Nonlinear dynamics and control of process systems with recycle

Process systems with material and energy recycle are well-known to exhibit complex dynamics and to present significant control challenges, due to the feedback interactions induced by the recycle streams. In this paper, we address the dynamic analysis and control of such process systems. Initially, we establish, through an asymptotic analysis, that (i) small recycle flowrates induce a weak coupling among individual processes, whereas (ii) large recycle flowrates induce a time scale separation, with the dynamics of individual processes evolving in a fast time scale with weak interactions, and the dynamics of the overall system evolving in a slow time scale where these interactions become significant; these slow dynamics is usually nonlinear and of low order. Motivated by this, we present (i) a model reduction methodology for deriving nonlinear low-order models of the slow dynamics induced by large recycle streams, and (ii) a controller design framework consisting of properly coordinated controllers in the fast and the slow time scales. The theoretical results are illustrated in a reaction-separation network with a large recycle compared to the throughput.