Journal of Advances in Mathematics and Computer Science

A problem of suppressing vibrations of elastic structures through controlling their finitedimensional approximations was addressed in various publications which primarily utilize collocated sensors and actuators. This engineering approach, however, raised concerns that a control designed for a finite dimensional model could excite or destabilize its abandoned infinitedimensional complement, which reflects in so known spillover phenomenon. This paper developed a novel design of an output controller, which eliminates spillover in control and marginalizes its contribution to observer design. This consequently leads to an efficient control of beam vibrations, which can be attained by non-collocated sensors and actuators located nearly anywhere on the beam. We show in simulations that the proposed methodology leads to stabilization of postcritical buckling and an efficient reduction of the beam’s resonance vibrations enforced by loads comprised of an axial force and unknown transverse bounded disturbances. We infer controllability and observability conditions which pinpoint areas on the beam where locating actuators/sensors should be avoided and estimated the contribution of discarded part of the initial system.

Retraction Notice: After formal procedures editor(s) and publisher have retracted this paper on 29^th July-2016. Related policy is available here: http://goo.gl/lI77Nn