Exact time response computation of control systems with fractional order lag and lead compensators

• Main Authors: Tan, N., Atherton, DP, Yüce, A., Deniz, FN
• Other Authors: İnönü Üniversitesi
• Format: Article in Journal/Newspaper
• Language: English
• Published: North Atlantic University Unio 2016
• Subjects: Fractional order control system; Fractional order lag and lead compensators; Frequency response; Impulse response; Step response; Time response; Time response from frequency response; North Atlantic
• Online Access: http://hdl.handle.net/11616/14193

In this paper, two exact methods are developed for the computation of unit step and unit impulse responses of closed loop control systems with fractional order lag and lead compensators. The methods are based on using the frequency response data of the closed loop fractional order control system. It is shown that the unit step and unit impulse responses of a feedback control system including a fractional order lag or lead controller can be computed exactly using Fourier series of a square wave and inverse Fourier transform of frequency response information namely gain and phase values. Time response equations which are the function of controller parameters are derived. A design procedure is given for estimating the parameters of a fractional order lag or lead compensator which give specified performance values of the closed loop system. Numerical examples are provided to show the success of the presented method. © 2016, North Atlantic University Union. All rights reserved.