Analysis of feedback control of piezoelectric transducers

Velocity control feedback may be required for implementation in large underwater acoustic arrays to mitigate the effects of strong acoustic field coupling when specific beam pattern performance over a variety of operating conditions is desired. This paper presents an analysis of velocity control with piezoelectric loads using motional current monitoring [as an extension to Aronov, J. Acoust. Soc. Am. 119(6), 3822-3830 (2006) and Bachand, Brown, and Aronov, J. Acoust. Soc. Am. 124(4), 2568 (2008)], with particular interest in automated wideband acoustic beamforming. The analysis is applicable to other forms of motional feedback control such as accelerometer or displacement signal feedback. Topics presented include the control loop's effectiveness, stability criteria, and the array equations governing the acoustical outputs. The conditions that can cause negative radiation impedance are also presented, concluding that in any velocity control system with acoustic interactions, the likelihood of a transmit channel absorbing more energy than it is transmitting increases with the feedback loop gain. This fundamental limitation must be considered before developing any practical acoustic velocity control system with strong inter-element acoustic field coupling.