Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle

Abstract

In this contribution the stability properties and regulation of a class of convective systems described by first order hyperbolic partial differential equations are studied. The systems' setting is consistent with the first and second laws of thermodynamics, allowing to use the entropy functional as a storage function and the internal entropy production as the dissipation in an analogue context to Hamiltonian systems. It is found that the difference of the entropy evaluated at the boundaries is directly proportional to the supply rate, fulfilling the dissipation inequality. Furthermore, the dynamics of the entropy balance allows to define a saturated Proportional-Integral controller with variable parameters, whose design is achieved through a cascade structure. The inner loop tracks an entropy reference, while the outer loop tracks a process variable. The main advantage of the regulation design is that only a lumped actuator is needed with continuous measurements at the boundaries. The controller is designed for an adiabatic plug flow reactor with a recycle of the output stream into the input stream, where the recycle rate is used as the control variable. Finally, the controller is tested to track a set point under several disturbances.