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

Abstract

Analytical design scheme of a Proportional Integral controllers for the stability and performance of second order plus time delay systems is presented in this paper. The method proposed in the study achieves general computation equations for mentioned systems. Inspired from the Bode’s ideal transfer function characteristics, gain crossover frequency and phase margin specifications are considered for the system. Then, these specifications are used to obtain the parameters of the 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.

Keywords

• second order plus time delay plant
• pi controller
• bode’s ideal loop
• i̇kinci derece zaman gecikmeli sistem
• oransal integral denetleyici
• bode’nin i̇deal çevrim