Stability Analysis and Optimal Control of a Photochemical Heat Engine

Stanley J. Watowich, Jeffrey L. Krause and R. Stephen Berry
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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

Chapter 9 in Applications of Computer Algebra, 1985, pp 183-209 from Springer

Abstract: 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.

Keywords: Computer Algebra; Linear Stability Analysis; Heat Engine; Stable Steady State; Multiple Steady State (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4684-6888-5_9

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