A Dynamic Observer for a Class of Infinite-Dimensional Vibrating Flexible Structures

TL;DR

This paper develops a dynamic observer for infinite-dimensional vibrating structures using Hamiltonian formulation, providing convergence conditions and demonstrating effectiveness through numerical simulations.

Contribution

It introduces an explicit observer construction with arbitrary gains for infinite-dimensional systems, extending control techniques to flexible structures.

Findings

Observer convergence is proven under certain conditions.

Numerical simulations confirm effective error decay.

Applicable to flexible beams with distributed actuators.

Abstract

Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain coefficients. Sufficient conditions for the convergence of the constructed observer are obtained on the basis of the invariance principle. This result is applied to a flexible beam model attached to a mass-spring system with lumped and distributed actuators. The estimation error decay is illustrated with numerical simulations of finite-dimensional approximations of the observer dynamics.