Application of nonlinear dynamic analysis to the identification and control of nonlinear systems—III. n-Dimensional systems

In two previous publications, the authors have shown that normal form theory, a method used extensively in dynamic analysis, can be applied in the structure identification of nonlinear systems. In particular, normal form theory bridges the gap between structure of a nonlinear, low order polynomial dynamical system and the behavior it is able to predict or represent. This is important because knowing a systemʹs dynamic behavior automatically leads to a simple nonlinear normal form model that can be used for (nonlinear) control. Previously, only two-dimensional normal form models were derived. For this paper, simple, n-dimensional, low order polynomial dynamical models will be derived that can represent a nonlinear system with multiple steady states or a limit cycle in the operating region of interest. Using as a plant the nonisothermal Continuous Stirred Tank Reactor with consecutive reactions (A~B~C), it is shown that identification and control of this three-dimensional system using the aforementioned normal form models is feasible.