A time/space separation-based Hammerstein modeling approach for nonlinear distributed parameter processes

Modeling of distributed parameter systems (DPSs) is very difficult because of their infinite-dimensional, spatio-temporal nature and nonlinearities. A low-order, simple nonlinear and parsimonious model is often required in real applications. In this study, a time/space separation-based Hammerstein modeling approach is proposed for unknown nonlinear DPS. Firstly, the Karhunen-Loève (KL) method is used for the time/space separation, where the spatio-temporal output is decomposed into a few dominant spatial basis functions with temporal coefficients. Secondly, a low-order parsimonious Hammerstein model is identified from the low-dimensional data to reconstruct the system dynamics, where the parsimonious model structure is determined by the orthogonal forward regression and the parameters are estimated using the least squares estimation and the singular value decomposition. The algorithm does not require nonlinear optimization and it is numerically robust. This modeling is very suitable for control design. The simulations are presented to show the effectiveness of the proposed modeling method.