On the use of growing harmonic exponentials to identify static nonlinear operators

Author

Lory, H.J. ; Lai, D.C. ; Huggins, W.

Author_Institution

Johns Hopkins University, Baltimore, MD, USA

Volume

4

Issue

2

fYear

1959

fDate

11/1/1959 12:00:00 AM

Firstpage

91

Lastpage

99

Abstract

The following paper describes a method of obtaining a polynomial characteristic function for a nonlinear static system. This function, $F(x) = hx + mx^{2} + dx^{3}$ , is obtained by the application of a growing exponential $x = \\exp(t)$ to the input of the system and the filtering of the output $h \\exp(t) + m \\exp(2t) + d \\exp(3t)$ , into its separate components $h \\exp(t), m \\exp(2t)$ , and $d \\exp(3t)$ . The values of these three components at $t = 0$ are the polynomial coefficients $h, m$ , and $d$ respectively. The identification of systems not exactly describable by a cubic gives rise to an error minimization problem; the technique described in this paper minimizes the weighted mean-square error, with a weighting function $1/x$ . This method is compared with the more widely known sinusoidal analysis of nonlinear systems. Experimental results are given.

Keywords

Eigenvalues and eigenfunctions; Filtering; Filtration; Frequency; Instruments; Nonlinear dynamical systems; Nonlinear systems; Polynomials; Power harmonic filters; Testing;

fLanguage

English

Journal_Title

Automatic Control, IRE Transactions on

Publisher

ieee

ISSN

0096-199X

Type

jour

DOI

10.1109/TAC.1959.1104853

Filename

1104853