Characteristic Value Techniques to Approximate Warburg Diffusion Devices

In this contribution, a model order reduction (MOR) strategy for systems characterized by Warburg-type impedance behavior, frequently encountered in electrochemical applications, is addressed. In particular, the interest is focused on the time-domain approach for deriving low-order models of such a system, in contrast to the current approaches based on the frequency domain. By exploiting the peculiar structure of positive real (PR) systems, a characteristic value technique relying on the Riccati Equation Balancing strategy is introduced to approximate such models with reduced complexity. The characteristic values of the system are used to define suitable reduced-order models. A numerical case study is presented to validate the effectiveness of the proposed method. The model is also compared against experimental data from the literature, confirming its capability to capture dominant Warburg behavior. Performance indices are computed to quantitatively assess the approximation accuracy across different model orders. The results are critically compared with those obtained using conventional MOR techniques, allowing a thorough assessment of accuracy, stability, and implementation feasibility.