Fractional order adaptive controller for stabilised systems via high-gain feedback

Controllers based on fractional order calculus are gaining more and more interests from the control community. This type of controllers may involve fractional integration, fractional differentiation and/or fractional systems in their structure or implementation. They have been introduced in the control applications in a continuous effort to enhance the system control quality performances and robustness. In this study, a new scheme of fractional order adaptive controller via high-gain output feedback for a class of linear, time-invariant, minimum phase and single input-single output systems of relative degree one is proposed. The basic idea of the new design is a further modification in the adaptive proportional control law by the introduction of a fractional integration besides of the regular one of the squared output of the system in the adaptation gain of the control strategy. An analytical stability proof of the feedback control system is presented. The control quality enhancement of the proposed control scheme compared with the classical one has been presented through the simulation results of an illustrative example.