Boundary control of the Timoshenko beam with free-end mass/inertial dynamics

In this paper, we design a control strategy for a cantilevered Timoshenko beam with free-end mass/inertial dynamics. The control strategy which is composed of boundary force and torque inputs applied to the beam's free-end, requires measurements of the free-end displacement, slope, rotation due to bending, slope of the rotation due to bending and the time dervatives of these quantities. The initially develop a model-based control law which exponentially stabilizes the beam displacement and rotation. We then illustrate how the model-based control law can be redesigned as an adaptive controller which asymptotically stabilizes the beam displacement and rotation while compensating for parametric uncertainty. Experimental results are included to illustrate the control performance.