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Stability Analysis and Optimal Control of a Photochemical Heat Engine

In: Applications of Computer Algebra

Author

Listed:
  • Stanley J. Watowich

    (The University of Chicago, Department of Chemistry and the James Franck Institute)

  • Jeffrey L. Krause

    (The University of Chicago, Department of Chemistry and the James Franck Institute)

  • R. Stephen Berry

    (The University of Chicago, Department of Chemistry and the James Franck Institute)

Abstract

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.

Suggested Citation

  • Stanley J. Watowich & Jeffrey L. Krause & R. Stephen Berry, 1985. "Stability Analysis and Optimal Control of a Photochemical Heat Engine," Springer Books, in: Richard Pavelle (ed.), Applications of Computer Algebra, chapter 9, pages 183-209, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-6888-5_9
    DOI: 10.1007/978-1-4684-6888-5_9
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