On the stability and convergence rate analysis for the nonlinear uncertain systems based upon active disturbance rejection control
Yongshuai Wang, Junjie Liu, Zengqiang Chen, Mingwei Sun, Qinglin Sun
Abstract
Summary Emerging as an effective control method, active disturbance rejection control technique (ADRC) can well deal with disturbances and uncertainties. Then focusing on the general nonlinear uncertain systems, this article illustrates the relation among stability, uncertainties, and parameters of linear ADRC controller when perturbation occurs in control input. On the one hand, if the reference and uncertainties satisfy particular conditions, the estimation and output errors are proved to be ultimately and globally bounded by Lyapunov function and Gronwall‐Bellman inequality, together with rigorous mathematical deducing and simulation verification. On the other hand, a globally and asymptotically stable result is obtained applying Lyapunov method and Cauchy inequality, and the convergence rate can be estimated when uncertainties exist. Besides, numerical simulations are carried out to fully display the correctness and dependability of results and proofs.