Model Predictive Control for Fractional-order System - A Modeling and Approximation Based Analysis

Abstract

A widely recognized advanced control methodology model predictive control is applied to solve a classical servo problem in the context of linear fractional-order (FO) system with the help of an approximation method. In model predictive control, a finite horizon optimal control problem is solved at each sampling instant to obtain the current control action. The optimization delivers an optimal control sequence and the first control thus obtained is applied to the plant. An important constituent of this type of control is the accuracy of the model. For a system with fractional dynamics, accurate model can be obtained using fractional calculus. One of the methods to implement such a model for control purpose is Oustaloup's recursive approximation. This method delivers equivalent integer-order transfer function for a fractional-order system, which is then utilized as an internal model in model predictive control. Analytically calculated output equation for FO system has been utilized to represent process model to make simulations look more realistic by considering current and initial states in process model. The paper attempts to present the effect of modeling and approximations of fractional-order system on the performance of model predictive control strategy.