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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9733806/ |
| _version_ | 1818307722597105664 |
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| author | Marco A. Zarate-Navarro Stevan Dubljevic Armando Campos-Rodriguez Efren Aguilar-Garnica J. Paulo Garcia-Sandoval |
| author_facet | Marco A. Zarate-Navarro Stevan Dubljevic Armando Campos-Rodriguez Efren Aguilar-Garnica J. Paulo Garcia-Sandoval |
| author_sort | Marco A. Zarate-Navarro |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T07:02:54Z |
| format | Article |
| id | doaj.art-62113893c69f45deafc7b3b7fde783eb |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-13T07:02:54Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-62113893c69f45deafc7b3b7fde783eb2022-12-21T23:55:53ZengIEEEIEEE Access2169-35362022-01-0110309393094810.1109/ACCESS.2022.31573359733806Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass RecycleMarco A. Zarate-Navarro0https://orcid.org/0000-0001-7415-8503Stevan Dubljevic1https://orcid.org/0000-0002-1889-1599Armando Campos-Rodriguez2https://orcid.org/0000-0002-3973-2685Efren Aguilar-Garnica3J. Paulo Garcia-Sandoval4https://orcid.org/0000-0001-6889-0140Departamento de Biotecnológicas y Ambientales, Universidad Autónoma de Guadalajara, Zapopan, MexicoDepartment of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, CanadaDepartamento de Biotecnológicas y Ambientales, Universidad Autónoma de Guadalajara, Zapopan, MexicoDepartamento de Biotecnológicas y Ambientales, Universidad Autónoma de Guadalajara, Zapopan, MexicoDepartamento de Ingeniería Química, Universidad de Guadalajara, Guadalajara, MexicoIn 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.https://ieeexplore.ieee.org/document/9733806/Non-equilibrium thermodynamicsfirst order hyperbolic systemsboundary controlmass recyclePFRPDE |
| spellingShingle | Marco A. Zarate-Navarro Stevan Dubljevic Armando Campos-Rodriguez Efren Aguilar-Garnica J. Paulo Garcia-Sandoval Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle IEEE Access Non-equilibrium thermodynamics first order hyperbolic systems boundary control mass recycle PFR PDE |
| title | Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle |
| title_full | Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle |
| title_fullStr | Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle |
| title_full_unstemmed | Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle |
| title_short | Dissipative Boundary Control for an Adiabatic Plug Flow Reactor With Mass Recycle |
| title_sort | dissipative boundary control for an adiabatic plug flow reactor with mass recycle |
| topic | Non-equilibrium thermodynamics first order hyperbolic systems boundary control mass recycle PFR PDE |
| url | https://ieeexplore.ieee.org/document/9733806/ |
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