• Rush D. RobinettIII
  • David G. Wilson
Part of the Understanding Complex Systems book series (UCS)


In this book, we present an innovative control system design methodology. This design methodology is based on the latest research and development results at Sandia National Laboratories within the renewable energy electric power grid integration program. This research focused on the convergence of three goals. The first goal was to create a unifying metric to compare the value of different energy sources integrated into the electric power grid such as a coal-burning power plant, wind turbines, solar photovoltaics, etc., instead of the typical metric of costs/profit. The second goal was to develop a new nonlinear control tool that applies power flow control, thermodynamics, and complex adaptive systems theory to the energy grid in a consistent progression. The third goal was to apply collective robotics theories to the creation of high-performance teams of people and optimal individuals. This is one approach to account for the effects of individuals and groups of people that will be controlling and selling power into a distributed, decentralized electric power grid. Concepts from thermodynamics, mechanics, stability and control, and advanced control design are presented in Part I. This provides the reader with the fundamental building blocks of the Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) design plus analysis process. HSSPFC is applied to eight case studies in Part II. These range from integrating renewable energy generators into the grid and microgrids to satellite reorientation maneuvers to control of robotic manipulators. The last part, Part III, develops design and analysis tools for self-organizing systems.


Wind Turbine Stability Boundary Power Flow Sandia National Laboratory Limit Cycle Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Murray, R.M. (ed.): Control in an Information Rich World: Report of the Panel on Future Directions in Control, Dynamics, and Systems. SIAM, Philadelphia (2003) MATHGoogle Scholar
  2. 2.
    Greven, A., Keller, G., Warnecke, G.: Entropy. Princeton University Press, Princeton (2003) MATHGoogle Scholar
  3. 3.
    Schrödinger, E.: What Is Life? Cambridge University Press, Cambridge (1992). Reprint edn. Google Scholar
  4. 4.
    Kondepudi, D., Prigogine, I.: Modern Thermodynamics: From Heat Engines to Dissipative Structures. Wiley, New York (1999) Google Scholar
  5. 5.
    Nicolis, G., Prigogine, I.: Exploring Complexity: An Introduction. Freeman, New York (1989) Google Scholar
  6. 6.
    Meirovitch, L.: Methods of Analytical Dynamics. McGraw-Hill, New York (1970) Google Scholar
  7. 7.
    Robinett III, R.D., Wilson, D.G.: Collective systems: physical and information exergies. Sandia National Laboratories, SAND2007 Report (March 2007) Google Scholar
  8. 8.
    Robinett III, R.D.: Collective Groups and Teams. Draft book (January 2007) Google Scholar
  9. 9.
    Nicolis, G., Prigogine, I.: Self-organization in Non-equilibrium Systems. Wiley, New York (1977) Google Scholar
  10. 10.
    Prigogine, I., Stengers, I.: Order out of Chaos. Bantam Books, New York (1984) Google Scholar
  11. 11.
    Heylighen, F.: The science of self-organization and adaptivity. Principia Cybernetic Web.
  12. 12.
    Robinett III, R.D., Wilson, D.G., Reed, A.W.: Exergy sustainability for complex systems. InterJournal Complex Systems, 1616, New England Complex Systems Institute (2006) Google Scholar
  13. 13.
    Robinett III, R.D., Wilson, D.G.: Exergy and irreversible entropy production thermodynamic concepts for nonlinear control design. Int. J. Exergy 6(3), 357–387 (2009) Google Scholar
  14. 14.
    Chetayev, N.G.: The Stability of Motion. Pergamon, Elmsford (1961) Google Scholar
  15. 15.
    Junkins, J.L., Kim, Y.: Introduction to Dynamics and Control of Flexible Structures. AIAA, Washington (1993) MATHGoogle Scholar
  16. 16.
    Gopinath, A.K., Beran, P.S., Jameson, A.: Comparative analysis of computational methods for limit-cycle oscillations. In: 47th AIAA Structures, Structural Dynamics and Materials Conference, Newport, Rhode Island, May 2006 Google Scholar
  17. 17.
    Hall, K.C., Thomas, J.P., Clark, W.S.: Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA J. 40(5), 879–886 (2002) CrossRefGoogle Scholar
  18. 18.
    Price, S.J., Lee, B.H.K., Alighanbari, H.: Post-instability behavior of a two-dimensional airfoil with a structural nonlinearity. J. Aircr. 31(6), 1395–1401 (1994) CrossRefGoogle Scholar
  19. 19.
