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 usingmultiple pairs combining PZT actuators and PVDF sensors distributed (and not necessarilycollocated) on the panel. Frequency domain gradient and Newton-Raphson adaptation ofdecentralized control were analyzed, both in terms of performance and stability conditions. Thestabilization of the closed loop by adjusting the convergence coefficient was especiallyinvestigated through an adjustable control effort term in the quadratic cost function. Variousnecessary or sufficient stability conditions derived from the transfer matrix were obtained andranked from the most restrictive to the less restrictive condition. One of them, the strictlypositive real condition of the transfer matrix appears to be very useful. This stability condition isobtained when the open-loop system is dissipative. Simulation and experimental results arepresented in the case of a simply-supported panel with 4 PZT-PVDF pairs distributed on thepanel. The experimental results were obtained with a decentralized harmonic controllerdemonstrated equivalent to any narrow band disturbance control methods. Decentralizedvibration control is shown to be highly dependent of the actuator and sensor configurations, butcan be as effective as a fully centralized control even when the transfer matrix is not diagonaldominant.