In this paper, we propose a novel control structure that can achieve fast, safe and precise landing of a VTOL (vertical takeoff and landing) UAV onto a vertically oscillating landing pad. The control structure consists of three modules to achieve these goals: a motion estimation module, a trajectory generation module and a tracking control module. In the tracking control module, an ARC (Adaptive Robust Controller) is designed to robustly adapt the nonlinear ground effect to enable a quadrotor accurately track a given reference trajectory. In the trajectory generation module, a time-optimal reference trajectory for the quadrotor is generated such that it converges from the initial height precisely to the platform height with zero relative velocity (for smooth landing). The landing time duration is as short as possible, and physical safety constraints (position, velocity, acceleration bounds etc.) are satisfied during the entire landing process. The above two modules use the motion information of the quadrotor and the platform in absolute coordinate system (inertial frame). In the motion estimation module, we estimate the UAV and platform positions online from only the measurement of the relative distance between the UAV and the platform, as well as the inertia measurement of the UAV. An UKF (unscented Kalman Filter) is constructed and the estimated parameters are fed to the other two modules in real time. Comparative simulation and experimental results are presented to validate the performances of the proposed control structure.