Fractional active disturbance rejection control

Li, Dazi; Ding, Pan; Gao, Zhiqiang

doi:10.1016/j.isatra.2016.01.022

Cited by 86 publications

(59 citation statements)

References 29 publications

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“…In it, 1 , 2 are the system state and its first derivative, respectively; V is the control reference; ℎ 0 is the filtering factor; is the time ruler; sign is a sign function; and ℎ is a constructed nonlinear function shown in (2) [16,32].…”

Section: The Adrc Control Methodsmentioning

confidence: 99%

“…In it, is the error between the estimated state and system output; 1 , 2 , and 3 are the estimations of the system states ; 01 , 02 , and 03 are gain coefficients; is the control signal; is the system output; and are the parameters of function; and 1 are the outputs of function; is another constructed nonlinear function shown in (4) [16,32].…”

Section: The Adrc Control Methodsmentioning

confidence: 99%

“…After this transformation, the proposed algebraic substitution method and its structure can convert (32) into to a cascaded integral system according to ( (8)- (17)), which will not be repeated here. Then, the ADRC controller can be directly and easily used to control the converted cascaded integral system.…”

Section: Application In the Oscillation Control Of A Flexible Armmentioning

confidence: 99%

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An ADRC Method for Noncascaded Integral Systems Based on Algebraic Substitution Method and Its Structure

Huang

Liu

et al. 2018

Mathematical Problems in Engineering

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The Active Disturbance Rejection Control (ADRC) prefers the cascaded integral system for a convenient design or better control effect and takes it as a typical form. However, the state variables of practical system do not necessarily have a cascaded integral relationship. Therefore, this paper proposes an algebraic substitution method and its structure, which can convert a noncascaded integral system of PID control into a cascaded integral form. The adjusting parameters of the ADRC controller are also demonstrated. Meanwhile, a numerical example and the oscillation control of a flexible arm are demonstrated to show the conversion, controller design, and control effect. The converted system is proved to be more suitable for a direct ADRC control. In addition, for the numerical example, its control effect for the converted system is compared with a PID controller under different disturbances. The result shows that the converted system can achieve a better control effect under the ADRC than that of a PID. The theory is a guide before practice. This converting method not only solves the ADRC control problem of some noncascaded integral systems in theory and simulation but also expands the application scope of the ADRC method.

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Section: The Adrc Control Methodsmentioning

confidence: 99%

Section: The Adrc Control Methodsmentioning

confidence: 99%

Section: Application In the Oscillation Control Of A Flexible Armmentioning

confidence: 99%

See 1 more Smart Citation

An ADRC Method for Noncascaded Integral Systems Based on Algebraic Substitution Method and Its Structure

Huang

Liu

et al. 2018

Mathematical Problems in Engineering

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“…Then, he constructed an approximated synthetic function fhan for the time‐optimal control, as shown in Equation . (–) This function can quickly track an input signal without overshoot and chattering and can produce a good differential signal, which can be expressed as

({, \begin{array}{l} italicfhan = - ({, \begin{array}{l} italicrsign false(a false) & (||, a) > d \\ r \frac{a}{d} & (||, a) \leq d \end{array}) \\ d = {rh}_{0} \\ d_{0} = h_{0} d \\ y = x_{1} false(t false) + h_{0} x_{2} false(t false) \\ a_{0} = \sqrt{d^{2} + 8 r (||, y)} \\ a = ({, \begin{array}{l} x_{2} false(t false) + \frac{a_{0} - d}{2} italicsign false(y false) & (||, y) > d_{0} \\ x_{2} false(t false) + \frac{y}{h_{0}} & (||, y) \leq d_{0} . \end{array}) \end{array})

…”

Section: The Data‐driven Td Methods and Its Extensionmentioning

confidence: 99%

A data‐driven approximate solution to the model‐free HJB equation

Huang

Zhang

et al. 2017

Optim Control Appl Methods

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Summary It is generally impossible to analytically solve the Hamilton‐Jacobi‐Bellman (HJB) equation of an optimal control system. With the coming of the big‐data era, this paper first derives a new data‐driven and model‐free Hamilton function for the HJB equation. Then, a data‐driven tracking differentiator method is proposed to solve the Hamilton function. Finally, the simulation for a classic example shows that the optimal control policy can be approximated with the proposed method. Thus, an online data‐driven model‐free approximate solution to the HJB equation is achieved. This method is only driven by the measured system states. All other variables and derivatives can be derived from the data‐driven model‐free Hamilton function and tracking differentiator. The method has a complete mathematical support and works like a controller. It does not need neural networks and has no training or iterative convergence problem. Thus, this paper adds an online data‐driven model‐free method to the existing literature on the approximate solution to the HJB equation.

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“…This has been proved to be an effective tool in stabilizing the one dimensional PDEs, multi‐dimensional PDEs, stochastic differential equations, among many others. The generalization of ADRC to the systems described by fractional differential equations can also be found in recent works but the ADRC for fractional PDEs has not yet been addressed, which motivates this study.…”

Section: Introductionmentioning

confidence: 99%

Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance

Zhou

Guo

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper addresses the Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control subject to the control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted for developing the control law. A state‐feedback scheme is designed to estimate the disturbance by constructing two auxiliary systems: One is to separate the disturbance from the original system to a Mittag‐Leffler stable system and the other is to estimate the disturbance finally. The proposed control law compensates the disturbance using its estimation and stabilizes system asymptotically. The closed‐loop system is shown to be Mittag‐Leffler stable and the constructed auxiliary systems in the closed loop are proved to be bounded. This is the first time for ADRC to be applied to a system described by the fractional partial differential system without using the high gain.

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Fractional active disturbance rejection control

Cited by 86 publications

References 29 publications

An ADRC Method for Noncascaded Integral Systems Based on Algebraic Substitution Method and Its Structure

An ADRC Method for Noncascaded Integral Systems Based on Algebraic Substitution Method and Its Structure

A data‐driven approximate solution to the model‐free HJB equation

Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance

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