Stability of a nonlinear electronic controller for an electrostrictor actuator

Electrostrictor transducers are attractive because of their (relatively) large displacements. However, they exhibit a quadratic nonlinearity between the charge and displacement as well as a nonlinear relationship between charge and voltage. These nonlinearities limit the useful range for linear output. For example, in acoustic applications, these nonlinearities limit the range of displacements that do not generate higher order harmonics. In this paper we describe a nonlinear electronic controller to mitigate the effects of the material nonlinearity. We also provide a stability proof for the nonlinear controller. This proof is based on a Lyapunov stability proof for a nonlinear capacitor with modifications.