An improved fractional-order active disturbance rejection position angle controller and its control method

Abstract

This invention discloses a position angle controller and its control method based on an improved fractional-order active disturbance rejection (ADRROC) module. The position angle controller includes a TD module, a FO-ESO module, and a FO-NLSEF module. The output of the TD module is connected to the input of the FO-NLSEF module. The output of the FO-NLSEF module is connected to the controlled object and the FO-ESO module. The input of the FO-ESO module is connected to the controlled object, and its output is connected to the FO-NLSEF module. This invention utilizes improved ADRROC technology to achieve motor position angle control. By improving the convergence, continuity, and differentiability of the nonlinear function and adding a fractional-order module, the performance of the ADRROC position angle controller is improved and enhanced.

Description

Technical Field

[0001] This invention belongs to the field of controller design technology, and relates to the design of position angle controllers, specifically to an improved fractional-order active disturbance rejection position angle controller and its control method. Background Technology

[0002] Although traditional active disturbance rejection controllers have shown strong robustness and adaptability, they still have many shortcomings, such as the unresolved high-frequency chatter problem near the origin and insufficient active disturbance rejection capability, which will reduce the control performance of the active disturbance rejection controller.

[0003] The nonlinear function is the core component of the active disturbance rejection controller (ADRC), therefore, designing a reasonable nonlinear function is an important part of the design process. The following factors should be considered when designing the nonlinear function:

[0004] (1) It exhibits good convergence near the origin;

[0005] (2) It is continuous at the origin and the function value is 0.

[0006] Conventional active disturbance rejection controllers use the fal(·) function, whose expression is as follows:

[0007]

[0008] The characteristics of this nonlinear function are as follows: the magnitude of α affects the degree of nonlinearity of the fal(·) function; the nonlinearity is strongest when α = 0, and the linearity is strongest when α = 1. The magnitude of δ affects the length of the linear segment interval of the fal(·) function. Therefore, when the input is an error signal, the parameters of the fal(·) function can be adjusted so that the feedback loop produces a smaller feedback gain when the error is large, and a larger feedback gain when the error is small, thus ensuring the stability of the system while enabling the system to reach stability quickly.

[0009] However, while the above fal(·) function is continuous, it is not differentiable. If the error varies within the linear segment, the oscillation effect is eliminated. If the value of δ is small, the abrupt change in the derivative will lead to a deterioration in system performance, and cannot avoid high-frequency flutter, or even generate larger oscillations.

[0010] Therefore, a new technical solution is needed to solve the above problems. Summary of the Invention

[0011] Purpose of the invention: In order to overcome the shortcomings of the existing technology, an improved fractional-order active disturbance rejection (ADRR) position angle controller and its control method are provided. The improved ADRR is used to realize the position angle control of the motor. By improving the convergence, continuity and differentiability of the nonlinear function and adding a fractional-order module, the performance of the ADRR position angle controller is improved and enhanced. It has better high-frequency chatter resistance and better anti-interference capability than the traditional ADRR controller.

[0012] Technical Solution: To achieve the above objectives, this invention provides a position angle controller based on an improved fractional-order active disturbance rejection system, comprising a TD (Tracking Differential Controller) module, a FO-ESO (Fractional-Order Extended State Observer) module, and a FO-NLSEF (Fractional-Order Nonlinear Feedback Control Law) module. The output of the TD module is connected to the input of the FO-NLSEF module, the output of the FO-NLSEF module is connected to the controlled object and the FO-ESO module, and the input of the FO-ESO module is connected to the controlled object, while its output is connected to the FO-NLSEF module.

[0013] Furthermore, the algorithm expression of the FO-ESO module is as follows:

[0014]

[0015] Where Z1 is the tracking signal of the input signal Y, ε1 is the observation error, Z2 is the differential signal of the input signal Y, Z3 is the observation signal of the total disturbance of the active disturbance rejection controller; u is the control output, β1, β2, β3 are the gains of the fractional extended state observer (FO-ESO), α1, α2, α3 are nonlinear factors, δ is the linear interval width of the newfal(·) function, and b is the compensation coefficient.

[0016] Furthermore, the algorithm expression of the FO-NLSEF module is as follows:

[0017]

[0018] Where: e0, e1, e2 are the derivative of the error, the error itself, and the derivative of the error, respectively; a1, a2, a3 are nonlinear factors; β4, β5, β6 are the integral gain of the error, the gain of the error itself, and the gain of the derivative of the error, respectively.

