Coupled Linear Feedback and Sliding Model Control for a Serially Connected Euler-Bernoulli Beam

A system of serially connected string and Euler-Bernoulli beam with coupled linear feedback control and sliding model control is studied in the present paper. The system is formulated by partial differential equations with the boundary conditions. The eigenvalues and eigenfunctions of the system operator are discussed in the appropriate Hilbert spaces. A sliding model control is applied to the serially connected beam and it has been shown that the actual sliding mode of the system can be approximated by ideal sliding modes in any accuracy under certain conditions. In this paper, a significant semigroup property of restriction of the system operator is derived.