A novel combustion control, i.e. The trajectory-based combustion control, was proposed previously. This control is enabled by free piston engines (FPEs) and utilizes the FPE's controllable piston trajectory to enhance thermal efficiency, reduce emissions and realize variable fuels applications. On top of that, a control-oriented model was also developed aimed to implement the trajectory-based combustion control in realtime. Specifically, a unique phase separation method was proposed in the model, which separates an engine cycle into four phases (pure compression, ignition, heat release and pure expansion) and employs the minimal reaction mechanism accordingly. In this paper, the framework of the previous control-oriented model is extended to variable fuels, such as methane, n-heptane and bio-diesel. Such an extension is reasonable since the separated four phases are representative in typical combustion processes of all fuels within an engine cycle. Besides, a least-squares optimization is formulated to calibrate the chemical kinetics variables for each fuel. At last, simulation results and the related analysis show that all the derived control-oriented models have high fidelity and much lighter computational burdens to represent the HCCI combustion of each fuel along variable piston trajectories.