Flexible modeling and control of capacitive-deionization processes through a linear-state-space dynamic Langmuir model

Abstract

Abstract While black-box models such as neural networks have been powerful in many applications, direct physical modeling (white box) remains crucial in many fields where experimental data are difficult or time-consuming to obtain. Here, we demonstrate with an example from desalination by capacitive deionization (CDI), how an existing physical model could be strengthened by combining a general modeling framework with physical insights (gray box). Thus, a dynamic Langmuir (DL) model is extended to a linear-state-space DL model (LDL). Results obtained show the new LDL model could incorporate general structural and operational modes, including membrane CDI and constant-current operation. The formulation removes the need for direct measurements of detailed device properties without adding model complexity, and MATLAB code for automatically implementing the model is provided in the Supplementary Information. We conclude the new LDL model is widely applicable, offering great flexibility in calibration data, and enabling prediction over general operating modes.