On asymptotic stability for nonlinear ADRC based control system with application to the ball-beam problem

Jie Li, Xiaohui Qi, Yuanqing Xia, Zhiqiang Gao

Abstract: Active disturbance rejection control (ADRC) is a relatively new but very practical technology, which shows much promise in replacing PID as industry workhorse with unmistakable advantage in performance and practicality. This paper mainly concerns with a problem of fundamental nature: the asymptotic stability of nonlinear ADRC based control system, and applies ADRC to the ball-beam system to check the presented methods and the performance of ADRC. Firstly, the general nonlinear ADRC algorithm is introduced; then the asymptotical stability problem is transformed into that of determining whether a matrix or interval matrix is Hurwitz; finally the results of theoretical analysis are verified in simulations and experiments using the ball-beam platform, demonstrating the convenience and effectiveness of the proposed methods, in addition to the good performance of ADRC.