Control-Relevant System Identification using Nonlinear Volterra and Volterra-Laguerre Models

摘要

One of the key impediments to the wide-spread use of nonlinear control in industry is the availability of suitable nonlinear models. Empirical models, which are obtained from only the process input-output data, present a convenient alternative to the more involved fundamental models. An important advantage of the empirical models is that their structure can be chosen so as to facilitate the controller design problem. Many of the widely used empirical model structures are linear, and in some cases this basic model formulation may not be able to adequately capture the nonlinear process dynamics. One of the commonly used nonlinear dynamic empirical model structures is the Volterra model, and this work develops a systematic approach to the identification of third-order Volterra and Volterra-Laguerre models from process input-output data.First, plant-friendly input sequences are designed that exploit the Volterra model structure and use the prediction error variance (PEV) expression as a metric of model fidelity. Second, explicit estimator equations are derived for the linear, nonlinear diagonal, and higher-order sub-diagonal kernels using the tailored input sequences. Improvements in the sequence design are also presented which lead to a significant reduction in the amount of data required for identification. Finally, the third-order off-diagonal kernels are estimated using a cross-correlation approach. As an application of this technique, an isothermal polymerization reactor case study is considered.In order to overcome the noise sensitivity and highly parameterized nature of Volterra models, they are projected onto an orthonormal Laguerre basis. Two important variables that need to be selected for the projection are the Laguerre pole and the number of Laguerre filters. The Akaike Information Criterion (AIC) is used as a criterion to determine projected model quality. AIC includes contributions from both model size and model quality, with the latter characterized by the sum-squared error between the Volterra and the Volterra-Laguerre model outputs. Reduced Volterra-Laguerre models were also identified, and the control-relevance of identified Volterra-Laguerre models was evaluated in closed-loop using the model predictive control framework. Thus, this work presents a complete treatment of the problem of identifying nonlinear control-relevant Volterra and Volterra-Laguerre models from input-output data.