VIBRATION CONTROL OF FLEXIBLE STRUCTURES USING PIEZOELECTRIC DEVICES AS SENSORS AND ACTUATORS (DAMPING)

The problem of the active control of linear elastic structures using piezoceramic transducers as sensors and actuators has been investigated by a combined theoretical and experimental approach. The optimal rate feedback gain distribution of an active structure with multiple collocated sensors and actuators has been obtained by using a limited state feedback approach which resulted in an increase in system damping. To model the active structure for the optimal control problem, a finite element model has been developed. An active element consisting of a simple beam element with a bonded unimorphic piezoceramic sensors and actuators has been obtained. The model incorporates the electromechanical coupling of the transducers, bonding effects and a mathematical model for the feedback signal conditioning circuitry. The resulting discrete degrees of freedom model is in the form of a set of coupled ordinary differential equations which describe the dynamic behavior of the active structure. To obtain the unknown dynamic coupling coefficients that represent the effects of bonding and other parameters of the model accurately, parameter identification methods have been used. Modal control has also been experimentally demonstrated by conditioning the output of each individual sensor with an adjustable bandpass filter, phase shifting and gain circuits. The identification of biorthogonal modes of the resulting non self adjoint system when non collocated sensors and actuators has also been accomplished. The identified discrete degrees of freedom model and a quadratic performance index have been used in obtaining optimal control laws. In this phase, the problem has been treated as a regulator with limited state feedback. As a next step, the optimal control problem has been solved by considering the active structure as a distributed parameter system. An optimal control law has been obtained by maximizing the decrease of the time derivative of a Lyapunov functional of a cantilever beam with a collocated sensor and actuator occupying a subdomain of the structure with rate feedback control. The developed control law has been validated by using an explicit finite difference method. The governing partial differential equations have been solved for the system subject to excitations and control.