Transfer Function Analysis and Algorithm Order Reduction for Active Disturbance Rejection Control

This paper presents the transfer function analysis of the closed-loop system with an active disturbance rejection control (ADRC) algorithm. Although the classical interpretation of the extended state observer (ESO) and control algorithm (state feedback) in the state space usually allows for achieving satisfactory control quality, the presented analysis enables calculation of the obtained pole values in the closed-loop system. Furthermore, reduction of the algorithm order by omitting the non-dominant poles of the control plant has also been proposed. The experiments were carried out on a third-order mechanical object, a ball balancing table (BBT) setup. In addition to reducing computational complexity, the presented order reduction procedure allows one to improve the properties of a closed-loop system in the case of poles with large modules affecting the control quality.