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

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