《System Identification Project Report》.pdf

System Identication Project Report Fei Gao 11th August 2013 1 Introduction The goal of this project is to identify the best linear model of a Wiener- Hammerstein nonlinear system. With a limited maximum input magnitude, an approximation can be made which assumes that the system is linear but disturbed by nonlinear distortions. In other words, the nonlinear system is considered as a linear model plus a noise source. This linear model is called the best linear approximation (BLA) of the nonlinear system. The identication procedure starts from measuring the frequency re- sponse function (FRF) of the BLA. A random phase multi-sine signal is designed as the input of the system. This signal is periodic, so that multiple periods can be measured during each realisation. This allows us to char- acterise the variation induced by the random measurement noise. Several realisations are performed. For each realisation, the input excitation signal has the same spectrum and root mean square (RMS) value, however a dier- ent set of random phases. As a result, the variation induced by the nonlinear eect can then be estimated. An advanced method is also introduced which requires only one realisation of measurement. The result of the FRF measurements provides a nonparametric model of the system. This nonparametric model consists of the transfer function only at a selected set of frequencies. Furthermore, a more general transfer function can be generated from this measurement result. This transfer function is a parametric model of the system which employs a nite number of parameters. 2 Nonparametric Modelling This section describes the measurement steps for identifying the best linear approximation (BLA) of a Wiener-Hammerstein nonlinear system. First of