Sliding manifold approach to vibration control of flexible systems subject to narrow-band disturbances

A control strategy for vibration reduction of flexible structures subject to persistent narrow band disturbances is presented. The controller is developed using the singular perturbation theory. In particular, the controller is designed by means of a suitable time-varying sliding surface which ensures bounds on control amplitude and on its rate of variation. Moreover, the surface is designed to eliminate the modes close to disturbance frequencies in order to reduce the vibration, without modifying the remaining ones. The control scheme is implemented on two different pinned-pinned beam with uniform and nonuniform cross section, respectively.