Modeling and Control of a Thermoelastic Beam

Abstract

The objective of this paper is to model a thermoelastic beam and use thermoelectric heat actuators dispersed over the beam to control not only its vibration, but also its temperature. The model is represented by two coupled partial differential equations governing the elastic bending displacement and temperature variation over the length of the beam. The partial differential equations are replaced by a set of ordinary differential equations through discretization. The first-order ordinary differential equations are cast in the compact state-space form to be used in the thermoelastic analysis and control. The Linear Quadratic Gaussian (LQG) is used for control design. An numerical application to a uniform cantilever beam demonstrates the coupling between the temperature and the elastic displacement and feasibility of using thermoelectric actuators in controlling the vibration and temperature simultaneously.