Wavelet-based modulation in control-relevant process identification

The identification of models from operating data for process controller design requires that the information from the process be extracted in pieces that are localized in both time and frequency. Such an extraction process would allow the separation of valuable signal information from the effects of nonstationary disturbances and noise. The wavelet transform provides an efficient approach for such a decomposition, which is organized in a multiscale, hierarchical fashion. By using the method of modulating functions in conjunction with the wavelet decomposition, it is demonstrated that recursive state-space models, which are multiscale in character and suitable for the design of model-predictive controllers, may he readily constructed with lower levels of modeling error than yielded by traditional techniques. The method is especially suitable for the identification of time-varying and nonlinear models, where the nonlinear process is represented by a set of linear models. The multiscale character of the wavelet basis makes it particularly suitable for multirate, multivariable processes. A series of examples illustrates various aspects of the proposed approach and its inherent advantages.