Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations

Abstract

In this chapter, we consider stabilization problems of Euler-Bernoulli beam equations arising in the area of space and industrial robots with lightweight and flexible arms, as well as in the area of flexible space structures. We shall first derive a general model for a Euler-Bernoulli beam with a rigid tip body. The model is more general than those models in the existing literature in the sense that both bending and torsional vibrations of the beam will be considered, and the tip body is allowed to be a rigid body. Although the derived model looks complicated, it can be reformulated into a simple abstract equation in some appropriately defined Hilbert spaces. For this reason, in the sections which follow, we shall consider a simplified version of this model by assuming a free beam (with no tip bodies) without loss of generality.