The Active Disturbance Rejection Control

This chapter analyzes the active disturbance rejection control closed loop (ADRC) composed of the tracking differentiator (TD), extended state observer (ESO) and ESO-based output feedback control, where the TD is used to recover the derivative of the reference signal and the ESO is used to recover the system state and the total disturbance. The linear ESO is used for the state and total disturbance estimation and the functions in the feedback control are also linear. If the uncertainty is the external disturbance only, the ADRC method also has the advantage of needing less information for the external disturbance than the internal model principle (IMP). The efficiency of the ADRC in dealing with vast uncertainty is demonstrated by simulations. The chapter discusses the ADRC to boundary feedback stabilization for a one-dimensional wave equation with boundary disturbance and distributed anti-damping, as an illustrative application of the ADRC to systems described by partial differential equations.