This paper provides the model predictive control (MPC) of fractional order systems. The direct method will be used as internal model to predict the future dynamic behavior of the process, which is used to achieve the control law. This method is based on the Grünwald–Letnikov's definition that consists of replacing the noninteger derivation operator of the adopted system representation by a discrete approximation. The performances and the efficiency of this approach are illustrated with practical results on a thermal system and compared to the MPC based on the integer ARX model.

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