Analytical Design of PD Controllers for Time Delay Systems in the Second Order

This paper intends to present the design scheme of a Proportional Derivative controller for stability and performance of time delay systems in the second order. Inspired from Bode’s ideal system characteristics, phase margin and gain crossover frequency specifications are considered for the system. Then, these specifications are used to obtain the parameters of the controller. The method proposed in the study achieves general computation equations for mentioned systems. Analytically derived formulas by the proposed method are tested with existing plants in the literature and the results are illustrated graphically. It is shown that the tuning method satisfies desired gain crossover frequency and phase margin specifications