Stability Analysis and Optimal Control of a Photochemical Heat Engine

  • Stanley J. Watowich
  • Jeffrey L. Krause
  • R. Stephen Berry


We examine a class of heat engines in which selectively absorbed radiant energy drives an exothermic reaction. The chemical reactor, a cylinder fitted with a piston, Incorporates the dissipative losses of friction and heat conduction. Analysis by computer algebra yielded an algorithm for performing a general linear stability analysis of the system. Bifurcation sets mapping regions of single and multiple steady states are generated. In regions sustaining multiple steady states, driving the engine In a cycle about an unstable steady state generates net power output. Optimal control analyses determine piston trajectories yielding maximum power. A linear stability analysis of the optimally controlled system divides the parameter space into regions where the behavior of a steady state moves from an unstable focus to an unstable node. Using parameter sets which map to the unstable focus, the explicit optimal piston trajectory is determined numerically.


Computer Algebra Linear Stability Analysis Heat Engine Stable Steady State Multiple Steady State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    EUNICE MACSYMA Release 305, Copyright (c) 1976, 1983 by Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Enhancements, Copyright (c) 1983 by Symbolics, Inc., 243 Vasser St., Cambridge, Massachusetts 02139.Google Scholar
  2. 2.
    Curzon, F.L. and Ahlborn, B., Am. J. Phys. 43, 22 (1975).CrossRefGoogle Scholar
  3. 3.
    Andresen, B., Salamon, P. and Berry, R.S., J. Chem. Phys. 66, 1571 (1977)CrossRefGoogle Scholar
  4. 3a.
    Andresen, B., Berry, R.S., Nltzon, A. and Salamon, P., Phys. Rev. A 15, 2086 (1977)Google Scholar
  5. 3b.
    Gutkowlcz-Krusln, D., Procaccla, I. and Ross, J., J. Chem. Phys. 69, 3898 (1978)Google Scholar
  6. 3c.
    Rubin, M.H., Phys. Rev. A 22, 1741 (1980)Google Scholar
  7. 3d.
    Salamon, P., Nltzan, A., Andresen, B. and Berry, R.S., Phys. Rev. A 21, 2115 (1980).Google Scholar
  8. 4.
    Naslln, P., Essentials of Optimal Control (Boston Technical Publishers, Inc., Cambridge, Massachusetts, 1969)Google Scholar
  9. 4a.
    Gottfried, B.S. and Welsman, J., Introduction to Optimization Theory (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973).Google Scholar
  10. 5.
    Mozurkewlch, M. and Berry, R.S., J. Appl. Phys. 54, 3651 (1983).CrossRefGoogle Scholar
  11. 6.
    Wheatley, J., Hofler, T., Swift, G.W. and Mlgllorl, A., Phys. Rev. Lett. 50, 499 (1983).CrossRefGoogle Scholar
  12. 7.
    Nltzan, A. and Ross, J., J. Chem. Phys. 59, 241 (1973)CrossRefGoogle Scholar
  13. 7a.
    Zlmmermann, E.C. and Ross, J., J. Chem. Phys. 80, 720 (1983).Google Scholar
  14. 8.
    Taylor, C.F., The Internal Combustion in Theory and Practice (MIT, Cambridge, Massachusetts, 1966), Vol. 1, pp. 312–355.Google Scholar
  15. 9.
    Porter, B, Stability Criteria for Linear Dynamical Systems (Oliver and Boyd, Edinburgh, 1967), pp. 80–82.Google Scholar
  16. 10.
    Crane, R.L., Hillstrom, K.E. and Mlnkoff, M., “Solution of the General Non Linear Programming Problem with Subroutine VMCON” (ANL-80–64, Argonne National Laboratory, Argonne, Illinois 1980). The VMCON program was kindly provided by M. Mlnkoff.Google Scholar
  17. 11.
    Watowlch, S., Hoffmann, K.H. and Berry, R.S., manuscript In preparation.Google Scholar

Copyright information

© Kluwer Academic Publishers 1985

Authors and Affiliations

  • Stanley J. Watowich
    • 1
  • Jeffrey L. Krause
    • 1
  • R. Stephen Berry
    • 1
  1. 1.Department of Chemistry and the James Franck InstituteThe University of ChicagoChicagoUSA

Personalised recommendations