Fractional order proportional derivative control for time delay plant of the second order: The frequency frame

This paper intends to tune fractional order proportional derivative controller for the performance, stability and robustness of second order plus time delay plant. The tuning method is based on the previously proposed "frequency frame" which is a rectangular frame enclosing gain and phase margins limited with gain and phase crossover frequencies in the Bode plot. Edges of the frame are tuned to achieve desired crossover frequencies and margins. By shaping the curves of the Bode plot, improvements are observed in the performance and robustness of the second order plus time delay system controlled by a fractional order proportional derivative controller. Generalized equations to obtain the parameters of the fractional order proportional derivative controller for second order plus time delay plant are given. In contrast to existing studies, this method reduces mathematical complexity when providing desired properties. Three examples are considered and effectiveness of the frequency frame is shown. (c) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.