Computing step and impulse responses of closed loop fractional order time delay control systems using frequency response data

Abstract

This paper deals with the computation of accurate step and impulse responses of fractional order control systems with time delay. Two elegant methods which are extensions of the methods previously obtained by the authors for systems without a time delay are given. The first method is called the Fourier series method and the second method is the inverse Fourier transform method. The results obtained from these methods are exact since the methods use frequency domain data of fractional order transfer functions which can be computed exactly. Time response equations which are functions of the frequency response data of the fractional order PID, lag or lead controllers, and plant are derived. Numerical examples are given to illustrate the results.