Robustness Of I-PD PD-PI And PI-PD Controllers Used With Second-Order Processes

Abstract 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 I-PD PD-PI and PI-PD controllers 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 controllers. With I-PD controller controlling an underdamped second order process the variation in process natural frequency and damping ratio has almost no effect on the maximum percentage overshoot maximum percentage undershoot settling time and the phase margin of the control system. The variation of the process natural frequency produced a maximum change of 33 in the system gain margin. The damping ratio change does not affect the gain margin of the system. With PD-PI controller controlling the underdamped second order process the variation in process natural frequency and damping ratio has almost no effect on the maximum percentage overshoot maximum percentage undershoot gain margin and the phase margin of the control system. The variation of the process natural frequency produced a maximum change of 56.5 in the system settling time. The damping ratio change does not affect the settling time of the system. With PI-PD controller controlling the underdamped second order process the variation in process natural frequency and damping ratio has almost no effect on the maximum percentage overshoot maximum percentage undershoot and gain margin of the control system. The variation of the process natural frequency produced a maximum change of 5.2 in the system settling time and 3.67 in the phase margin. The variation of the process damping ratio produced a maximum change of 0.05 in the system settling time and has no effect on the system phase margin.