Application of nonlinear dynamic analysis in the identification and control of nonlinear systems—II. More complex dynamics

Abstract

This paper proposes a novel identification and controller design method for nonlinear systems. The identification algorithm is based upon normal form theory, a method borrowed from the dynamic analysis area. The goal of normal form theory is to derive simple nonlinear systems with polynomial vector fields. These polynomial models, derived around singularities (points in the parameter space which organize certain dynamic behavior) yield simple dynamic models. Knowing the qualitative dynamics which the singularity contains and the structure of the normal form, the relationship between structure of a simple dynamic model and its dynamics is resolved. By finding normal forms for many singularities, and thus many different types of dynamics, the relationship between model structure and dynamics can be tabulated. To use these tabulated model structures, one must know a priori the qualitative nature of the plant dynamics in the operating region of interest; then one selects the appropriate dynamic normal form model which becomes the basis for the design of a controller. Extending the previous work 1 , this paper treats the case of complex two-dimensional dynamics characterized by higher codimension singularities. The identification algorithm will be illustrated with reference to the ubiquitous nonisothermal Continuous Stirred Tank Reactor as a plant to be controlled. This plant exhibits very interesting nonlinear behavior and is thus a very good example to illustrate this novel identification technique. Plant data will be obtained in many operating regions containing interesting nonlinear behavior. Simple nonlinear normal form models are chosen from the above list, and these models are shown to be sufficient for control in the operating region using a nonlinear geometric controller.