A sliding model control for an Euler-Bernoulli beam with boundary shear force feedback

Abstract

A flexible Euler-Bernoulli beam formulated by partial differential equations subject to the boundary shear force feedback is investigated in this paper. First, an abstract evolution equation corresponding to the beam system is established in an appropriate Hilbert space. Then, a spectral analysis and semigroup generation of the operator of the beam system are discussed. Finally, a sliding model control is proposed associated with an equivalent control equation, and a significant result that the solution of the beam system can be approximated by the ideal sliding mode under a sliding model control is proposed and proved.