S. E. Forsythe
Naval Res. Lab., Underwater Sound Reference Detachment, P.O. Box 568337, Orlando, FL 32856
A technique has been developed at USRD to drive transducers to amplitudes at which nonlinearities in the output normally become evident while maintaining the output signal as a faithful copy of the drive signal. This is done by preprocessing the desired signal using a transducer model that includes the transducer's nonlinearity. The model is stated as a system of coupled ordinary differential equations (ODEs) which define the dynamic variables of the system (positions, velocities, accelerations) as well as the parameters of the system (masses, stiffnesses, viscosities, etc.). Instead of integrating the ODEs using the known drive, as would be done to predict the system's output, the ODEs are explicitly solved ``backwards'' given the desired output. This solution typically requires the accurate numerical calculation of derivatives as well as the point-by-point solution of simultaneous nonlinear equations. Techniques for the efficient solution of the equations as well as solubility issues are discussed. [Work support by Space & Naval Warfare Systems Command.]