Control-oriented modeling of Stirling engine regenerators

This paper considers the problem of developing a low order, control-oriented model of typical regenerator components in Stirling engines. We begin with a first principles model which is in the form of a 1-dimensional nonlinear partial differential equation incorporating advection, diffusion and heat transfer between the regenerator metal matrix and the working gas. Perturbation analysis is proposed as a possible method of model reduction in order to obtain models useful for engine optimization and control. Several small parameters are identified which determine which terms in the governing equations can be neglected. The resulting relations are then used in the simulation of a Stirling engine and the results are compared to those wherein the original PDE is modeled using a nonlinear finite difference scheme. A comparison of the two responses shows that they produce qualitatively similar behavior.