System identification of fractional order dynamic models for electrochemical systems

Fractional order differential equations (FODE) provides a more flexible approach to describe dynamic systems. However, the extra flexibility poses a difficult problem in system identification, which requires not only the estimation of model coefficients but also the determination of fractional orders. They are coupled nonlinearly. In addition, the model coefficients in a FODE are shown nonlinearly coupled with respect to the often used Sum Squared Error (SSE) objective function. In this article, a two-layer approach is designed to estimate fractional orders and model coefficients iteratively. An intermediate step that estimates model coefficients is also introduced to address the nonlinear coupling of coefficients in a SSE. In the subsequent simulation for electrochemical systems, it is found that prior knowledge on physical systems being modeled is necessary to create optimization constraints and justify the results.