Asymmetrical Barrier Function-Based Adaptive Vibration Control for Nonlinear Flexible Cantilever Beam With Obstacle Restriction

Shilun Li,Ping He,Xiaohan Lin

doi:10.1109/access.2021.3072990

Abstract

In this paper, a novel adaptive asymmetrical barrier function-based vibration control law is proposed for the nonlinear flexible cantilever beam system with obstacle restriction, model uncertainties, and distributed disturbances. Firstly, by employing the Hamilton’s principle and the Galerkin projection method, the dynamic of the nonlinear flexible cantilever beam with the piezoelectric actuator is constructed in partial differential equations and simplified to nonlinear ordinary differential equations for the control law design. Then, by introducing the fast nonsingular terminal sliding mode surface, a novel asymmetrical barrier function based sliding mode control law is proposed, in which by means of a novel asymmetrical barrier Lyapunov function is used to guarantee the finite time stability with the obstacle restriction. Further, to deal with the model uncertainties, an adaptive updating law is incorporated with the fast nonsingular terminal sliding mode control law based on asymmetrical barrier function, stability proof shows that the proposed control law can ensure the distributed disturbance rejection and the model uncertainties compensation simultaneously. Finally, the effectiveness of the proposed control laws is demonstrated by the numerical simulations.

Highlights

With the development of precision science, recent years have witnessed significant requirements on the researches of spatial structure, which can be applied in solar panels, robotic arms, and optical motion detection systems
MAIN RESULTS A fast nonsingular terminal sliding mode surface is first employed which can both accelerate the convergence rate and avoid the singular phenomenon
Based on the obtained results, the asymmetrical barrier function based adaptive fast nonsingular terminal sliding mode control law is proposed via an adaptive updating law, estimating the unknown nonlinear uncertainty parts in (15)-(16)

Summary

INTRODUCTION

With the development of precision science, recent years have witnessed significant requirements on the researches of spatial structure, which can be applied in solar panels, robotic arms, and optical motion detection systems. By combining with a backstepping technique, a robust sliding mode boundary control method was proposed to suppress vibration for a pinned–pinned Euler– Bernoulli beam in [5]. Motivated by the aforementioned literature, this paper is concerned to investigate vibration control problems of the nonlinear flexible cantilever beam system under obstacle restriction with model uncertainties and distributed disturbances. (1) It proposes a novel asymmetrical barrier function-based sliding mode control law for vibration suppression of the nonlinear flexible cantilever beam system, where guarantees the convergence speed while constraint the partial maximum displacement of the flexible beam.

PROBLEM FORMULATIONS AND PRELIMINARIES

SIMULATION ANALYSIS

CONCLUSION