The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors

Abstract This paper proposes a thermodynamical pseudo-Hamiltonian formulation of Continuous Stirred Tank Reactor model in which takes place some chemical reaction. This is done both in the isothermal and non isothermal cases. It is shown that the Gibbs free energy and the opposite of entropy can be chosen as Hamiltonian function respectively. For the non isothermal case, the so-called Interconnection and Damping Assignment Passivity Based Control method is applied to stabilize the system at a desired state. For this general reaction scheme, the control problem is shown to be easy to solve as soon as the closed loop Hamiltonian function is chosen to be proportional to the so-called thermodynamic availability function. Simulation results based on a simple first order reaction and operating conditions leading to multiple steady states of the CSTR are given to validate the proposed control design procedure.

[1]  Katalin M. Hangos,et al.  Thermodynamic approach to the structural stability of process plants , 1999 .

[2]  Bernhard Maschke,et al.  An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes , 2007 .

[3]  Romeo Ortega,et al.  On the control of non-linear processes: An IDA–PBC approach , 2009 .

[4]  Françoise Couenne,et al.  Thermodynamic approach for Lyapunov based control , 2009 .

[5]  Kendell R. Jillson,et al.  Process networks with decentralized inventory and flow control , 2007 .

[6]  Antonio A. Alonso,et al.  Process systems and passivity via the Clausius-Planck inequality , 1997 .

[7]  P. Glansdorff,et al.  Thermodynamic theory of structure, stability and fluctuations , 1971 .

[8]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[9]  van der Arjan Schaft,et al.  50th IEEE Conference on Decision and Control and European Control Conference, 2011 , 2011 .

[10]  Miroslav Grmela,et al.  Reciprocity relations in thermodynamics , 2002 .

[11]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[12]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[13]  Daizhan Cheng,et al.  Generalized Hamiltonian realization of time-invariant nonlinear systems , 2003, Autom..

[14]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[15]  Gerd Behrmann,et al.  IFAC World Congress , 2005 .

[16]  William L. Luyben,et al.  Process Modeling, Simulation and Control for Chemical Engineers , 1973 .

[17]  B. Erik Ydstie,et al.  Passivity based control of transport reaction systems , 2005 .

[18]  Martin Guay,et al.  Equivalence to dissipative Hamiltonian realization , 2008, 2008 47th IEEE Conference on Decision and Control.

[19]  József Bokor,et al.  Hamiltonian view on process systems , 2001 .

[20]  S. Smale.  On the mathematical foundations of electrical circuit theory , 1972 .

[21]  Arjan van der Schaft,et al.  Robust Nonlinear Control. Port-controlled Hamiltonian Systems: Towards a Theory for Control and Design of Nonlinear Physical Systems. , 2000 .

[22]  Frank Allgöwer,et al.  An introduction to interconnection and damping assignment passivity-based control in process engineering , 2009 .

[23]  A.J. van der Schaft,et al.  Port contact systems for irreversible thermodynamical systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[24]  Denis Dochain,et al.  Thermodynamics and chemical systems stability: The CSTR case study revisited , 2009 .

[25]  Denis Dochain,et al.  Power-Shaping Control of an Exothermic Continuous Stirred Tank Reactor (CSTR) , 2009 .

[26]  Gábor Szederkényi,et al.  Local dissipative Hamiltonian description of reversible reaction networks , 2008, Syst. Control. Lett..

[27]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[28]  Françoise Couenne,et al.  Lyapunov Based Control for Non Isothermal Continuous Stirred Tank Reactor , 2008 .

[29]  Bernhard Maschke,et al.  Bond graph modelling for chemical reactors , 2006 .

[30]  Antonio A. Alonso,et al.  Stabilization of distributed systems using irreversible thermodynamics , 2001, Autom..

[31]  van der Arjan Schaft,et al.  Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9-11, 2008, Cancún, Mexico , 2008, CDC.

[32]  Nicolas Robidoux,et al.  UNIFIED APPROACH TO HAMILTONIAN SYSTEMS, POISSON SYSTEMS, GRADIENT SYSTEMS, AND SYSTEMS WITH LYAPUNOV FUNCTIONS OR FIRST INTEGRALS , 1998 .

[33]  Bernhard Maschke,et al.  Boundary control for a class of dissipative differential operators including diffusion systems , 2006 .

[34]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[35]  B. Ydstie,et al.  Process systems, passivity and the second law of thermodynamics , 1996 .

[36]  Y. L. Gorrec,et al.  Hamiltonian formulation and IDA-PBC control of non isothermal continuous stirred tank reactors , 2010 .