| Summary: | This thesis carries out a detailed study of a nonlinear spectral theory that is useful for modeling and controlling chemical reactors. The motivation for this work originates from a few reports which have demonstrated in the past that the nonlinear spectral method offers a useful mathematical framework for classifying and quantifying nonlinear complexities of large degrees of freedom, as well as for qualifying a general nonlinear dynamic behavior. We present and discuss this new theory and show that it extends the familiar linear systems notion of characteristic modes (eigenmodes), as well as the notions of mathematical quantities known as the eigenvectors, and eigenvalues, into a multi-dimensional nonlinear domain, i. e., applies to model dimensions one, two, three and higher. This approach offers a new insight into nonlinear phenomena, and as such has a significant theoretical and practical value. In the theory of nonlinear systems the spectral framework provides some useful answers regarding the issues of multivariate process complexity, stability and control. Similarly, in applications it often leads to a simple relation between a desired process behavior and control parameters. We demonstrate this by showing how a process operating point, its behavior, and its domain of attraction are determined by nonlinear structures which characterize both a process and its control realization. In addition, we show that by a correctly modeling and regulating process nonlinearities one can obtain a nonlinear control solution that often outperforms the conventional first-order realizations. That is, there exist important nonlinear structural and dynamic process relations which determine a feasibility of a control realization. This is demonstrated by studying control behaviors of several highly exothermic continuously stirred tank reactor processes.
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