Symbolic finite element discretization and model order reduction of a multiphysics model for IPMC sensors

The multiphysics model of ionic polymer-metal composite (IPMC) sensors proposed by Zhu has a significant advantage of being able to describe the dynamic sensor response, which highly depends on humidity, by explicitly considering solvent dynamics. However, it is difficult to perform analysis and simulation because Zhu's model is represented by complex non-linear partial differential equations. This paper describes the symbolic finite element discretization of Zhu's model and further discusses the essential dynamics of the reduced-order model extracted from the finite element model. The obtained linear ordinary differential equations, or the state equation, can be easily implemented in simulators via common programming languages. The simulation results of an in-house simulator implemented by MATLAB code show good agreement with those of direct numerical simulation by using commercial software, COMSOL. To further simplify the model, the minimum order required for an appropriate approximation is numerically investigated by using a model order reduction technique. This paper reveals that the dynamic response of an IPMC sensor can be consequently approximated by a first-order or second-order linear time-invariant system.