A UNIFIED APPROACH FOR REALIZATION OF DISCRETE-TIME FRACTIONAL-ORDER PROPORTIONAL DERIVATIVE CONTROLLER FOR TWO CLASSES OF PLANT MODELS

In this work, a method has been proposed for the realization of a discrete -time fractional -order proportional derivative (FOPD) controller for two different classes of plant models. The methodology has been developed in two stages. In the first stage, the continuous -time FOPD controller has been designed from some of the standard frequency domain specifications employing a graphical approach, namely a vector model method. In the second stage, a generating function has been framed in a delta domain using alpha approximation or parameterized Al-Alaoui approximation. The proposed generating function is named the Modified Al Alaoui-Delta (MALD) approximation, which has been expanded using the continued fraction expansion (CFE) method to realize the discrete -time FOPD controller. The discrete -time realization of the controller has been executed in a delta domain instead of a traditional z -domain, as the delta operator offers unification between a discrete -time system and its continuous -time counterpart at the low sampling time limit. The efficacy of the proposed controller realization method, has been justified over some of the existing methods taking suitable examples from the literature.