Active disturbance rejection control design for high-order integral systems

Active disturbance rejection control (ADRC) is designed for regular processes frequently, due to its strong ability to reject disturbances and handle system uncertainties. However, ADRC design for high-order integral systems existing in many natural systems is always ignored. The controller design for high-order integral systems is different from the regular systems due to no pole in the left and right half s-planes. The ADRC design for high-order integral systems is studied to explain this question theoretically in this paper. Based on the equivalent form of ADRC, a theorem about the necessary condition of ADRC is proven which can guarantee the closed-loop system's stability. Additionally, the advantages of ADRC over proportional-integral-derivative (PID) controller in sensor noise rejection and control signal variation are analyzed theoretically. In order to achieve expected control performance for high-order integral systems, a practical design procedure of ADRC is summarized by the single variable method. Several comparative simulations and an experiment based on a ball and beam system are carried out. Running data verify that ADRC can obtain better control performance with strong robustness than PID controller. Eventually, a 100th order ADRC is designed for a 100th order integral system, and simulation results show that ADRC can be designed for high-order integral systems conveniently. Based on theoretical analyses and experimental verifications, ADRC shows some advantages for high-order integral systems.