Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamilton's principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H2 are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.