Analytical Design of PI Controllers for First Order plus Time Delay Systems

This study proposes an analytical design method of a Proportional Integral controller for the stability and performance of first order plus time delay systems. The method proposed in the study achieves general computation equations for such systems. Inspired from Bode’s ideal loop, gain crossover frequency and phase margin specifications are considered for the system. Then, these specifications are used to obtain the parameters of the proportional integral controller. 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