Modeling and identification of nonlinear systems using MIMO LEM-Hammerstein structure

Abstract

This paper extends the LEM-Hammerstein models already presented in the literature to MIMO systems. Instead of linear time-invariant subsystems in association with static nonlinearities, LEM-Hammerstein and LEM-Wiener systems exhibit nonlinear static features and operating-point dependent dynamics, and can therefore model a broader class of system than the conventional block-oriented models. In order to avoid the problem of solving the partial differential equations necessary for the construction of the steady-state mapping that appears in the model, a modified controller normal form is proposed, and the model is constructed on the basis of an extended, non-minimal state-space realization. Moreover, the identification strategy already used with LEM systems can be applied in order to construct such models from experimental data, and the techniques destined for analysis and control of Hammerstein systems can be applied promptly. An application of these concepts to the modeling and identification is demonstrated in the numerical example of a level system constituted by six connected tanks.