On the Robust Stability of Active Disturbance Rejection Control for SISO Systems

Active disturbance rejection control (ADRC) is a new practical control technique, which can integrally and effectively deal with various nonlinearities, uncertainties and disturbances (collectively called the total disturbance throughout this paper). This paper addresses the problem of the robust stability analysis and design of linear and nonlinear ADRC for SISO systems. Firstly, a nonlinear ADRC-based control system with total disturbances is transformed into a perturbed indirect Lurie system. Then, the Popov–Lyapunov method is used to study its global or local stability and derive the robust stability bound on allowable total disturbance. Furthermore, if the total disturbance of the system is known, an estimated region of attraction can be obtained. In addition, the paper illustrates how the modeled linear dynamics can be easily integrated into ADRC to improve both the performance and stability characteristics. The above approach can also be extended to a linear ADRC-based control system. A numeral example is presented to verify the convenience and practicability of the proposed method.