Time delay stability analysis for vibration suppression of a smart cantilever beam with hysteresis property

Ting Zhang,Guo Ping Cai,Hong Guang Li

doi:10.1177/1461348420924148

Abstract

A stability analysis for a smart beam with an adaptive controller is presented in the paper when considering the time delay phenomenon. With the Lagrange equation and the assumed modes method, a dynamical model is constructed to describe the hysteresis nonlinearity of the smart beam. By simulation and experiment, the nonlinear model is proved effectively using the strain response near the root of the beam when the piezoelectric actuator is applied on with a chirp voltage. Based on the dynamical model, a stability analysis method is proposed with an eigenmatrix in the discrete control system. Through some simulation verifications, it is concluded that a proper time delay will be useful to improve the stability of the smart beam with an adaptive controller. Furthermore, it is verified by the experiments that the free vibration amplitude of the smart beam with an artificial time delay 0.05 s is smaller compared with that at no time delay.

Highlights

Vibration control problems of various flexible structures by smart materials have been studied for several decades.[1,2,3,4] In addition, achieving a precise position for the smart structure needs to design a proper controller to suppress the external disturbance.[5]
A dynamical model of a smart flexible beam with hysteresis nonlinearity is constructed using the assumed modes method and the Lagrange equation, and the theoretical model is verified by simulations and
Based on the dynamical model, an eigenmatrix is derived for analyzing the stability of the smart beam with time delay in the discrete adaptive control system

Summary

Introduction

Vibration control problems of various flexible structures by smart materials have been studied for several decades.[1,2,3,4] In addition, achieving a precise position for the smart structure needs to design a proper controller to suppress the external disturbance.[5]. Some simulations and experiments (the experimental setup and the corresponding parameters of the smart beam are shown in Table 1) are implemented to verify the effectiveness of the model for describing the dynamic characteristic and the hysteresis nonlinearity between the input voltage and the out stain by equation (12).

Results

Conclusion