A variable structure control for a Flexible Euler-Bernoulli Beam

Abstract

The variable structure control has been widely used for industry. The variable structure system is a system whose structure is intentionally changed with a discontinuous control and it drives the phase trajectory to a hyperplane or manifold El-Ghezawi et al[6], Fu and Liao [7]. In this paper, the variable structure control for a Flexible Euler-Bernoulli Beam formulated by partial differential equations with initial and boundary conditions is investigated by means of semigroup of linear operators and spectral analysis. The evolution equations for the system in the appropriate Hilbert spaces are established. A variable structure control is designed and studied for the beam system. It is shown that the beam system with designed variable structure control is asymptotically stable.