Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method

Wu, Dan; Chen, Ken

doi:10.1109/tie.2012.2203777

Cited by 133 publications

(65 citation statements)

References 18 publications

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“…(3) Some ADRC applications were limited to the control system with an explicit cascaded integral system. For example, the nonlinear ADRC has been applied to the fast tool servo systems [14,31], which are cascaded integral systems with two stages.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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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“…Consider a system with the linear plant given by equations (14) and (15) 22 and v n1 = 6.5 rad/s. In order to agree with our intuition, the Nyquist plots of W(jv) and 21/N 1 (A, v n1 ) are shown in Figure 10, and the intersection 1 denotes the desired oscillation (A n1 , v n1 ).…”

Section: Hysteresis Compensationmentioning

confidence: 99%

Oscillation design of sampling proportional–derivative sliding-mode systems for linear plants with hysteresis

Shen

2016

Advances in Mechanical Engineering

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This article deals with the self-sustained oscillation appearing in the sliding-mode system. The oscillation provides considerable robust performance and, meanwhile, leads to detrimental effects such as the reduced control precision, mechanical wear, and resonance. A graphical method is introduced to design the sliding-mode controller with proportional-derivative terms. The method indicates how to determine the proportional-derivative coefficients and the desired oscillation frequency and amplitude for the stability of systems. The analysis shows that the zero-order holder plays an important role in the robustness of systems which can be improved by shorter sampling periods. The influences of the hysteresis on the oscillations are also discussed, and a method of tuning the coefficients of proportional-derivative terms is used to compensate the hysteresis. The first simulation shows the design processes of the graphical method in a specific system, and the second simulation confirms the validity of the method of hysteresis compensation. The design process is also demonstrated via the experiment on an inverted pendulum.

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“…However, the amount of noise was substantial when the differential was estimated. Wu and Chen 21 and Lin et al 22 regarded the inertia filtering function as a known part of a system, and thus, the number of parameters that should be set was reduced. Nevertheless, noise was still not eliminated in this system because the power function was used in ADRC.…”

Section: Introductionmentioning

confidence: 99%

Pitching axis control for a satellite camera based on a novel active disturbance rejection controller

Liu

Jin

Zhu

et al. 2017

Advances in Mechanical Engineering

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The pitching axis of a satellite camera is controlled under the weightless environment. A novel active disturbance rejection controller is designed to eliminate the influences of the pitching axis. The novel active disturbance rejection controller is designed based on a new nonlinear function, and thus, this function is first established. The function exhibits better continuity and smoothness than previously available functions, hence, it can effectively improve the high-frequency flutter phenomenon. Therefore, the novel active disturbance rejection controller based on the new nonlinear function can eliminate disturbances of the pitching axis. The novel active disturbance rejection controller is composed of a tracking differentiator, a novel extended state observer, and a novel nonlinear state error feedback. The tracking differentiator is used to arrange the transient process. Nonlinear dynamics, model uncertainty, and external disturbances are extended to a new state. The novel extended state observer is utilized to observe this state. The overtime variation of the system can be predicted and compensated using the novel extended state observer. The novel nonlinear state error feedback is adopted to restrain the residual errors of the system. Finally, simulation experiments are performed, and results show that the novel active disturbance rejection controller exhibits better performance than the traditional active disturbance rejection controller.

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Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method

Cited by 133 publications

References 18 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

Oscillation design of sampling proportional–derivative sliding-mode systems for linear plants with hysteresis

Pitching axis control for a satellite camera based on a novel active disturbance rejection controller

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