Fast tool servo (FTS) based on piezoelectric is considered as one of the most promising ultra-precision machining technologies for its high bandwidth, high precision and high frequency response. However, in the current processing process, the tracking property of the FTS is affected by the nonlinearity of the system structure, model uncertainty and external complex and multi-source disturbance, which seriously affect the quality and precision of the system processing. In view of the above problems, we propose the robust tracking control method for the processing requirements of piezo-driven fast tool servo, so as to improve the tracking property and anti-disturbance property of the system in current processing process. A robust repetitive control scheme based on the disturbance observer can suppress equivalent disturbance on the tracking performance of the system. However, in practical application, the solution of the inverse model of the controlled object may increase the uncertainty and causality of the control system, thus worsening the control effect. In the interest of promote the performance of disturbance observer, we present a learning disturbance observer.