A STUDY OF THE CONTROL OF A TUBULAR REACTOR WITH RECYCLE I. Theoretical Results for a Zero-order Exothermic Reaction

The topic of interest in this paper is the behavior of a plug-flow tubular reactor with recycle under feedback control of the rcgutalor type. Attention is devoted mainly to the problem of stabilizing those sicady-slatc profiles which are unstable in the absence of control, but the investigation also includes the controlled behavior of those steady states which arc naturally liable. The study reported in this paper is theoretical; it invokes methods of linear stability analysis and computer simulations in considering two separate cases involving different controlled and manipulated variables. The class of controller functions considered includes the conventional proporIionaI-integraderivative controller. The principal discovery is that the presence of any time delay, regardless of its magnitude, in the controller response prevents stabilization of a naturally unstable state by means of control Strategics of this type. In one of the cases considered, It Is shown that if time delay in the control action is totally absent, stabilization can be achieved; in the other case, stabilization is shown to be possible only if both the time delay in the controller and the transportation lag in the recycle line are zero. The study reported here is based on a hypothetical zero-order reaction, but the icsutls ate linked Io prior experimental observations. Also, other realistic aspects of the basic problem are discussed, and the need for further work is pointed out.