Backstepping Boundary Controllers and Observers for the Slender Timoshenko Beam: Part II---Stability and Simulations

We present the stability analysis and numerical results for our controller and observer designs for the slender Timoshenko beam with Kelvin-Voigt (internal material) damping. Our designs, introduced in a companion ACC '06 paper, use a combination of classical "damping boundary feedback" ideas with backstepping. The main advantage of our techniques over the previous boundary damping results is that they apply to the readily implementable "anti-collocated" architecture, which uses actuation only at the beam's base and sensing only at the beam's tip

I. INTRODUCTION

The Timoshenko beam model [3], [6], [7], [8], [11], [12], [13] consists of two coupled second-order-in-space/second-order-in-time wave equations. This model is the most involved of the four beam models as it includes the effects of lateral displacement, bending moment, shear deformation and rotary inertia [2].