This　study　presents　a　free　piston　expander-linear　generator　(FPE-LG)　for　engine　waste　heat　recovery.　The　control　strategies　based　on　displacement　(control　strategy　A)　and　valve　timings　(control　strategy　B)　are　proposed.　The　operation　and　output　characteristics　with　different　control　strategies　are　conducted.　The　results　show　that　control　strategy　has　significant　effect　on　the　FPE-LG　performance.　When　FPE-LG　operates　with　control　strategy　A,　the　operation　frequency　is　determined　by　the　intake　pressure,　advanced　exhaust　duration,　fixed　position　point　and　external　load　resistance,　whereas　it　is　only　related　with　the　intake/exhaust　time　and　advanced　exhaust　duration　(ta)　for　control　strategy　B.　The　external　load　resistance　has　slight　influence　on　the　stroke　length　for　these　two　control　strategies.　For　control　strategy　A,　when　advanced　exhaust　duration　is　more　than　40　ms,　the　stroke　length　rises　with　the　intake　pressure,　whereas　it　first　rises　and　then　reduces　when　advanced　exhaust　duration　is　less　than　40　ms.　There　exist　the　optimal　external　load　resistance　and　advanced　exhaust　duration　to　achieve　the　maximum　power　output　with　control　strategy　A,　whereas　the　average　power　output　reduces　with　the　increasing　advanced　exhaust　duration　when　using　control　strategy　B.　Stable　operation　and　high　power　output　can　be　obtained　by　using　different　control　strategies　and　adjusting　relevant　operation　parameters.　©　2021,　Science　Press,　Institute　of　Engineering　Thermophysics,　CAS　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.