Grey Wolf and Weighted Whale Algorithm Optimized IT2 Fuzzy Sliding Mode Backstepping Control with Fractional-Order Command Filter for a Nonlinear Dynamic System

Seongik Han

doi:10.3390/app11020489

Abstract

In this study, a fractional-order sliding mode backstepping control method was proposed, which involved the use of a fractional-order command filter, an interval type-2 fuzzy logic system approximation method, and a grey wolf and weighted whale optimization algorithm for multi-input multi-output nonlinear dynamic systems. For designing the stabilizing controls of the backstepping control, a novel fractional-order sliding mode surface was suggested. Further, the transformed errors that occurred during the recursive design steps were easily compensated by the controllers constructed using a new fractional-order command filter. Thus, the differentiation issue of the virtual control in the conventional backstepping control design could be bypassed with a simpler controller structure. Subsequently, the unknown plant dynamics were approximated by an interval type-2 fuzzy logic system. The uncertainties, such as the approximation error and the external disturbance, were compensated by the fractional-order sliding mode control that was added in the backstepping controller. Furthermore, the controller parameters and the fuzzy logic system were optimized via a grey wolf and weighted whale optimization algorithm to obtain a faster tuning process and an improved control performance. Simulation results demonstrated that the fractional-order sliding mode backstepping control scheme provides enhanced control performance over the conventional backstepping control system. Thus, in this paper, a fractional-order sliding mode surface and fractional-order backstepping control are studied, which provide more rapid convergence and enhanced robustness. Furthermore, a hybrid grey wolf and weighted whale optimization algorithm are proposed to provide an improved learning performance than those of conventional grey wolf optimization and weighted whale optimization methods.

Highlights

Advanced nonlinear control methods are required to adapt to the rapid technical developments of several industrial fields
We proposed a new hybrid grey wolf optimization (GWO) and weighted whale optimization algorithm (WWOA) technique that demonstrated a better optimization performance than those of the conventional
Simulation results based on the FSBSC system, in which the controller’s parameters are optimized by GWO-WWOA technique of the previous section are presented

Summary

Introduction

Advanced nonlinear control methods are required to adapt to the rapid technical developments of several industrial fields. The complexity of the steps involved in the controller design, and the stability proof appears due to the compensation of the filtering errors. Bypassing the repeated differentiation of a virtual control can alter the BSC system into a better controller as compared to the DSC system. Based on this concept, in recent years, the finite-time command filter method, was studied to partially overcome these issues [11,12]. In recent years, the finite-time command filter method, was studied to partially overcome these issues [11,12] This method ensures the finite-time control convergence and prevents the repeated differentiation of the intermediate virtual control. The complexity issues associated with the design and robustness of the controller have not been addressed

Methods

Results

Conclusion