Robustness of PD and PID Controllers used with Second-Order Processes

Robustness is one of the requirements used in controllers and compensators design. The designs presented in the previous papers did not consider the robustness of the controller or compensator. Therefore, the objective of this paper is to investigate the robustness of PD and PID controllers when used to control second-order processes against uncertainty in the process parameters. A variation of ± 20 % in process parameters is considered through simulation to study its effect on the system performance parameters using the tuned PD and PID controllers. With PD controller controlling an overdamped second order process, the variation in process damping ratio has no effect on the maximum percentage overshoot, maximum percentage undershoot and settling time of the closed-loop control system. The variation of the process natural frequency produced a change of 55.5 % in the settling time and zero change in maximum percentage overshoot and undershoot. For PID controller controlling an underdamped second order process, changing the damping ratio and natural frequency of the process by ± 20 % results in increasing the maximum percentage overshoot using the tuned controller by 18.3 % and 61.3 % respectively. This does not affect the maximum percentage undershoot and the settling time.