Absolute stability analysis of non-linear active disturbance rejection control for single-input–single-output systems via the circle criterion method

Abstract This paper presents a practical verification of an Active Disturbance Rejection Control (ADRC) method in governing a multidimensional system. The experiments were conducted on a two degrees of a freedom planar manipulator with only partial knowledge about the mathematical model of the plant. This multi input multi output system was controlled with a set of two, independent, single input single output ADRC controllers, each regulating one of the manipulator degree of freedom. Modeling uncertainty (nonlinearities, cross-coupling effects, etc.) and external disturbances were assumed to be a part of the disturbance, to be estimated with an observer and cancelled on-line in the control loop. The ADRC robustness was experimentally compared with the results obtained from using two decentralized, classic PID controllers. Both control methods were tested under various conditions, e.g. changing the inertial parameters of the plant. Significantly better results, in terms of parametric robustness, have been reported for the ADRC approach.

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Absolute stability analysis of nonlinear active disturbance rejection control for electromagnetic valve actuator system via linear matrix inequality method

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651818775900 ◽

2018 ◽

Vol 232 (9) ◽

pp. 1134-1145

Author(s):

Da Shao ◽

Sichuan Xu ◽

Aimin Du

Keyword(s):

Stability Analysis ◽

Linear Matrix Inequality ◽

Disturbance Rejection ◽

Absolute Stability ◽

Linear Matrix ◽

Active Disturbance Rejection Control ◽

Matrix Inequality ◽

Single Input Single Output ◽

Active Disturbance Rejection ◽

Disturbance Rejection Control

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

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Nonlinear Active Disturbance Rejection Control of VGT-EGR System in Diesel Engines

Energies ◽

10.3390/en13205331 ◽

2020 ◽

Vol 13 (20) ◽

pp. 5331

Author(s):

Pingyue Zhang ◽

Jingyu Zhang ◽

Yingshun Li ◽

Yuhu Wu

Keyword(s):

Disturbance Rejection ◽

External Disturbance ◽

Intake Manifold ◽

Active Disturbance Rejection Control ◽

Single Input Single Output ◽

Single Output ◽

Active Disturbance Rejection ◽

Disturbance Rejection Control ◽

Nonlinear Extended State Observer ◽

Intake Manifold Pressure

In this paper, a nonlinear active disturbance rejection control (NLADRC) strategy based on nonlinear extended state observer (NLESO) is proposed to solve the unmodeled dynamics, coupling and disturbance due to change of working point in the variable geometry turbine (VGT) and exhaust gas recirculation (EGR) system, so as to achieve accurate control of intake manifold pressure and mass air flow in a diesel engine. To achieve decoupling, the double-input double-output (DIDO) VGT-EGR system is decomposed into two single-input single-output (SISO) subsystems, and each subsystem has a separate nonlinear active disturbance rejection controller. At the same time, the convergence proof of the designed NLESO is also given theoretically. Finally, the NLADRC controller is compared with linear active disturbance rejection controller and proportional–integral–derivative (PID) controller. Through simulation, it is indicated that the proposed NLADRC controller has better transient response performance, resistance to external disturbance and robustness to the change of engine operating point.

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Novel Active Disturbance Rejection Control Based on Nested Linear Extended State Observers

Applied Sciences ◽

10.3390/app10124069 ◽

2020 ◽

Vol 10 (12) ◽

pp. 4069

Author(s):

Wameedh Riyadh Abdul-Adheem ◽

Ahmad Taher Azar ◽

Ibraheem Kasim Ibraheem ◽

Amjad J. Humaidi

Keyword(s):

Disturbance Rejection ◽

Estimation Error ◽

Tracking Error ◽

Rate Of Change ◽

Estimation Accuracy ◽

Active Disturbance Rejection Control ◽

Extended State ◽

Single Input Single Output ◽

Active Disturbance Rejection ◽

Disturbance Rejection Control

In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended State Observer (LESO) used in Conventional ADRC (C-ADRC) with a nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized disturbance. Increasing the bandwidth improves the estimation accuracy which may tolerate noise and conflict with H/W limitations and the sampling frequency of the system. Therefore, an alternative scenario is offered without increasing the bandwidth of the inner-loop LESO provided that the rate of change of the generalized disturbance estimation error is upper bounded. This was achieved by the placing of an outer-loop LESO in parallel with the inner one that estimates and eliminates the remaining generalized disturbance originating from the inner-loop LESO due to bandwidth limitations. The stability of LESO and nested LESO was investigated using Lyapunov stability analysis. Simulations on uncertain nonlinear single-input-single-output (SISO) system with time-varying exogenous disturbance revealed that the proposed nested LESO could successfully deal with a generalized disturbance in both noisy and noise-free environments, where the Integral Time Absolute Error (ITAE) of the tracking error for the nested LESO was reduced by 69.87% from that of the LESO.

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