Time delay problem in the active vibration feedback control of a piezoelectric laminated plate

The use of active feedback control of distributed-parameter structures such as plane wings and space antennas is becoming increasingly popular. These structures contain piezoelectric elements which strain in response to an electric field (actuating effect) and generate a charge when strained (sensing effect) within a feedback loop. Time delay is a significant problem in such feedback systems, since the control system with a certain time delay may become unstable by a certain time delay, or its efficiency may deteriorate, resulting in decrease in damping. This dissertation investigates the time delay problem in the feedback control of a distributed-parameter piezoelectric laminated plate. Analytical expressions for time delay limit and time delay compensation in the case of modal uncoupled control have been formulated. This dissertation also investigates the effect of time delay and suggests a methodology for time delay compensation in modal coupled control. The topics discussed in this dissertation include modeling of a piezoelectric laminated plate, discretization of distributed-parameter structures, time delay limits and compensation in modal uncoupled and coupled control.