Band Limited Realization of Fractional-Order Proportional Integral Controller for a Class of Finite Dimensional System

Abstract

Fractional-order controller (FOC) is an important area of study nowadays in control science. Due to their infinite dimensional nature, these controllers are approximated within a finite band for practical uses. In this paper, a fractional-order proportional integral controller (FOPI) has been realized within a limited band for a class of finite dimensional plant model. Firstly, the FOC has been tuned for the defined plant model to achieve a set of frequency domain objectives and then, the Oustaloup approximation has been employed to realize it within a limited band. The impact of the control design scheme is tested by connecting both the original FOC and the approximated FOC seperately with the plant model and subsequently comparing the open loop frequency responses with respect to the proposed design objectives through simulation studies. The robustness of the overall controlled system is also studied deviating the plant gain by a significant amount.