Modelling and control of nonlinear resonating processes: part I—system identification using orthogonal basis function

Abstract

Resonating systems show oscillatory characteristics. System identification of resonating systems and design of their model based control strategy always draw special attention. This work presents a Wiener type system identification technique for nonlinear resonating systems. Orthogonal basis function (henceforth termed as OBF) is employed to capture the linear dynamic part of the Wiener structure while the static nonlinear mapping is described by two means, viz., wavelet decomposition and least squares support vector machine. Use of OBF leads to a parsimonious nature in the resulting nonlinear model. Two types of OBFs have been used in this work viz. Laguerre filter and Kautz filter. The Kautz filter has capability of modelling systems with complex conjugate poles. A case study has been performed with continuous stirred tank reactor (henceforth referred as CSTR) which is a reasonably nonlinear resonating systems. Degree of nonlinearity as well as resonance increases with series-connected CSTR. Simulations are carried out using \(\hbox {MATLAB}^\circledR \) software in order to evaluate the performances of various Wiener structures, and identify the OBF–Wiener model best suited for designing a model based controller.