This paper

reasons the bifurcation characteristics of a nonlinear process system under P control with each mode of controller as bifurcation parameter. The locations and properties of simple bifurcation and Hopf biiurcation points are presented by using a few theorems thus derived. Numerical routines initiated by local bifurcation analysis are given to trace all solution branches in the gain space and to locate the region in which the set-point is globally stable. The bifurcation characteristics of a simplified distillation model with two variables and two loops under P control is revealed by numerical simulation with the above theorems. The distillation system may show multiplicity for closed-loop.