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

In this contribution the stability properties and regulation of a class of convective systems described by first order hyperbolic partial differential equations with boundary recycle is studied. The system's 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 similarly to Hamiltonian systems, usually not well defined for systems with mass flows. 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 allow to define a saturated Proportional-Integral controller with a cascade structure: The inner loop tracks an entropy reference, while the outer loop regulates a process variable. The regulation is achieved with a lumped actuator, using continuous measurements at the boundaries. The controller is applied to an adiabatic plug flow reactor with a recycle of the output stream, a configuration known to be potentially unstable with dissociation reactions. Finally, the controller is tested to track a set point facing several disturbances using the recycle rate as the control variable.