(569e) Passivity Based Control of Chemical Reactors Using Reaction Invariants

We develop an approach to deal with the nonlinear control of the CSTR using the concept of using passivity based control to control one or more reaction invariants. More precisely, the paper shows that the CSTR dynamics can be split into reaction variant and reaction invariant dynamics through the use of linear combinations of system variables (called inventories). This separation is based the stoichiometric information only. As the reaction invariants are exponentially stable, the control design for an exponential stabilization of the reactor is simply solved by stabilizing the reaction variants. In this paper we show how this can be achieved using a combination of nonlinear (adaptive) feed-forward and passivity based feedback control of the reaction variants. In some applications there may be more variants than it is possible to independently stabilize using nonlinear control. In such cases the uncontrolled variants may or may not be stable. We show how the stability of these dynamics can be analyzed using Feinberg’s reaction network theory based on deficiency analysis. The theoretical results of the paper are illustrated by application of the theory to example systems. These include a first order chemical reaction with multiplicity behavior, second order and higher order systems. Non-adaptive and adaptive control systems are shown to give the same asymptotic behavior after the learning phase has been completed. During the course of the paper presentation we will reveiw briefly the historical background of the use of reaction invariants in the area of process control, starting with the seminal work of Fjeld, Asbjornsen and Astrom leading to our own contribtions and the the work of Bonvin and his students at EPFL.