Generalised methods for rational approximation and controller design for fractional order systems with application to wheeled mobile robot

Abstract

The aim of the research work undertaken is two-fold: firstly, to develop a generalised newlinemethod for rational approximation of fractional-order (FO) system (FOS) and secondly, newlineto develop a generalized method for FO controller (FOC)/integer-order (IO) controller newline(IOC) design for FOS/IO system (IOS). newlineProposed rational approximation method utilises matching of an appropriate number newlineof approximate generalised time moments (AGTMs)/approximate generalised Markov newlineparameters (AGMPs) of squared magnitude function of the FOS to those of its newlineapproximant. The proposed method preserves the stability/instability property, newlineminimum phase/non-minimum phase characteristics of the FOS in its approximant. The newlinedeveloped method ensures that steady-state response for the FOS, for a certain input, is newlineretained in its approximant. The developed algorithm is a generalised one and is newlineapplicable to single-input-single-output (SISO)/multiple-input-multiple-output newline(MIMO), minimum phase/non-minimum phase, stable/unstable FOS. Numerical newlineexamples are taken to show the efficiency of the proposed method. Comparative newlineanalyses have been carried out with those in the literature. newlineA streamlined algorithm for selection of a reference model M(s) based on linear newlinequadratic regulator (LQR) design procedure with the inclusion of integral action, is newlinepresented. Formulation of an M(s) to be used in model-matching controller design for a newlineMIMO system, has been a difficult task due to the presence of cross-coupling effect. In newlinethe present work, elements of weighting matrices of the LQR design procedure are newlinetuned such that resulting optimal state-feedback closed-loop system embodies desired newlinetime-domain specifications and fixed/optimum level of cross-coupling dynamics. The newlinestate-feedback closed-loop system is taken as the M(s). newline