Estimating the time response of control systems with fractional order PI from frequency response

This paper deals with the time response computation of closed loop control systems with fractional order PI controllers using the frequency response data of the closed loop system. The time response of fractional order transfer functions from frequency response data was first obtained by the authors using Fourier Series Method(FSM) and Inverse Fourier Transform Method(IFTM). In this paper, these methods are further extended for estimating unit step and unit impulse responses of control systems with fractional order PI controllers from the frequency response information of the closed loop system.