Gray-box identification of block-oriented nonlinear models

This paper describes a gray-box identi®cation approach to three classes of block-oriented models: Hammerstein models, Wiener models, and the feedback block-oriented models introduced recently for modeling processes with output multiplicities. Here, we restrict consideration to processes with nonlinear steady-state characteristics that are known a priori and do not exhibit steady-state multiplicities. Under this assumption, simple identi®cation procedures may be developed for all three of these model structures, which may be viewed as three di€erent ways of combining a single static nonlinearity with a linear dynamic model with speci®ed steady-state gain constraints. In particular, if the steady-state gain of the linear dynamic model is constrained to be 1, the steady-state character- istic of the overall model is determined entirely by the static nonlinearity. If the steady-state characteristic of the process is known, the nonlinear component of the model may be determined from this knowledge, and the parameters of the linear model may be estimated from input-output data. Detailed descriptions of simple least squares solutions of this identi®cation problem are presented, and the approach is illustrated for a simple ®rst-principles model of a distillation column.