Optimal control of precision paraboloidal shell structronic systems

Paraboloidal shells of revolution are commonly used in advanced aerospace, civil and telecommunication structures, e.g., antennas, reflectors, mirrors, rocket fairings, nozzles, solar collectors, dome structures, etc. A structronic shell system is defined as an elastic shell embedded, bonded or laminated with distributed piezoelectric sensors and actuators and it is governed by either in situ or external control electronics. A closed-loop control system of paraboloidal shell structronic system consists of distributed sensors/actuators and controller coupled with an elastic paraboloidal shell. State equation for the paraboloidal shell structronic system is derived and optimal linear quadratic state feedback control is implemented, such that the “best” shell control performance with the least control cost can be achieved. The gain matrix is estimated based on minimizing a performance criterion function. Optimal control effects are compared with controlled responses with other non-optimal control parameters. Control effects of identical-sized sensor/actuator patches at different locations are studied and compared. Modal control effects for different natural modes are also investigated.