Control of a chaotic polymerization reaction using linear and nonlinear controllers

Abstract

Chaos has been found in a number of nonlinear chemical processes including electrochemical reactions, fluidized beds, pulsed combustors, and polymerization reactions. While the control of chaos has recently a received a great deal of attention, the performance of traditional control schemes is poorly understood. Rather than implement a specific chaos control scheme, such as the well-known OGY method, we examine the feedback control of a chaotic polymerization reaction to a steady state using conventional linear and nonlinear control techniques. We show that it is possible to control a chaotic reaction system using a simple proportional controller, a discrete controller, a nonlinear model predictive controller which includes process-model mismatch. The performance of each control scheme is evaluated from the basin of successful control. While model predictive control yields a the most extensive basin and thus the best performance, in all cases the basin has a fractal structure for some values of the control parameter. The implications of a fractal basin to the robustness of the controller and the likelihood of successful control are discussed.