Assessment of damping coefficients ranges in design of a free piston Stirling engine: Simulation and experiment

Abstract

This paper concentrates on investigating the robustness of the free piston Stirling engine (FPSE) considering the uncertainty of the damping coefficients of power and displacer pistons using the vanishing perturbation. First, error state equations of the FPSE possessing nonlinear springs are derived. Next, the passivity-based control method without applying the uncertainty term is employed to achieve the limit cycle for power and displacer pistons motions. Afterwards, the vanishing perturbation is considered to study the robustness of the system against the allowable increase of the power and displacer pistons’ damping coefficients through finding the upper bound. Consequently, the presented paper, first, studied the FPSE behavior without considering the uncertainty term and then, probes the consideration of the uncertainty term. Accordingly, the motions and velocities of pistons as well as the existence of limit cycles in the system response are investigated in detail. Next, the validity of the presented scheme is experimented through a prototype model, namely SUTech-SR-1. Finally, according to the achieved upper bound, the proposed work not only appropriately predicts the FPSE behavior, but also the obtained simulation data are found to be in an acceptable agreement with those of the experiment.