Distributed controllers for flexible structures using piezo-electric actuator/sensors

A natural control synthesis for distributed parameter systems (DPS) consists of distributed controllers which can adequately manipulate and force every point of the spatial domain to conform to the desired function. The traditional actuators and sensors such as shakers and accelerometers are localized (point-wise) devices. New sensors/actuators made of smart materials such as piezoelectric ceramic or PVDF have been proposed as alternatives for traditional controllers. In this paper a theoretical approach is introduced to establish the shape design for these materials to make them to perform as distributed controllers in active damping and stabilization of flexible structures. Based on the dissipativity of energy functional, a criteria for the design of the shape of piezoelectric material or electrode, which can achieve the task of distributed control, is derived. Unlike previous efforts, which could find piezoelectric shape for dissipativity of one mode, it is proved that the suggested shape guarantees the dissipativity of energy function for all modes of the system