Stability Analysis and Optimal Control of a Photochemical Heat Engine

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.