Robust tracking control design for fractional-order interval type-2 fuzzy systems

Ramasamy Kavikumar,Palanisamy Selvaraj,Rathinasamy Sakthivel,Oh-Min Kwon

doi:10.1007/s11071-021-07163-y

Abstract

This paper is concerned with an uncertainty and disturbance estimator-based tracking control problem for a class of interval type-2 fractional-order Takagi-Sugeno fuzzy systems subject to time-varying delays. The footprints of the uncertainty of the underlying fuzzy systems are taken into account to capture and model different levels of uncertainties. The uncertainty and disturbance estimator is used to promote the tracking behavior of rejecting disturbance in the control system. First, by applying the Lyapunov approach, we focus on the examination of stability and performance of the fractional-order tracking error system. Next, unknown system uncertainties, external disturbances and nonlinearities are accurately estimated via an appropriate filter design. Particularly, the proposed control technique does not require any prior knowledge about above said unknown factors and it only requires the bandwidth information about the low-pass filter. Then, four numerical examples with simulation results are presented in the end, to show the potential of the theoretical results of the proposed control method.

Highlights

In recent few decades, the study of nonlinear control systems has paid much attention since many real-world happenings are governed by nonlinear differential and difference equations [1,2,3,4]
Recent studies of control theory have mainly resolved this issue with the aid of various advanced linearisation techniques, where the actual nonlinear systems are approximated as linear systems and various linear control techniques are applied [5,6,7]
Support of T-S fuzzy model technique, the nonlinear system is approximated as sum of a collection of linear subsystems with their weighting membership functions (MFs)

Summary

Introduction

The study of nonlinear control systems has paid much attention since many real-world happenings are governed by nonlinear differential and difference equations [1,2,3,4]. To handle this 2 Problem formulation issue, many modern control techniques are developed to estimate them [34,35,36,37] Among such techniques, uncertainty As presented in [38], Caputo derivative is well understood in and disturbance estimator (UDE)-based control design pro- physical situations and more applicable to real-world probposed by Zhong and Rees in [36], has been widely used lems. The Caputo operator is utilized in this work to investigate fractional-order IT2FSs. Consider the following FO IT2FSs with mfuzzy rules subject to unknown uncertainties, nonlinearities and external disturbances: Plant rule l: IF δ1(ρ(t)) is El1, δ2(ρ(t)) is El2, . If the filter has a wide enough bandwidth, the UDE is able to accurately and quickly estimate the lumped uncertainty

Main results

Numerical simulations

Conclusion