Abstract
The method proposed in this paper is able to identify a certain class of nonlinear systems which consist of some nonlinear gains and linear systems. The connection among the elements within the nonlinear system is assumed to be known a priori.
The output of the nonlinear gain is approximately represented by the polynomial of the input whose coefficients are unknown parameters. The dynamics of the linear system is represented by using the impulse response whose discrete samples are also considered to be unknown parameters. These parameters are determined to minimize the sum of squares of the error between the actual output and mathematical model output. Some linearization techniques such as the Gauss-Newton method are usually used where the model's parameters are corrected iteratively so as to approach the corresponding system parameters, but the convergence of iteration is not always guaranteed. In this paper, it is proved that a technique to vary the step size of the correcting action makes it possible to dicrease the error criterion monotonously. Further this method uses such an algorithm that some parameters corresponding to the coefficients of the polynomial are estimated successively from lower order terms to higher ones without estimating all parameters at once. By means of this algorithm, the values of the parameters at the first iteration can be taken in the neighborhood of the absolute minimum point so that the estimated parameters may converge to the true values in a few iterations.
Through the digital simulation, it is shown that the dynamic characteristics of the nonlinear system, which has a nonlinear gain and a linear system connected in series, can be correctly estimated by the above method. It is also confirmed that the method is applicable even when the linear system within the nonlinear system is not self-regulatory.
