Signal Design for the Identification of Nonlinear and Time-Varying Systems

The identification setting is turned to systems with nonlinearities and time-varying properties. The treatment of systems with nonlinearities is first considered where the signal design is shown to be highly dependent on the objectives of the identification test. The identification of the best linear approximation is discussed next. This concept is very useful when a nonlinear process is to be linearised around its operating point. While the best linear approximation depends on the perturbation signal applied, those with Gaussian amplitude distribution are advantageous, particularly, in the identification of block-oriented systems. For the measurement of Volterra kernels, it is shown that multisine signals with specially designed harmonics enable the kernels to be measured without interharmonic distortion. Finally, a method based on frequency domain analysis which allows the quantification of the effects of nonlinearities, noise and time variation is expounded. The technique requires only a single experiment and in the case of multi-input systems, makes use of a set of signals which are uncorrelated with one another. The effectiveness of the technique is illustrated on a mist reactor system.