Nonlinear system identification for cascaded block model: an application to electrode polarization impedance

An algorithm developed to identify a system divided into cascaded blocks of dynamic linear, static nonlinear, and dynamic linear (LNL) subsystems based strictly on the input-output relationship is presented. The nonlinear element is assumed to be equicontinuous or must be satisfied by the Weierstrass criterion. Therefore, it could either be a continuous type, as represented by polynomial approximation, or an abrupt type, as represented by piecewise-linear segments. The process uses a series of multilevel inputs to decouple the two linear subsystems from the nonlinear subsystem and then applies the predictor-corrector algorithm to minimize a cost function to obtain the parameter of the subsystem. The method does not restrict the type of input signal, and no prior knowledge of the subsystems is necessary. A numerical example for a prescribed system is given, and the results show almost identical values by any one of the three types of input, namely: step, sinusoidal, or white noise. Three computer programs are developed for the identification of the system with odd, even, and piecewise abrupt types of nonlinearity. The method is applied to model the interfacial phenomenon of a noble metal electrode (Pt) at the nonlinear range, and the algorithm is verified by comparison with a previous result.