Adaptive Control with Fractional Order Reference Model

Over the few last years the idea of introducing fractional calculus and systems in adaptive control has found a great interest, for the benefit one can win in the performances given by such systems. In adaptive control, the dynamic behavior of the system is defined by a chosen reference model and an adaptation algorithm modifies the correction to minimize the process output error. In this work, an adaptive control with a fractional order reference model is suggested. The main idea consists of making beforehand an approximation of the fractional reference model using one of the frequency domain approximation methods. After that, we use a classical algorithm of the adaptive control with the resulting reference model. Our objective is to find a control which takes the system to the desired state (the referential signal) with an improved behavior when compared to the integer order model scheme. The results of simulation have confirmed the efficiency proposed fractional order reference model adaptive controller.