This　paper　investigates　the　stable　control　problem　of　unmanned　aerial　manipulator　(UAM)　in　the　presence　of　lumped　disturbance,　including　modelling　uncertainties　and　external　inferences.　These　disturbances　typically　involve　limited　prior　knowledge　and　change　rapidly,　presenting　considerable　challenges　to　real-time　control　accuracy.　To　address　this　issue,　a　Takagi-Sugeno-Kang　estimator　(TSKE)　with　K-closest　fuzzy　rules　interpolation　(K-FRI)　is　proposed　to　derive　an　approximation　for　the　uncertain　disturbances.　The　incorporation　of　K-FRI　enhances　the　accuracy　and　convergence　rate　of　the　estimation　under　the　conditions　of　a　sparse　fuzzy　rule　base　with　an　incomplete　fuzzy　quantity　space.　Subsequently,　a　backstepping　controller　with　arbitrary　convergence　time　is　introduced　to　guarantee　the　rapid　and　precise　control　of　the　UAM.　The　stability　of　both　the　TSKE　and　the　controller　with　arbitrary　convergence　time　is　analysed　through　Lyapunov　theory.　The　feasibility　and　performance　of　the　proposed　control　strategy　are　validated　via　comparative　experimental　simulations,　demonstrating　its　ability　for　robust　estimation　capability　with　stable　control　performance,　at　any　convergence　time　of　the　UAM　working　under　lumped　disturbance.