Design And Analysis Of A Fractional-Order State-Space Adaptive Controller For Second-Order Systems

Abstract

This article proposes an adaptive control method for a class of second-order fractional-order dynamic systems characterized by distinct eigenvalues in the state space. The control scheme developed is a generalization of the MRAC (Model Reference Adaptive Control) framework to scalar systems with fractional derivatives. To ensure accurate tracking of a reference model that is also fractional, an adaptive state feedback controller is designed. This is based on the tracking error between the outputs of the system and the model, incorporating a fractional-order adaptation law to ensure parameter convergence. Numerical simulations validate the effectiveness of the proposed approach and, through comparison with conventional MRAC control, highlight its superior performance in terms of tracking accuracy and robustness in the presence of uncertainties.