Adaptive-robust Control of a Smart Beam with Support Excitation Using Piezoelectric Layers

In this paper, vibrations of a beam with support excitation and a tip mass are suppressed using piezoelectric layers. The beam is fixed to a motion support from one end and the other end is free with an attached mass. The beam is considered as an Euler-Bernoulli beam. The governing equations of motion are derived based on the generalized function theory and Lagrange-Rayleigh-Ritz technique. An adaptive-robust control scheme is applied to control the vibrations of the beam. The mathematical modelling of the beam with control algorithm is derived and in purpose to study the effect of the amount of tip mass, size and location of the piezoelectric layers and the type of the support excitation on the beam vibrations, the system is simulated. Finally, the results of simulation are presented.