System identification in frequency domain using wavelets: Conceptual remarks

Model identification plays a central role in any activity associated with process operations. With control being done on different levels, different models are required for the same plant, each for a different range of dynamics. Besides that most identification methods apply to the linear models, they also do not allow for selecting a frequency range. Wavelet-based methods have the intrinsic ability to select time and frequency windows, and, to some extent, are also applicable to non-linear processes.The paper presents an approach, in which the wavelet transform is employed for system identification enabling the selection of the particular frequency range of interest. We will show the use of some wavelet filters with a property of superior selectivity in the frequency domain and having compact support in the time domain, which, in turn, influences an accurate implementation. These properties provide us with a possibility of the measured data analysis in the frequency domain without any loss of information. Selection of a proper filter allows us to identify the system on a desired frequency range, or to identify a number of systems for distinct frequency ranges. This is specifically convenient for the systems with dominant modes, such as singularly perturbed systems. The possibility of selection of the specific frequency range can be utilized for application-based identification such as control, when only a limited frequency range is required. We conclude with a case study, where the proposed algorithms are tested and results are presented.