Analytical approach on the design of fractional order proportional-integral controller for second order plus time delay models

Abstract

Purpose: This paper presents the design scheme to tune fractional order proportional-integral controller for models described by second order plus time delay transfer functions. Theory and Methods: Main purpose of the design is to tune the gain crossover frequency, the phase crossover frequency and the phase margin simultaneously towards researchers' desire. Tuning these frequency properties will let us control the output behavior of the system. Main contribution of the method comes from computation of the frequency specifications simultaneously and the flattening procedure of the phase curve. In spite of the similar existing studies, the phase curve is simply flattened by tuning the above mentioned frequency specifications. For example, we can flatten the phase curve by extending the distance between Ωgcand Ωpcreducing the PM in Figure A. In this way, the curve can be flattened without mathematical complexity. Results: The proposed method is applied on two different models selected from the literature. By the analytically derived equations, desired frequency specifications are successfully achieved. With the proper selection of these specifications, the phase curve is considerably flattened thus, the systems gained improved robustness against variations in the plant or controller gain. Conclusion: Simulation results showed that the proposed method successfully achieved desired design specifications and significantly improved the robustness of the system. © 2022 Gazi Universitesi Muhendislik-Mimarlik. All rights reserved.