Power-shaping control: Writing the system dynamics into the Brayton-Moser form

Power-shaping control is an extension of energy-balancing passivity-based control that is based on a particular form of the dynamics, the Brayton–Moser form. One of the main difficulties in this control approach is to write the dynamics in the suitable form since this requires the solution of a partial differential equation (PDE) system with an additional sign constraint. Here a general methodology is described for solving this partial differential equation system. The set of all solutions to the PDE system is given as the solution of a linear equation system. Furthermore a necessary condition is given so that a solution of the linear system which meets the sign condition exists. This methodology is illustrated on the case of a chemical reactor, where the physical knowledge of the system is used to find a suitable solution.

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

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

[3]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[4]  Jacquelien M. A. Scherpen,et al.  Power-based control of physical systems , 2010, Autom..

[5]  S. Bhat,et al.  Modeling and analysis of mass-action kinetics , 2009, IEEE Control Systems.

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

[7]  Julio R. Banga,et al.  From irreversible thermodynamics to a robust control theory for distributed process systems , 2002 .

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

[9]  B. O'neill.  Elementary Differential Geometry , 1966 .

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

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

[12]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[14]  Audrey Favache.  Thermodynamics and process control , 2009 .

[15]  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).

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

[17]  Denis Dochain,et al.  Power-shaping control of reaction systems: The CSTR case , 2010, Autom..

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

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

[20]  P. Glansdorff,et al.  On a general evolution criterion in macroscopic physics , 1964 .

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

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

[23]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[24]  Denis Dochain,et al.  Analysis and control of the exothermic continuous stirred tank reactor: the power-shaping approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.