Robust model predictive control of uncertain fractional systems: a thermal application

In this study, a robust model predictive control of fractional-order systems with real uncertain parameters is presented. The Grünwald-Letnikov´s method is used as an internal model to predict the plant future dynamic behaviour. This method consists in replacing the non-integer derivation operator of the adopted system representation by a discrete approximation. Therefore a robust fractional model predictive control is developed based on an uncertain fractional model. Moreover, the output deviation approach is adopted to design the j-step ahead output predictor, and the corresponding control law is obtained by the resolution of a min-max optimisation problem that takes into account the uncertainties of the fractional-order model parameters and under input constraints. The efficiency and the performances of the proposed predictive controller are illustrated with practical results of a thermal system.