Fractional adaptive high-gain control with σ-modification

Robust control based on fractional order calculus is gaining more and more interests from the control community. In this paper we present a fractional order adaptive high-gain based controllers with σ-modification concept for the class of linear, time-invariant, minimum phase, SISO systems of relative degree one. The basic idea of the proposed design is a further modification in the σ-modification adaptive high-gain concept by introducing fractional differentiation in the adaptation gain of the control strategy instead of the regular differentiation. The control quality of the proposed control scheme compared to the regular case is investigated through the simulation results of an illustrative example.