Tuning of linear active disturbance rejection controllers for second-order underdamped systems with time delay

Second-order plus dead-time systems are difficult to tune for a PID controller due to its special structure, especially the underdamped systems that have oscillatory responses. As a control technique with strong disturbance rejection ability, linear active disturbance rejection control is widely used as a substitute for PID controllers. This paper proposes a tuning formula for second-order linear active disturbance rejection control for underdamped second-order plus dead-time systems via internal model control. The formula is derived by minimizing the integral of time squared error index under certain robustness measure condition. Simulation results show that the linear active disturbance rejection controller tuned from the proposed formula can achieve satisfactory control performance for oscillatory systems.