(583c) Single-Step Formulation of Feedback Control for an Exothermic Plug-Flow Reactor

This work proposes a single-step full state feedback control design of first order non-linear hyperbolic partial differential equations which model an exothermic plug-flow reactor. Optimal heat exchanger temperature profile of exothermic tubular reactor is determined by plug-flow characteristics at the steady-state of interest. A cost criterion is defined to enable a trade-off between process performance and heat loss. An analytical solution is obtained according to the minimum principle of Pontryagin optimal control theory. However, it is shown by numerical simulation that the optimal temperature and reactant concentration profiles of interest are unstable steady-states. Therefore, linear and quadratic full state feedback control design are proposed by single-step linearization and simultaneous coordinate transformation for first order hyperbolic transport reaction system. The control is obtained by single step state nonlinear transformation and feedback control law with prescribed closed loop dynamics. The solution is guaranteed by the Lyapunov's auxiliary theorem and is realized in one step, avoiding the restrictions existing in other approaches. The temperature and reactant concentration of open-loop system can be successfully stabilized at optimal steady-states of interest with linear and non-linear control. The results are illustrated by numerical simulations.