On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics

2007 ◽  
Author(s):  
Qing Zheng ◽  
Linda Q. Gaol ◽  
Zhiqiang Gao
Keyword(s):  
Stability Analysis ◽  
Disturbance Rejection ◽  
Time Varying ◽  
Active Disturbance Rejection Control ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control

A Novel Time-Varying Spectrum Based Approach to Active Disturbance Rejection Control

2017 ◽  
Author(s):  
Zhiqiang Pu ◽  
Xiangmin Tan ◽  
Ruyi Yuan ◽  
Jianqiang Yi
Keyword(s):  
Disturbance Rejection ◽  
Parameter Tuning ◽  
Stability And Convergence ◽  
Time Varying ◽  
Active Disturbance Rejection Control ◽  
Loop Control ◽  
Active Disturbance Rejection ◽  
State Dependent ◽  
Disturbance Rejection Control ◽  
Improved Performance

This paper presents a comprehensive framework for developing a novel time-varying spectrum based active disturbance rejection control (TVS-ADRC) technique. It complements conventional linear or nonlinear ADRC by introducing time-varying components, including time-varying extended state observer, time-varying tracking differentiator, and time-varying feedback, to offer better design flexibility and improved performance in command filtering, disturbance observation, and closed-loop control. First, skeleton stability and convergence analysis is introduced based on differential algebraic spectral theory. Then parameter tuning is categorized into two time-varying principles: a time-based profile and a state-dependent function, and a unified parameterization approach is given by assigning time-varying eigenvalues. Typical applications are pointed out which demonstrate great advantages of TVS-ADRC in consideration of varying plant or environment features and physical limits in practical systems. Challenges and future work for the TVS-ADRC technique are also summarized in the end.

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

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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