On the interpretation and practice of dynamical differences between Hammerstein and Wiener models

It is suggested that the differences between the Hammerstein and Wiener models be interpreted and understood in terms of the system eigenvalues. In particular, it is shown that the Wiener representation should be preferred when the system dynamics vary with the operating point. Conversely, when only the system gain varies with the operating point, Hammerstein models generally outperform the Wiener representation. The paper also points out connections between such models and the more general non-linear autoregressive model with exogenous inputs (NARX) polynomial representation. From a practical control engineering point of view, the results presented seem to be more helpful than other ways of distinguishing between such model types. The main ideas are illustrated by means of three examples that use simulated and measured data.