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The design of servo controllers for flexible ball screw drives with matched and mismatched disturbances and uncertainties is focused to improve the tracking performance and bandwidth of ball screw drives. A two degrees of freedom mass model is established based on the axial vibration characteristics of the transport ball screw, and the controller of an adaptive integral sliding mode is proposed combining the optimal design of state feedback gain matrix K to restrain the vibration and the matched disturbances and uncertainties. Then for the counteraction of the mismatched disturbances and uncertainties, a nonlinear disturbance observer is also developed. The trajectory tracking performance experiments and bandwidth analysis were conducted on experimental setup with the proposed control method. It is proved that the adaptive integral sliding mode controller has a high tracking performance and bandwidth especially for the axial vibration characteristics model of ball screw drives. And the ball screw tracking accuracy also has a considerable improvement with the application of the proposed nonlinear disturbance observer.