Dynamics of a driven Stirling engine

We study the nonlinear dynamics of an idealized driven Stirling engine model. The model is analogous to an oscillator with a nonlinear dependence of the spring constant on the state and input signal, with a rich complexity of behaviors depending on frequency ratios and amplitudes. We employ a change of coordinates where input-to-state boundedness questions can be answered. Furthermore, a fixed point argument is used to show that for each periodic input forcing, the system posses at least one periodic orbit of the same period. We elaborate on the significance of this fact to input signal design for the driven Stirling engine.

[1]  C. Byrnes.  Topological Methods for Nonlinear Oscillations , 2010 .

[2]  Ruzhu Wang,et al.  Energy efficiency and economic feasibility of CCHP driven by stirling engine , 2004 .

[3]  C. M. Place,et al.  Ordinary Differential Equations , 1982 .

[4]  Necati Ulusoy.  Dynamic analysis of free piston Stirling engines , 1994 .

[5]  Jean Mawhin,et al.  Topological Fixed Point Theory and Nonlinear Differential Equations , 2005 .

[6]  Bassam Bamieh,et al.  Optimal Periodic Control of an Ideal Stirling Engine Model , 2015 .

[7]  Vinod Kumar Gopal,et al.  Active Stirling engine , 2009, TENCON 2009 - 2009 IEEE Region 10 Conference.

[8]  Adam Hawkes,et al.  Cost-effective operating strategy for residential micro-combined heat and power , 2007 .

[9]  Theocharis Tsoutsos,et al.  Technical and economical evaluation of solar thermal power generation , 2003 .

[10]  E.J. Barth,et al.  Control-based design of free-piston stirling engines , 2008, 2008 American Control Conference.

[11]  Eberhard Zeidler,et al.  Applied Functional Analysis: Applications to Mathematical Physics , 1995 .

[12]  Eric J. Barth,et al.  Modeling and Validation of Free-Piston Stirling Engines Using Impedance Controlled Hardware-in-the-Loop , 2011 .

[13]  Peter E. Caines,et al.  An Isothermal Energy Function State Space Model of a Stirling Engine , 2015 .

[14]  Eric J. Barth,et al.  A Lumped-Parameter Dynamic Model of a Thermal Regenerator for Free-Piston Stirling Engines , 2009 .

[15]  Somchai Wongwises,et al.  A review of solar-powered Stirling engines and low temperature differential Stirling engines , 2003 .