive system is expanded into a new state variable, and a new state space equation is constructed according to the new state variable;

[0008] S2. Construct an extended state observer from the new state space equation, use the speed feedback value and total disturbance observed by the observer, and use the total disturbance to perform feedforward compensation;

[0009] S3. Design a high-pass filter and a linear feedback controller to track the speed reference signal and suppress the periodic fluctuation of the speed caused by the internal disturbance of the motor drive system.

[0010] Furthermore, the specific implementation of S1 is as follows:

[0011] The motion equation of the motor is expressed as:

[0012]

[0013] In the formula, ω r is the motor speed, J is the motor moment of inertia, n p is the number of motor pole pairs, ψ f is the permanent magnet flux of the motor, i q is the q-axis current, T L is the load torque of the motor, B is the viscosity coefficient of the motor, f 1 is the unknown disturbance in the motor drive system, where is the total disturbance of the motor system;

[0014] Expand the total disturbance f of the motor into a new state variable x 2 , the expression of constructing the new state space equation is:

[0015]

[0016] Where: x 1 , x 2 is the state variable of the system, b is the control gain, u is the control quantity of the speed loop of the motor drive system, y is the output of the motor drive system, and x 1 =ω r , x 2 =f,

[0017] Furthermore, the specific implementation of S2 is as follows:

[0018] According to the state space equation, the corresponding extended state observer for the second-order system is established as:

[0019]

[0020] Where: β 1 , β 2 is the gain of the extended state observer, z 1 , z 2 They are the state variables x 1 , x 2 The observed value of , e is the intermediate variable.

[0021] Furthermore, the bandwidth method is used in S2 to determine the gain of the observer:

[0022] make where β 1 ,β 2 is the gain of the extended state observer, ω bIt is the bandwidth of the extended state observer. The bandwidth of the extended state observer is determined according to the requirements of the system dynamic performance, thereby determining the gain of the observer, selecting the appropriate extended state observer gain, and using the total disturbance observed by the extended state observer for feedforward compensation.

[0023] Furthermore, the specific process in S3 is as follows:

[0024] A high-pass filter is used to extract the high-frequency signal in the speed feedback value, which is superimposed on the original feedback signal to eliminate high-frequency interference, suppress the periodic fluctuation of speed caused by various disturbances in the motor control system, and design a proportional controller to achieve non-steady-state static error control;

[0025] The control rate of the adopted ADRC is as follows:

[0026]

[0027] Where: * is a given speed, k p is the proportionality coefficient, k b and ω 0 is the gain and cutoff frequency of the high-pass filter, u 0 is the uncompensated control quantity.

[0028] Furthermore, the disturbance observation value z is obtained in S3 2 The transfer function between and the actual disturbance f:

[0029]

[0030] Then we get the following expression:

[0031]

[0032] Beneficial effects of the present invention:

[0033] The present invention improves the linear active disturbance rejection controller, combines the linear active disturbance rejection control algorithm with a high-pass filter, and superimposes the observed value of the speed with the original feedback after high-pass filtering to achieve speed control of the permanent magnet synchronous motor; compared with the traditional linear active disturbance rejection control, the harmonic content in the speed fluctuation can be effectively suppressed.

[0034] Therefore, the present invention can greatly improve the speed stability and anti-interference performance of the permanent magnet synchronous motor drive system at low speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0036] Figure 1 It is a flow chart of the active disturbance rejection control method of the present invention;

[0037] Figure 2 It is a schematic diagram of the active disturbance rejection control structure of the present invention;

[0038] Figure 3 is a Bode schematic diagram of the high-pass filter of the present invention;

[0039] Figure 4 It is a schematic diagram comparing the speed waveforms of the motor under the three control methods of the traditional PI control, the linear anti-disturbance control, and the linear anti-disturbance control based on the high-pass filter in the present invention;

[0040] Figure 5 It is a schematic diagram of the harmonic component analysis of the motor under three control methods: traditional PI control, linear anti-disturbance control, and linear anti-disturbance control based on a high-pass filter in the present invention. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] An auto-disturbance rejection control method based on high-pass filter linear feedback controller optimization, such as Figure 1 As shown, the following steps are included:

[0043] S1. 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;

[0044] S2, use the new state space equation in S1 to construct an extended state observer, and transform the total disturbance z observed by the extended state observer into 2 Perform feed-forward compensation;

[0045] S3. Design a high-pass filter and a linear feedback controller to track the speed reference signal and suppress the periodic fluctuation of the speed caused by the internal disturbance of the motor drive system.

[0046] Since the speed fluctuation caused by the internal disturbance of the motor has a strong periodicity, the present invention adopts a high-pass filter to compensate for the harmonic components in the speed, retaining the advantages of the traditional linear anti-disturbance controller that can effectively observe sudden disturbances and low-frequency disturbances and perform feedforward compensation, while realizing compensation for the speed fluctuation caused by the internal periodic disturbance of the system, that is, realizing high-performance control of the system.

[0047] The present invention further improves the traditional linear anti-disturbance control strategy to obtain stronger anti-disturbance performance. Figure 2 The auto-disturbance rejection control based on the optimization of the linear feedback controller with high-pass filter is explained and analyzed:

[0048] S1 Specific implementation method:

[0049] The motion equation of the motor is expressed as:

[0050]

[0051] In the formula, ω r is the motor speed, J is the motor moment of inertia, n p is the number of motor pole pairs, ψ f is the permanent magnet flux of the motor, i q is the q-axis current, T L is the load torque of the motor, B is the viscosity coefficient of the motor, f 1 is the unknown disturbance in the motor drive system. Among them, is the total disturbance of the motor system.

[0052] Expand the total disturbance f of the motor into a new state variable x 2 , the expression of constructing the new state space equation is:

[0053]

[0054] Where: x 1 , x 2 is the state variable of the system, b is the control gain, u is the control quantity of the speed loop of the motor drive system, y is the output of the motor drive system, and x 1 =ω r , x 2 =f,

[0055] Specific implementation of S2: According to the state space equation, the corresponding extended state observer is established for the second-order system as follows:

[0056]

[0057] Where: β 1 , β 2is the gain of the extended state observer, z 1 , z 2 They are the state variables x 1 , x 2 The observed value of , e is the intermediate variable.

[0058] A second-order extended state observer is selected. For the selection of the extended state observer gain, in order to ensure the stability and excellent performance of the system, the present invention adopts the bandwidth method to determine the observer gain: where β 1 ,β 2 is the gain of the extended state observer, ω b is the bandwidth of the extended state observer. The bandwidth of the extended state observer is determined according to the requirements of the system dynamic performance, thereby determining the gain of the observer. Select an appropriate extended state observer gain and use the total disturbance observed by the extended state observer for feedforward compensation.

[0059] like Figure 2 As shown in the figure, the extended state observer is used to observe the speed z 1 and the actual speed x 1 The difference integral of 2 , and then use the observed total disturbance for feedforward compensation to reduce the speed fluctuation. 1 , β 2 , which can realize that the state observer can track the uncertain state of the system at a very fast speed, z 1 →x 1 , z 2 →f. However, due to the limited bandwidth of the extended state observer, it can only effectively compensate for disturbances with lower frequencies or sudden torque changes.

[0060] The specific implementation of S3 is as follows:

[0061] A high-pass filter is used, and its transfer function is:

[0062]

[0063] Where: 0 is the cutoff frequency of the high-pass filter.

[0064] The Bode plot of a high-pass filter is shown in Figure 3 As shown, it allows higher frequencies than ω 0 The frequencies pass through and the lower frequencies are greatly attenuated, removing unnecessary low-frequency components in the signal or removing low-frequency interference.

[0065] The high-pass filter is used to extract the high-frequency signal in the speed feedback value, and it is superimposed with the original feedback signal at a certain gain to eliminate high-frequency interference and suppress the periodic fluctuation of speed caused by various disturbances in the motor control system. The proportional controller is designed to achieve non-steady-state static error control.

[0066] The control rate of the adopted ADRC is as follows:

[0067]

[0068] Where: * is a given speed, k p is the proportionality coefficient, k b and ω 0 is the gain and cutoff frequency of the high-pass filter, u 0 is the uncompensated control quantity.

[0069] After obtaining the uncertainty f, the system becomes a more ideal pure integration link and is no longer affected by uncertain disturbances.

