Stability conditions in Decentralized Active Vibration Control of a Flexible Plate

摘要

This paper presents the analysis of decentralized active control of periodic panel vibration usingrnmultiple pairs combining PZT actuators and PVDF sensors distributed (and not necessarilyrncollocated) on the panel. Frequency domain gradient and Newton-Raphson adaptation ofrndecentralized control were analyzed, both in terms of performance and stability conditions. Thernstabilization of the closed loop by adjusting the convergence coefficient was especiallyrninvestigated through an adjustable control effort term in the quadratic cost function. Variousrnnecessary or sufficient stability conditions derived from the transfer matrix were obtained andrnranked from the most restrictive to the less restrictive condition. One of them, the strictlyrnpositive real condition of the transfer matrix appears to be very useful. This stability condition isrnobtained when the open-loop system is dissipative. Simulation and experimental results arernpresented in the case of a simply-supported panel with 4 PZT-PVDF pairs distributed on thernpanel. The experimental results were obtained with a decentralized harmonic controllerrndemonstrated equivalent to any narrow band disturbance control methods. Decentralizedrnvibration control is shown to be highly dependent of the actuator and sensor configurations, butrncan be as effective as a fully centralized control even when the transfer matrix is not diagonaldominant.