Modelling of Nonlinear Systems Using Normal Forms

Normal form theory, a method usually reserved for bifurcation analysis, is used in this paper to obtain simple nonlinear models for dynamic processes. To use these models, one must have a priori some knowledge about the dynamics of the process of interest. Once this is known, an appropriate model which contains these dynamics can be chosen. It only remains to identify the parameters of the model and then to design a nonlinear controller. Here, two normal form models are presented - one based on a hysteresis bifurcation and the other one based on a degenerate Hopf bifurcation. It is shown, using as an example plant the nonisothermal CSTR, that this method of identification and control performs very well.