The design of a non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order

Abstract

In this paper, the design of the fractional-order predictive functional controller (αPFC) for the linear fractional systems of arbitrary order has been presented. For this purpose, at first, the fractional order transfer function has been digitized via Grunwald–Letnikov definition to obtain the linear regression model of the system. Next, the non-minimal input–output fractional-order state space (αNMSS) model of the system has been derived. The fractional-order predictive functional controller (αPFC) has been then designed for the αNMSS model structure via defining a fractional order cost function over the fractional-order non-minimal state vector. Finally, genetic algorithm (GA) has been employed to obtain the optimal αPFC control coefficients. The fractional-order model of two rods thermal bench has been considered as the uncertain case study in this paper. Simulation results for temperature control of this fractional-order system are representative of better performance of the designed controller with respect to the NMSSPFC as well as the fractional GPC.