Design of Model Predictive Control for Linear Fractional-Order Systems

A widely recognized advanced control methodology model predictive control (MPC) 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, the current control action is obtained for each sampling instant by solving, a finite horizon optimal control problem. 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 nature, 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.