Physics-based irrational transfer function of IPMC sensor output voltage⋆

Abstract

Ionic Polymer-Metal Composite (IPMC) sensors are a kind of soft and wet polymeric sensors and are expected to be used in soft robotics. Zhu's model is one of the most promising physical models for IPMC sensors and is represented by a set of partial differential equations for cation concentration, water concentration, and potential. This paper first derives the exact solution of Zhu's sensor voltage model using the Laplace transform. Specifically, this paper derives irrational (infinite-dimensional) transfer functions from the deformation curvature to the outputs such as the cation concentration, the water concentration, the electric potential, and the sensor output voltage. The obtained frequency response of the sensor voltage is confirmed to be consistent with that of the finite element method in a previous study. Furthermore, this paper derives the DC gain and the peak gain of the transfer function of the open-circuit sensor voltage.