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Control of Structural Vibrations by Confinement in the Presence of Parameter Uncertainties and Disturbances

A strategy for the simultaneous confinement and suppression of vibrations in flexible structures is proposed. The strategy accounts for parameter uncertainties and persistent disturbances. Certain design considerations are discussed and lead to the development of norm bounds for the control effort, displacement and velocity. These bounds if minimized with respect to the feedback parameters yield a better handle for controller design. Conditions for robustness are also developed using the control law. Furthermore, a special design of feedback for constant and periodic disturbance signals is introduced. An illustrative example of a beam finite element model is presented to show the efficacy of the proposed strategy.