Currently, tiny, high-speed rotating machines frequently employ air foil bearings. Air is employed as the working medium, however, when the rotor speed is high, the rigidity of the air film is insufficient, which restricts the usage of air foil bearings. This study utilizes the external gas supply method of hydrostatic gas bearings to strengthen the air film stiffness of air foil bearings. The original air foil bearings are combined with external gas supply piping to create the hybrid gas foil bearing(HGFB), which may be utilized to increase the air film support stiffness of the bearings through the external gas supply. Additionally, by altering the gas supply pressure, this bearing may be used to actively manage the vibration characteristics of the shaft system, allowing the bearing performance to be adjusted to changing operating conditions. The static and dynamic properties of the HGFB with a 24 mm diameter are solved in this study using Newton's iterative approach and the finite difference method. The bearing-rotor system is modeled using this information. An Analysis is done on the impact of various air supply pressures and throttle hole widths on bearing performance and vibration characteristics of the shaft system. In this article, the vibration parameters of the bearing-rotor system are tested using an open-loop control test. The open-loop control experiment on the vibration response of the bearing-rotor system is performed using HGFBs with orifice sizes of 0 mm, 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm. The experimental results confirm the accuracy of the simulation results. Correspondingly, this paper conducted closed-loop control comparison experiments on the vibration properties of the bearing-rotor system using the PID control method and the fuzzy PID control method in succession. It then evaluated the control effect of the two control strategies on the vibration of the bearing-rotor system and managed to improve the conventional PID control method used for gas bearings.