[0019] Furthermore, the expression for the newfal() function in the FO-ESO module and the FO-NLSEF module is as follows:

[0020]

[0021] in,

[0022] The present invention also provides a control method based on an improved fractional-order active disturbance rejection position angle controller, comprising the following steps:

[0023] S1: Input the given signal X into the input terminal of the TD module;

[0024] S2: The output terminals of the TD module output tracking signals X1 and X2, and the output terminals of the FO-ESO module output signals Z1, Z2 and Z3.

[0025] The tracking signal X1 is compared with the Z1 signal output by the FO-ESO module to obtain the system error e1, which is then transmitted to the FO-NLSEF module. The tracking signal X2 is compared with the Z2 signal output by the FO-ESO module to obtain the system error e2, which is also transmitted to the FO-NLSEF module. The signal T is obtained by dividing the Z3 signal output by the FO-ESO module by the compensation coefficient b and comparing it with the signal u0 output by the FO-NLSEF module. L , will signal T L Transmitted to the output of the controlled object; simultaneously, signal T L Multiply by the compensation coefficient b and output to the FO-ESO module to compensate for the total disturbance.

[0026] Based on the above scheme, the innovations of this invention can be summarized as follows: a novel nonlinear (newfal(·)) function is designed to overcome the high-frequency flutter problem near the origin of the traditional function; the fractional extended state observer (FO-ESO) can accurately predict and compensate for the real-time changes in the position angle; and the fractional nonlinear feedback control law (FO-NLSEF) can effectively improve the anti-interference capability of the system.

[0027] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0028] 1. Compared with existing nonlinear functions, the novel nonlinear function designed in this invention has better continuity, differentiability, and smoothness near the origin. Therefore, the improved active disturbance rejection controller designed based on this novel nonlinear function has better high-frequency chatter suppression capability and better active disturbance rejection capability than traditional controllers.

[0029] 2. The novel active disturbance rejection controller of the present invention does not rely on an accurate model of the controlled object and can replace the traditional active disturbance rejection control technology.

[0030] 3. This invention employs a tracking differential controller to process the reference input, a fractional extended state observer (FO-ESO) to estimate system state disturbances, model uncertainties, and external disturbances, and a fractional nonlinear feedback control law (FO-NLSEF) to process the controller output signal, thereby enabling good control of the controlled object.

[0031] 4. The controller of the present invention has superior performance such as high stability and strong anti-interference ability for the controlled object, and has high engineering practical value. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the control signal connection of a position angle controller based on an improved fractional-order active disturbance rejection system according to the present invention;

[0033] Figure 2 This is a schematic diagram of the structure of a fractional-order extended state observer;

[0034] Figure 3 This is a schematic diagram of the fractional-order nonlinear feedback control law;

[0035] Figure 4 The graphs show the response curves of the two controllers to a step signal of 100 rad / s applied at 3s.

[0036] Figure 5 The graph shows the response curves of the two controllers to a step signal of 500 rad / s applied at 3s.

[0037] The markings in the diagram mean: 1-Tracking differential controller-TD, 2-Fractional order nonlinear feedback control law-FO-NLSEF, 3-Fractional order extended state observer-FO-ESO, 4-Controlled object. Detailed Implementation

[0038] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0039] like Figure 1 As shown, the present invention provides a position angle controller based on an improved fractional-order active disturbance rejection system, including a TD module 1, an FO-ESO module 3, an FO-NLSEF module 2, and a controlled object 4. The output terminal of the TD module 1 is connected to the input terminal of the FO-NLSEF module 2. The output terminal of the FO-NLSEF module 2 is connected to the controlled object 4 and the FO-ESO module 3. The input terminal of the FO-ESO module 3 is connected to the controlled object 4, and the output terminal is connected to the FO-NLSEF module 2.

[0040] like Figure 2The diagram shows the structure of the fractional-order extended state observer, specifically the structure of FO-ESO module 3, which is the core of the controller in this invention. It expands the nonlinear factors of the position angle, model uncertainties, and internal and external disturbances into a new state, which is then observed in real time through FO-ESO module 3.

[0041] Reference Figure 2 The algorithm expression for the FO-ESO module is as follows:

[0042]

[0043] Where Z1 is the tracking signal of the input signal Y, ε1 is the observation error, Z2 is the differential signal of the input signal Y, Z3 is the observation signal of the total disturbance of the active disturbance rejection controller; u is the control output, β1, β2, β3 are the gains of the fractional extended state observer (FO-ESO), α1, α2, α3 are nonlinear factors, δ is the linear interval width of the newfal(·) function, and b is the compensation coefficient.

[0044] like Figure 3 The diagram shows the structure of the fractional-order nonlinear feedback control law, which is the structure of FO-NLSEF module 2. FO-NLSEF module 2 uses a nonlinear state error feedback control law to perform nonlinear calculations on the proportional, derivative, and integral of the error signal in order to improve the control accuracy and robustness of the system.

[0045] Reference Figure 3 The algorithm expression for the FO-NLSEF module is as follows:

[0046]

[0047] Where: e0, e1, e2 are the derivative of the error, the error itself, and the derivative of the error, respectively; a1, a2, a3 are nonlinear factors; β4, β5, β6 are the integral gain of the error, the gain of the error itself, and the gain of the derivative of the error, respectively.

[0048] Based on the above scheme, this embodiment also provides a control method based on an improved fractional-order active disturbance rejection controller, referring to... Figure 1 It includes the following steps:

[0049] S1: Input the given signal X to the input terminal of TD module 1;

[0050] S2: The output terminal of TD module 1 outputs tracking signal X1 and tracking signal X2, and the output terminal of FO-ESO module 3 outputs signal Z1, signal Z2 and signal Z3.

[0051] The tracking signal X1 is compared with the Z1 signal output by FO-ESO module 3 to obtain the system error e1, which is then transmitted to FO-NLSEF module 2. The tracking signal X2 is compared with the Z2 signal output by FO-ESO module 3 to obtain the system error e2, which is also transmitted to FO-NLSEF module 2. The signal T is obtained by dividing the Z3 signal output by FO-ESO module 3 by the compensation coefficient b and comparing it with the signal u0 output by FO-NLSEF module 2. L , will signal T L Transmitted to the output of the controlled object; simultaneously, signal T L Multiply by the compensation coefficient b and output to FO-ESO module 3 to compensate for the total disturbance.

[0052] In order to verify the actual effect of the present invention, in this embodiment, the position angle controller provided by the present invention and the existing position angle controller (Reference [1] - Liu Bingyou, Zhu Chang'an, Guo Xingzhong, Meng Yibo. Rotor position angle control method of permanent magnet synchronous motor based on improved ADRC) are used to simulate the position angle of permanent magnet synchronous motor respectively. The simulation uses the same parameters, and the parameters are shown in Table 1.

[0053] Table 1 Parameters of Active Disturbance Rejection Controller

[0054]

[0055]

[0056] During simulation, the improved active disturbance rejection controller provided by this invention was compared with the active disturbance rejection controller designed in reference [1], and the results were as follows: Figure 4 and Figure 5 The response curves shown are comparative data. Figure 4 These are the response curves of the two controllers when a step signal of 100 rad / s is suddenly applied at 3s. Figure 5 These are the response curves of the two controllers when a step signal of 500 rad / s is suddenly applied at 3s.

[0057] from Figure 4 and Figure 5 It can be seen that the controller designed in this invention has strong anti-interference ability and is suitable for occasions with high interference intensity.

Claims

1. A position angle controller based on an improved fractional order active disturbance rejection controller, characterized in that, It includes a TD module, a FO-ESO module, and a FO-NLSEF module. The output of the TD module is connected to the input of the FO-NLSEF module. The output of the FO-NLSEF module is connected to the controlled object and the FO-ESO module. The input of the FO-ESO module is connected to the controlled object, and its output is connected to the FO-NLSEF module. The algorithm expression for the FO-ESO module is as follows: ； in, Input signal The tracking signal For observation error, It is the input signal The differential signal, The observed signal of the total disturbance for the active disturbance rejection controller; To control the output, , , Gain of the fractional-order extended state observer (FO-ESO) , , It is a non-linear factor. yes The width of the linear interval of the function. It is the compensation coefficient; The algorithm expression for the FO-NLSEF module is as follows: ； wherein: respectively are a differential of the error, an error, and a differential of the error; is a non-linear factor; respectively are a gain of an integral of the error, a gain of the error, a gain of a differential of the error; In the FO-ESO module and the FO-NLSEF module The expression of the function is: ； Here, tanh() represents a function.

2. The control method based on the improved fractional order active disturbance rejection position angle controller according to claim 1, wherein, Includes the following steps: S1: Input the given signal X into the input terminal of the TD module; S2: the output of the TD module outputs a tracking signal and the tracking signal , the FO-ESO module output outputs a signal, a signal and a signal; Tracking signal With the output of the FO-ESO module By comparing the signals, the system error can be obtained. And transmit it to the FO-NLSEF module; track the signal Signals output by the FO-ESO module By comparison, the systematic error is obtained. And transmit it to the FO-NLSEF module; based on the signal output by the FO-ESO module Divide by compensation coefficient The value and the signal output from the FO-NLSEF module output terminal The signal obtained by comparison , will signal Transmit the signal to the output of the controlled object; simultaneously, transmit the signal... Multiply by the compensation coefficient Output to the FO-ESO module.

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