Boundary control of a rotating Timoshenko beam

Abstract

The boundary control of a rotating beam is investigated. The beam is modelled by the Timoshenko beam equations, which are a system of two coupled wave equations that include the effects of shearing and the rotational inertia of cross-sections of the beam. The beam, which is pivoted at one end and free at the other, has physical parameters that may vary along the length of the beam. Conditions are found for which both the angle of rotation and the vibrations of the beam may be controlled by applying a force at the free end and a torque at the pivoted end. This is an improvement on previous work of the first author, who showed only that the vibrations may be controlled.