Asymptotic Stability of Active Disturbance Rejection Control for Linear SISO Plants with Low Observer Gains

This paper theoretically investigates the closed-loop performance of active disturbance rejection control (ADRC) on a third-order linear plant with relative degree 3, subject to a class of exogenous disturbances. While PID control cannot be guaranteed to be capable of stabilizing such plants, ADRC offers a model-free alternative. However, many existing works on ADRC consider the observer gains to be taken arbitrarily large, in order to guarantee desired performance, such as works which consider parameterizing ADRC by bandwidth. This work finds that, for constant exogenous disturbances, arbitrary eigenvalue assignment is possible for the closed-loop system under linear ADRC, thus guaranteeing the existence of an ADRC controller for desired performance without taking any gains arbitrarily large. We also find that stabilization is possible when the exogenous disturbance is stable, and show how ADRC can recover the performance of model-based observers. We demonstrate aspects of the resulting closed-loop systems under ADRC in simulations.