Robust MIMO adaptive observer-based control for a Timoshenko beam

Abstract

This paper addresses output regulation for a Timoshenko beam with unknown disturbances and references emanating from an exosystem. By transforming all uncertainties into measurable errors, we are able to estimate approximately the unknown references via a beam observer. However, this alone is insufficient to fully address the uncertainties inherent in state feedback controls. To bridge this gap, we start by estimating exosystem states through an MIMO exosystem observer. To tackle the unknown coefficients in the state feedback controls, we design adaptation laws that seamlessly integrate both the beam and exosystem observers, without the need for a persistent excitation condition. This thus gives adaptive observer-based controls. We rigorously prove the asymptotic convergence of tracking errors and the boundedness of system states. The effectiveness of the proposed controls is validated through numerical simulations.