Optimal vibration control by the use of piezoceramic sensors and actuators

Abstract

In this paper, a discrete degrees of freedom model has been formulated for a structural dynamic system consisting of a linear elastic structure, bonded piezoceramic sensors and actuators, and a feedback signal conditioning system. In addition, an optimal control procedure based on the minimization of a quadratic performance index of state and control vectors has been developed that uses output feedback methods. Finally, the application of the model and the control technique has been demonstrated through the example of a linear elastic beam with piezoceramic sensors and actuators occupying discrete subdomains of the beam upper and lower surfaces. A model for the linear elastic beam has been obtained by using test results and a structural dynamic system identification method based on an equation error approach. Results for various weights in the performance index are included, and implications for future applications are discussed. N the past few years, there has been considerable research activity in the field of active and passive control of vibra- tions of flexible structures. One of the methods of active con- trol of vibrations, termed electronic damping in some of the early literature,1'6 involves the placement of piezoceramic devices on a structure to sense and control dynamic strains induced by structural vibrations. The deformation of a sens- ing transducer results in an electrical current that is condi- tioned by operations such as amplification and shifting of the phase of the signal. The conditioned signal is then applied to another piezoceramic, electrostrictive, or magnetostrictive device placed at a selected location on the structure. This trans- ducer acts as an actuator and transmits mechanical energy to the structure. Depending on the applied voltage, electrome- chanical coupling of the forcing transducer to the structure, and the location of the transducers, a degree of vibration control of flexible structures can be achieved. To date, applica- tions of the aforementioned scheme have primarily been in the area of large space structures, such as in the work of Crawley and Deluis,7 but the scheme is applicable to any structure with lightweight components. This type of active control offers unique features that are not usually employed for control of structural vibrations. The dynamics of direct contact type sensors and actuators permit a wide frequency range of control. A measure of tunability is provided for the control of structural systems that age or grow. Finally, this method adds little mass to the controlled flexible structure so that the existing plant model does not need to be modified to account for the mass of the transducers. To utilize the advantages of piezoceramic transducers, it is necessary to select appropriate positions of the transducers and to select the sensor signals that are to be fed back to the actuators. The problem of selecting the locations of the transducers is a complete problem in itself and thus will not be addressed in this paper. There has been some work in