[0070] The perturbed observation value z can be obtained 2 and the transfer function between the actual disturbance f

[0071]

[0072] The following expression can be obtained:

[0073]

[0074] It can be seen from equation (12) that the extended state observer is similar to a low-pass filter. Although the control rate (11) is only a proportional link, the active disturbance rejection controller can achieve zero-steady-state error control.

[0075] The following conclusions can be drawn:

[0076] Because the bandwidth of the extended state observer cannot be infinite, disturbances above a certain frequency cannot be observed. At the same time, when the bandwidth of the extended state observer increases, a large amount of noise will be introduced, causing system instability. Since there are often a large number of harmonic disturbances of fixed frequencies in the motion system, in order to suppress such harmonic disturbances, the present invention introduces a high-pass filter into the linear feedback controller.

[0077] Experimental results:

[0078] Figure 4 and Figure 5The speed waveform and its harmonic analysis are respectively shown when the given speed is 10r / min under the three control methods. Specifically, the speed fluctuation range under the traditional PI control method is 3-28r / min, corresponding to a first harmonic content of 8.716; the speed fluctuation range under the ESO control method is 2-35r / min, corresponding to a first harmonic content of 7.542; the speed fluctuation range under the ESO+HPF control method is 3-23r / min, corresponding to a first harmonic content of 4.182.

[0079] Depend on Figure 4 and Figure 5 It can be found that the method of the present invention can obtain a speed waveform with a smaller fluctuation range, and at the same time, the first harmonic content in the speed waveform is also small, which shows that the method of the present invention can effectively suppress harmonic disturbances in the motor system.

[0080] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. An auto-disturbance rejection control method based on high-pass filter linear feedback controller optimization, characterized in that: The active disturbance rejection control method comprises the following steps: S1. Obtain the state space equation based on the motion equation of the motor, 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; S2. An extended state observer is constructed by the new state space equation, and the speed feedback value and total disturbance observed by the extended state observer are used to perform feedforward compensation using the total disturbance; S3, design a high-pass filter and a linear feedback controller to track the speed reference signal and suppress the periodic fluctuation of the speed caused by the internal disturbance of the motor drive system; The specific implementation of S1 is as follows: The motion equation of the motor is expressed as: In the formula, ω r is the motor speed, J is the motor moment of inertia, n p is the number of motor pole pairs, ψ f is the permanent magnet flux of the motor, i q is the q-axis current, T L is the load torque of the motor, B is the viscosity coefficient of the motor, and f1 is the unknown disturbance in the motor drive system, where: is the total disturbance of the motor system; Expand the total disturbance f of the motor into a new state variable x2, and construct the expression of the new state space equation as follows: Where: x1, x2 are the state variables of the system, b is the control gain, u is the control quantity of the speed loop of the motor drive system, y is the output of the motor drive system, and x1 = ω r , x2=f, The specific implementation of S2 is as follows: According to the state space equation, the corresponding extended state observer for the second-order system is established as: Where: β1, β2 are the gains of the extended state observer, z1, z2 are the observed values ​​of the state variables x1, x2 respectively, and e is the intermediate variable; The specific process in S3 is as follows: A high-pass filter is used to extract the high-frequency signal in the speed feedback value, which is superimposed on the original feedback signal to eliminate high-frequency interference, suppress the periodic fluctuation of speed caused by various disturbances in the motor control system, and design a proportional controller to achieve steady-state static error control; The control rate of the adopted ADRC is as follows: Where: * is a given speed, k p is the proportionality coefficient, k b and ω0 are the gain and cutoff frequency of the high-pass filter, and u0 is the uncompensated control quantity.

2. The method for active disturbance rejection control based on high-pass filter linear feedback controller optimization according to claim 1, characterized in that: The bandwidth method is used in S2 to determine the gain of the observer: Let β1=2ω b ,β2=ω b 2 , where β1 and β2 are the gains of the extended state observer, ω b It is the bandwidth of the extended state observer. The bandwidth of the extended state observer is determined according to the requirements of the system dynamic performance, thereby determining the gain of the observer, selecting the appropriate extended state observer gain, and using the total disturbance observed by the extended state observer for feedforward compensation.

3. The method for auto-disturbance rejection control based on high-pass filter linear feedback controller optimization according to claim 2, characterized in that: The transfer function between the disturbance observation value z2 and the actual disturbance f is obtained in S3: Then we get the following expression:

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