A Reduced Order Controller for Output Tracking of a Kelvin-Voigt Beam

TL;DR

This paper presents a low-order finite-dimensional controller for output tracking and disturbance rejection in a Kelvin-Voigt damped Euler-Bernoulli beam, utilizing spectral Galerkin and model reduction techniques.

Contribution

It introduces a novel reduced-order internal model controller combining spectral Galerkin and Balanced Truncation methods for beam control.

Findings

Controller achieves effective output tracking and disturbance rejection.

Numerical simulations demonstrate superior performance over low-gain controllers.

The approach reduces computational complexity while maintaining accuracy.

Abstract

We study output tracking and disturbance rejection for an Euler-Bernoulli beam with Kelvin-Voigt damping. The system has distributed control and pointwise observation. As our main result we design a finite-dimensional low-order internal model based controller that is based on a spectral Galerkin method and model reduction by Balanced Truncation. The performance of the designed controller is demonstrated with numerical simulations and compared to the performance of a low-gain internal model based controller.