Modeling of distributed parameter systems for applications—A synthesized review from time–space separation

Many industrial processes belong to distributed parameter systems (DPS) that have strong spatial–temporal dynamics. Modeling of DPS is difficult but essential to simulation, control and optimization. The first-principle modeling for known DPS often leads to the partial differential equation (PDE). Because it is an infinite-dimensional system, the model reduction (MR) is very necessary for real implementation. The model reduction often works with selection of basis functions (BF). Combination of different BF and MR results in different approaches. For unknown DPS, system identification is usually used to figure out unknown structure and parameters. Using various methods, different approaches are developed. Finally, a novel kernel-based approach is proposed for the complex DPS. This paper provides a brief review of different DPS modeling methods and categorizes them from the view of time–space separation.