On Fractional Adaptive Control

Introducing fractional operators in the adaptive control loop, and especially in Model Reference Adaptive Control (MRAC), has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. The idea of introducing fractional operators in adaptation algorithms is very recent and needs to be more established, that is why many research teams are working on the subject. Previously, some authors have introduced a fractional model reference in the adaptation scheme, and then fractional integration has been used to deal directly with the control rule. Our original contribution in this paper is the use of a fractional derivative feedback of the plant output, showing that this scheme is equivalent to the fractional integration, one with a certain benefit action on the system dynamical behaviour and a good robustness effect. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes.