Vibration Control Design for Nonlinear Systems using Frequency Response Function

TL;DR

This paper introduces an adaptive vibration control method for nonlinear mechanical systems using frequency response functions, leveraging convergence theory to derive nonlinear FRFs and tune controllers for desired responses.

Contribution

It presents a novel adaptive control approach that utilizes convergence theory to derive nonlinear frequency response functions for nonlinear systems.

Findings

Successfully applied to building structure with cubic stiffness

Effectively tuned controller gains for desired frequency response

Validated on satellite system with nonlinear dynamics

Abstract

A nonlinear frequency response based adaptive vibration controller is proposed for a class of nonlinear mechanical systems. In order to obtain the nonlinear Frequency Response Function (FRF), the convergence properties of the system are studied by using the convergence (contraction) theory. If the system under consideration is: 1) convergent, it directly enables to derive a nonlinear FRF for a band of excitation inputs, 2) non-convergent, first a controller is used to obtain the convergence and then the corresponding FRF for a band of excitation inputs is derived. Now the gains of the proposed adaptive controller are tuned such that a desired closed-loop frequency response, in the presence of excitation inputs is achieved. Finally, a building structure with nonlinear cubic stiffness and a satellite system are considered to illustrate the theoretical results.