In　this　paper,　based　on　the　system　linear　momentum　conversation　and　the　Lagrange　equation　of　second　kind,　the　dynamic　equation　of　the　space　manipulator　system　with　elastic　base　and　two　flexible　joints　is　established.　According　to　the　singular　perturbation　theory,　the　model　is　decomposed　into　a　rigid　subsystem　and　a　flexible　subsystem.　A　repetitive　learning　control　based　on　terminal　sliding　mode　is　proposed　for　the　rigid　subsystem　to　tracking　periodic　reference　signals　in　limited　time.　The　repetitive　learning　control　is　the　feed-forward　compensation　section,　which　is　designed　to　track　the　periodic　reference　signal.　Terminal　sliding　mode　control　is　a　feedback　part,　which　is　designed　to　suppress　periodic　or　non-periodic　interference.　The　combination　of　the　two　control　methods　allows　the　closed-loop　system　to　achieve　better　trajectory　tracking　accuracy.　Compared　with　traditional　controllers,　this　method　deals　with　highly　uncertain　controlled　systems　with　less　prior　knowledge.　The　implementation　of　this　scheme　does　not　require　dynamic　model　information　of　the　system,　can　track　periodic　signals　accurately　and　suppress　periodic　or　aperiodic　disturbances.　For　the　elastic　vibration　of　the　flexible　subsystem,　a　linear　quadratic　optimal　control　scheme　is　adopted　to　suppress　the　vibration.　Finally,　Lyapunov　theory　is　used　to　prove　the　global　asymptotic　stability　of　the　closed-loop　system.　Through　the　simulation　calculation,　the　validity　of　repetitive　learning　control　based　on　terminal　sliding　mode　is　verified.　Copyright　©　2019　by　the　International　Astronautical　Federation　(IAF).　All　rights　reserved.