Robust framework for simultaneous optimization of performance and stability in active free-piston stirling engines

Free-piston Stirling Engines (FPSEs) are highly promising for solar-to-electric conversion; however, passive designs lack adaptability and robustness. This paper introduces a pioneering unified framework based on a robust technique for optimizing the dynamics of active FPSEs. The framework simultaneously addresses three critical objectives: (1) quantifying the output power generation, (2) guaranteeing the existence of stable oscillations (the sufficient condition), and (3) precisely identifying the optimal operating resonance frequency. A robust control method, formulated using Lagrangian mechanics, regulates the displacer piston and significantly enhances the power piston’s amplitude. The core innovation lies in the methodology’s ability to effectively enhance system robustness against dynamic disturbances, prevent unwanted stabilization, and ensure optimal power extraction. Simulation results validated against the B10-B engine data reveal a crucial design insight: for each spring stiffness value, there exists a unique optimal operating frequency that maximizes performance. For instance, a stiffness of 1000 N/m yields a peak output power of 80.47 W at 90 rad/s. This synthesis of dynamic stability assurance and precise performance maximization via a robust methodology marks a significant step forward in the design of highly reliable and computationally efficient active FPSE systems.