On the use of Poisson wavelet transform for system identification

The Poisson wavelet transform (PWT) has been introduced and successfully applied to model estimation by Kosanovich et al. [K.A. Kosanovich, A.R. Moser, M.J. Piovoso, Poisson wavelets applied to model identification, J. Process Contr. 5 (4), (1995) 225–234]. In the original work the analytical expressions for the PWT of the step response of an FOPTD system is used to estimate the model parameters and verify the appropriateness of the FOPTD structure for the process. This set of analytical expressions, which are fundamental to the use of the PWT for identification are shown to be incomplete. The rectified versions of these expressions are provided in this paper. An additional contribution of this work is the development of a formal framework for the conditions for appropriateness of FOPTD as the proposed model structure based on sensitivity analysis of the PWT. It is shown that this framework can be used to determine the appropriateness of an SOPTD structure as well. Simulation studies are presented to support the above.