It is challenging to realize robotic catching of small fast-moving targets in a large workspace, especially for targets with random trajectories that are difficult to predict. It requires high-speed and accurate motion control, whereas these two aspects usually conflict with each other due to the robot's nonlinear dynamics and systematic uncertainties like backlash. Previously, we proposed a dynamic compensation concept for compensation of dynamical uncertainties. In this study, we propose to apply the dynamic compensation concept to the mentioned catching task with coarse-to-fine strategy. For implementation of the coarse-to-fine strategy, two model-independent algorithms are developed for control of the coupled two-plant system. Firstly, the pre-compensation fuzzy logic control (PFLC) algorithm is introduced to cope with the nonlinear dynamical disturbances brought from the main robot to the compensation actuator; secondly, a simple supervisory cooperation control (SCC) algorithm is addressed to realize the cooperative motion planning between two plants. Experiments show that for small targets randomly flying in one-dimensional space around 500 mm, the catch rate reached over 90% with ±2 mm clearance.