Bifurcation Characteristics of Nonlinear System under Two-Variable Control

The global stability of nonlinear system is much difficult to determine. This paper applies bifurcation theory, reasons the bifurcation characteristics of nonlinear system under PI control through each mode of controller as bifurcation parameter. The location and property of the simple bifurcation and Hopf bifurcation point are displayed through a few theorems. Numerical routines initiated by the local bifurcation analysis are presented to trace all solution branches in the gain space and to locate the region in which the set-point is globally stable. The bifurcation charateristics of a simplified distillation model under two-varible and two-loop contol is revealed by numerical simulation of above theorems. The distillation system may appear the multiplicity and limit-cycle. The results have somewhat guiding significance for industrial distillation control.