Optimal motion trajectory for the four-stroke free-piston engine with irreversible Miller cycle via a Gauss pseudospectral method

Abstract

A four-stroke free-piston engine with internal and external irreversibilities of finite combustion rate of the fuel, heat transfer and friction is investigated in this paper. Under the condition of the fixed fuel consumption per cycle, the optimal piston motion trajectory for maximizing the net work output of different cases is derived by applying optimal control theory. Considering the path constraints and boundary conditions of this free-piston Miller cycle, a Gauss pseudospectral method (GPM) is presented for solving optimal motion trajectory. The results show that the optimal piston trajectory improves the efficiency by more than 10% and also suitably reduces the heat transfer losses compared to the conventional piston motion. By optimizing the piston motion around the top dead center (TDC), the in-cylinder gas pressure and temperature have a remarkable improvement while the heat transfer losses have a suitable reduction. The effects of other parameters, such as combustion duration and the frictional coefficient on the piston trajectory, are also investigated. It is shown that optimizing the piston motion trajectory is a good approach for the free-piston engine to improve the efficiency and it can provide guidelines for the optimal control of the practical free-piston engine.