This paper proposes an output feedback trajectory tracking control based on the uncertainty and disturbance estimator (UDE) technique. The studied nonlinear system is single-input-single-output (SISO), bounded-input-bounded-output (BIBO), and Lipschitz smooth. The main idea is that the nonlinear system is firstly approximated by a proper first-order linear system plus a lumped uncertainty term, which is estimated and compensated through the UDE. The proposed control technique is modeling-free, and only uses the information of system output and the spectrum of the lumped uncertainty term. It also relaxes the structural constraint in the conventional UDE-based robust control. In order to improve the tracking performance, the internal model principle is adopted in the design of the filter in the UDE. The proposed control design is successfully applied to the position control of a piezoelectric nanopositioning system with hysteresis nonlinearity. The experimental results show that the piezoelectric stage can achieve a fine tracking at 1100Hz, which is 37.93% of the lowest resonant frequency, a significant improvement compared to the commercially available range at 1%-10%.