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

Abstract

Analyticaldesign scheme of a Proportional Integral controllers for the stability andperformance of second order plus time delay systems is presented in this paper.The method proposed in the study achieves general computation equations formentioned systems. Inspired from the Bode’s ideal transfer functioncharacteristics, gain crossover frequency and phase margin specifications areconsidered for the system. Then, these specifications are used to obtain theparameters of the controller. Analytically derived formulas by the proposedmethod are tested with existing plants in the literature and the results areillustrated graphically. It is shown that the tuning method satisfies desired gaincrossover 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