The　design　of　a　set-point　tracking　control　scheme　is　presented　for　typical　double-integrator　servo　systems.　The　control　scheme　adopts　the　framework　of　proximate　time-optimal　servomechanism　(PTOS).　An　extended　state　observer　(ESO)　is　utilized　to　estimate　the　un-measured　velocity　signal　and　the　unknown　disturbance,　and　a　disturbance　compensation　term　is　included　in　the　PTOS　control　law.　In　the　presence　of　speed　constraint,　a　speed　regulation　stage　is　incorporated　between　the　PTOS　acceleration　and　deceleration　stages.　The　control　scheme　is　then　applied　to　the　position　control　loop　in　a　permanent　magnet　linear　synchronous　motor　servo　system.　Experimental　verification　has　been　conducted,　based　on　the　TMS320F28335　digital　signal　controller　board.　The　results　confirm　that　the　proposed　control　scheme　can　track　a　wide　range　of　target　references　fast　and　accurately,　and　has　some　robustness　against　disturbance　and　uncertainties.