In order to investigate the essence of sticking for drill rod served in underground coal mine, a comprehensive solution combing finite element analysis with fuzzy proportion–integration–differentiation on the drilling rig is proposed. First, the structure and working mechanism of the drilling rig are studied; then, the static and modal analyses on the drill rod with finite element analysis are performed according to the actual working conditions of the drilling rig. Furthermore, a load-sensing hydraulic power system of the drilling rig is built, and the co-simulation with AMESim and Simulink is performed on the response, overshoot, and vibration, when the hydraulic power is controlled with the conventional control method, proportion–integration–differentiation control method, and fuzzy proportion–integration–differentiation method, respectively. The simulation results show that the strength, stiffness, and vibration frequency of the drilling rig model meet the working requirements, and no resonance occurs; furthermore, the load-sensing hydraulic power system with fuzzy proportion–integration–differentiation method is preferable than the other two control methods.