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

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3 Author(s)
Lory, H. ; Johns Hopkins University, Baltimore, MD, USA ; Lai, D. ; Huggins, W.

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.

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Automatic Control, IRE Transactions on  (Volume:4 ,  Issue: 2 )