Input Sequences for Nonlinear Modeling

Abstract

Empirical modeling represents a practical, popular approach to the development of the dynamic models required for nonlinear model-based process control. This approach requires the selection of a nonlinear model structure, the determination of dynamic order parameters, and the estimation of unknown model coefficients. The results we obtain at each of these steps can depend strongly on the input/output data on which they are based. This paper presents a brief but detailed discussion of input sequences for nonlinear empirical model development, beginning with the question ;of what constitutes a “good” input sequence. In particular, the following three criteria are proposed:

• (a) effectiveness in model structure discrimination;

• (b) effectiveness in model parameter determination;

• (c) conformance to practical constraints.

Examples are presented to illustrate these criteria and the differences between them; one of the points demonstrated by these examples is that compromises must generally be made between input sequence performance with respect to these three criteria. For simplicity, this paper restricts consideration to the problem of input sequence design for single-input, single-output nonlinear model identification; multivariable problems are certainly of practical interest, but the SISO problem is challenging enough to be worthy of a separate treatment first.

on leave from the DuPont Company