Combined Fractional Adaptive Control * *The results reported in this paper have been financed by CONICYT- Chile, under the Basal Financing Program FB0809 "Ad-vanced Mining Technology Center", FONDECYT Project 1150488, "Fractional Error Models in Adaptive Control and Applications"; and FONDECYT 3150007, Postdoctoral Program 2015".

Abstract

This paper presents the design of a fractional order combined model reference adaptive control scheme. This approach is based on the estimates of the plant unknown parameters and the adjusted controller parameters, which are obtained from adaptive laws using the identification error, the control error and the so called closed loop estimation errors. Fractional order indirect algebraic model reference adaptive control and fractional order indirect dynamic model reference adaptive control schemes are also proposed in this paper, which are used for comparison purposes with the combined approach. Boundedness of all the signals in the control schemes is analytically proved, as well as the convergence to zero of the mean values of the control, identification and closed loop estimation errors. Simulation results are presented to show the effectiveness of the proposed control strategies.