Application of nonlinear dynamic analysis in the identification and control of nonlinear systems—I. Simple dynamics

Nonlinear processes abound in the chemical industry. Although linear controllers work for some of these systems, processes that contain highly nonlinear behaviour typically require a method that takes these nonlinearities into account. Thus, in the last few years there has been an emphasis on nonlinear control strategies such as (nonlinear) model predictive control and geometric control. These methods rely heavily upon the model used. Therefore, it is of great importance to have an adequate model for the nonlinear process, and this model must be identified from process data in many cases. In this work, it is shown through normal form theory that a common model structure can be found for nonlinear systems undergoing similar dynamical behaviour. This structure, in general, contains a low order polynomial vector field characteristic of the particular system. Parameters for this structure are found through a nonlinear least squares algorithm with data from the process of interest. Control is then based upon the derived model. As an example, the nonisothermai Continuous Stirred Tank Reactor with irreversible exothermic reaction (A ~ B) is considered. The above strategy is used in two different operating regions--a region containing multiple steady states and one containing oscillations. In both these regions, a simple model is found and its parameters fit. Geometric controllers are designed based-on these simple models, and the resulting control is shown to be very good. Because of the generality of the models derived from normal form theory, a simple identification and control scheme is presented for two-dimensional systems in the form of a decision tree. The scheme relies entirely on the userʹs observation of the system dynamics and is aimed at simple dynamics such as oscillations and multiple steady states.