This paper focuses on the stability analysis of the active disturbance rejection control (ADRC)for a class of uncertain systems.To overcome the difficulty of defining a reasonable Lyapunov function and setting limitat...This paper focuses on the stability analysis of the active disturbance rejection control (ADRC)for a class of uncertain systems.To overcome the difficulty of defining a reasonable Lyapunov function and setting limitations of system parameters,the converse Lyapunov theorem and the disturbance theory are employed.This paper proves that the estimation error of the extended state observer (ESO)and the tracking error of the closed-loop system using ADRC are uniformly ultimately bounded and monotonously diminishing with the increase of their respective bandwidth,so that the stability of the ADRC system could be performed.In order to further illustrate the relationship between the stability range and bandwidths,it analyzes quantitatively the performance of ESO and ADRC based on the root locus and the step response.Finally,an example based on a typical control system is carried out,and simulation results verify the theoretical analysis proved in this paper.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61304026
文摘This paper focuses on the stability analysis of the active disturbance rejection control (ADRC)for a class of uncertain systems.To overcome the difficulty of defining a reasonable Lyapunov function and setting limitations of system parameters,the converse Lyapunov theorem and the disturbance theory are employed.This paper proves that the estimation error of the extended state observer (ESO)and the tracking error of the closed-loop system using ADRC are uniformly ultimately bounded and monotonously diminishing with the increase of their respective bandwidth,so that the stability of the ADRC system could be performed.In order to further illustrate the relationship between the stability range and bandwidths,it analyzes quantitatively the performance of ESO and ADRC based on the root locus and the step response.Finally,an example based on a typical control system is carried out,and simulation results verify the theoretical analysis proved in this paper.
基金Supported by National Natural Science Foundation of China （60872046） the Key Discipline Development Program of Beijing Municipal Commission （XK100080537）
