On comparison between Smith Predictor and Predictor Observer based ADRCs for nonlinear uncertain systems with output delay

This paper considers the control problem for a class of nonlinear uncertain systems with output delay. The methods of the predictive active disturbance rejection control (ADRC) are employed to achieve desired performance against external disturbance, unknown nonlinear dynamics and output delay. The comparison between two typical predictive ADRCs, i.e., Predictor Observer based ADRC and Smith Predictor based ADRC, is studied to provide some guidelines of using these ADRCs. The comparison includes three aspects, i.e., the stability, the estimation errors and the capability of dealing with the uncertainty. It is proven that stable nominal model is necessary for the stability of the closed-loop system with Smith Predictor based ADRC while not being required for that with Predictor Observer based ADRC. In addition, these two modified ADRCs generate the same estimations of the “total disturbance”, whereas they generate different estimations for the state vector. Furthermore, for the systems with constant disturbance, the different convergence rates of the tracking errors are precisely presented. The simulation for a motion control system is carried out to demonstrate our theoretical results.