BIFURCATION ANALYSIS OF MULTIVARIABLE FEEDBACK CONTROL SYSTEMS

Abstract

The closed-loop dynamic behavior of nonlinear, multivanable systems is often unpredictable due to complex internal structures unaccounted for by linear control theory. Bifurcation analysis is used to explore the characteristics of such systems governed by linear feedback control. Two new theorems are presented concerning the local stability of a broad class of nonlinear, multivanable systems utilizing Proportional and Proportional-Integral control. A dynamic simulation of a binary distillation column reveals a number of interesting phenomena including limit cycle behavior in asymptotically stable areas of the controller gain space and steady-state multiplicity if a controller gain has the wrong sign.

KEYWORDS:

• Bifurcation analysis
• Nonlinear systems
• Multivanable control
• Limit cycles
• Multiplicity

Additional information

Notes on contributors

MICHAEL F. SAUCIER

Present address: Honeywell Inc., Phoenix, Arizona.

HSUEH-CHIA CHANG

Present address: Dept. of Chemical Engineering, University of Notre Dame, Notre Dame, IN.