Power-Shaping Control of an Exothermic Continuous Stirred Tank Reactor (CSTR)

Abstract Abstract The exothermic continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. In this paper we present a general methodology to apply the power-shaping control approach to the exothermic CSTR study case. It results in a global Lyapunov function for the exothermic CSTR. This Lyapunov function is then reshaped by the means of a controller in order to stabilize the process at a desired temperature. Some considerations on the local and global convergence to the desired state are presented.

[1]  A. Schaft,et al.  On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems , 1999 .

[2]  Denis Dochain,et al.  Asymptotic observers for stirred tank reactors , 1992 .

[3]  Bayu Jayawardhana,et al.  European Control Conference 2007 , 2007 .

[4]  Julio R. Banga,et al.  A systematic approach to plant-wide control based on thermodynamics , 2007, Comput. Chem. Eng..

[5]  Denis Dochain,et al.  Contact structures: application to interconnected thermodynamical systems , 2007, 2007 European Control Conference (ECC).

[6]  J. K. Moser,et al.  A theory of nonlinear networks. I , 1964 .

[7]  Jacquelien M. A. Scherpen,et al.  On mechanical mixed potential, content and co-content , 2003, 2003 European Control Conference (ECC).

[8]  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.

[9]  Gábor Szederkényi,et al.  DYNAMIC ANALYSIS AND CONTROL OF CHEMICAL AND BIOCHEMICAL REACTION NETWORKS , 2006 .

[10]  B. Erik Ydstie,et al.  Process systems and inventory control , 1998 .

[11]  A. B. Poore,et al.  On the dynamic behavior of continuous stirred tank reactors , 1974 .

[12]  木山 健,et al.  16th IFAC World Congress , 2006 .

[13]  Bernhard Maschke,et al.  Energy-conserving formulation of RLC-circuits with linear resistors , 2006 .

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

[15]  R. Ortega,et al.  Energy-shaping of port-controlled Hamiltonian systems by interconnection , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[16]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[17]  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).

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

[19]  Rutherford Aris,et al.  An analysis of chemical reactor stability and control—I: The possibility of local control, with perfect or imperfect control mechanisms , 1958 .

[20]  Jacquelien M. A. Scherpen,et al.  A power-based description of standard mechanical systems , 2007, Syst. Control. Lett..

[21]  Mi Friswell,et al.  17th IFAC World Congress , 2008 .

[22]  Jacquelien M. A. Scherpen,et al.  Power shaping: a new paradigm for stabilization of nonlinear RLC circuits , 2003, IEEE Trans. Autom. Control..

[23]  Bernhard Maschke,et al.  From conservation laws to port-Hamiltonian representations of distributed-parameter systems , 2005 .

[24]  Jacquelien M. A. Scherpen,et al.  An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems , 2003, Autom..

[25]  Romeo Ortega,et al.  Power–based control of physical systems: two case studies , 2008 .

[26]  Julio R. Banga,et al.  From irreversible thermodynamics to a robust control theory for distributed process systems , 2000 .