An adaptive fuzzy dead-zone compensation scheme for nonlinear systems

TL;DR

This paper introduces an adaptive fuzzy control method for nonlinear systems with dead-zone nonlinearities, ensuring convergence and improved performance through Lyapunov-based stability analysis and practical application to a Van der Pol oscillator.

Contribution

It presents a novel adaptive fuzzy controller specifically designed for systems with dead-zone nonlinearities, with proven stability and convergence properties.

Findings

Successful application to a Van der Pol oscillator

Lyapunov stability of the control scheme proven

Numerical results demonstrate effective control performance

Abstract

The dead-zone nonlinearity is frequently encountered in many industrial automation equipment and its presence can severely compromise control system performance. Due to the possibility to express human experience in an algorithmic manner, fuzzy logic has been largely employed in the last decades to both control and identification of uncertain dynamical systems. In spite of the simplicity of this heuristic approach, in some situations a more rigorous mathematical treatment of the problem is required. In this work, an adaptive fuzzy controller is proposed for nonlinear systems subject to dead-zone input. The convergence properties of the tracking error will be proven using Lyapunov stability theory and Barbalat's lemma. An application of this adaptive fuzzy scheme to a Van der Pol oscillator is introduced to illustrate the controller design method. Numerical results are also presented in order to demonstrate the control system performance.