    Ko, J., Kurdila, A.J., Strganac, T.W.: Nonlinear control of a prototypical wing section with torsional nonlinearity. J. Guid. Control Dyn. 20(6), 1181–1189 (1997) MATHCrossRefGoogle Scholar
  20. 20.
    Lee, B.H.K., Jiang, L.Y., Wong, Y.S.: Flutter of an airfoil with a cubic nonlinear restoring force. AIAA paper AIAA-98-1725 Google Scholar
  21. 21.
    Clark, R.L., Dowell, E.H., Frampton, K.D.: Control of a three-degree-of-freedom airfoil with limit-cycle behavior. J. Aircr. 37(3), 533–536 (2000) CrossRefGoogle Scholar
  22. 22.
    Yingsong, G., Zhichun, Y.: Aeroelastic analysis of an airfoil with a hysteresis non-linearity. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island, May 2006 Google Scholar
  23. 23.
    Sabatini, M.: Limit cycle’s uniqueness for a class of plane systems. Technical Report UTM 662, Mathematica, University of Trento, Italy (February 2004) Google Scholar
  24. 24.
    Carletti, T., Villari, G.: A note on existence and uniqueness of limit cycles for Liénard systems. Preprint submitted to Journal of Mathematical Analysis and Applications, August 2007 Google Scholar
  25. 25.
    Boyce, W.E., DiPrima, R.C.: Elementary Differential Equations and Boundary Value Problems, 8th edn. Wiley, New York (2005) Google Scholar
  26. 26.
    Weinstock, R.: Calculus of Variations with Applications to Physics and Engineering. Dover, New York (1974) MATHGoogle Scholar
  27. 27.
    Dowell, E.H., Crawley, E.F., Curtiss, H.C. Jr., Peters, D.A., Scanlan, R.H., Sisto, F.: A Modern Course in Aeroelasticity. Sijthoff & Noordhoff, Rockville (1978) MATHGoogle Scholar
  28. 28.
    Flanigan, F.J.: Complex Variables—Harmonic and Analytic Functions. Dover, New York (1983) Google Scholar
  29. 29.
    Boas, M.L.: Mathematical Methods in the Physical Sciences. Wiley, New York (1966) MATHGoogle Scholar
  30. 30.
    Robinett III, R.D., Wilson, D.G.: Exergy and entropy thermodynamic concepts for control system design: slewing single axis. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, CO, August 2006 Google Scholar
  31. 31.
    Abramson, H.N.: An Introduction to the Dynamics of Airplanes. Ronald Press, New York (1958) Google Scholar
  32. 32.
    Ogata, K.: Modern Control Engineering. Prentice-Hall, Englewood Cliffs (1970) Google Scholar
  33. 33.
    Robinett III, R.D., Wilson, D.G.: Collective plume tracing: a minimal information approach to collective control. In: Proceedings of the 2007 American Control Conference, New York, July 2007 Google Scholar
  34. 34.
    Robinett III, R.D., Wilson, D.G.: Decentralized exergy/entropy thermodynamic control for collective robotic systems. In: Proceedings of the ASME 2007 International Mechanical Engineering Congress and Exposition, Seattle, WA, November 2007 Google Scholar
  35. 35.
    Robinett III, R.D., Hurtado, J.E.: Stability and control of collective systems. J. Intell. Robot. Syst. 39, 43–55 (2004) CrossRefGoogle Scholar
  36. 36.
    Hurtado, J.E., Robinett III, R.D., Dohrmann, C.R., Goldsmith, S.Y.: Decentralized control for a swarm of vehicles performing source localization. J. Intell. Robot. Syst. 41, 1–18 (2004) CrossRefGoogle Scholar
  37. 37.
    Robinett III, R.D., Wilson, D.G.: Hamiltonian surface shaping with information theory and exergy/entropy control for collective plume tracing. Int. J. Systems, Control and Communications 2(1/2/3) (2010) Google Scholar
  38. 38.
    Berg, T.: Fisher information: its flow, fusion, and coordination. Sandia National Laboratories, SAND2002-1969 Report (June 2002) Google Scholar
  39. 39.
    Schwartz, M.: Information Transmission, Modulation, and Noise: A Unified Approach to Communication Systems, 3rd edn. McGraw-Hill, New York (1980) Google Scholar
  40. 40.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948), 623–656 MathSciNetMATHGoogle Scholar
  41. 41.
    Frieden, B.R.: Physics from Fisher Information: A Unification. Cambridge University Press, Cambridge (1999) Google Scholar
  42. 42.
    Cooper, J.A., Robinett III, R.D.: Structured communication and collective cohesion measured by entropy. J. Syst. Safety 41(4) (2005) (electronic) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations