Nonlinear modeling of a Free Piston Stirling Engine combined with a Permanent Magnet Linear Synchronous Machine

•Linear and nonlinear models of a β-type Stirling engine are developed and compared.•Nonlinear model of Stirling engine is validated with available experimental results.•State equations of a Stirling engine combined with a linear generator are developed.•Combined system of a Stirling engine with a generator is modeled and controlled.