The　lubricating　medium　of　the　aerostatic　spindle　is　gas,　with　relatively　low　rigidity,　which　is　easy　to　cause　rotor　offset　and　additional　vibration　under　the　action　of　external　load,　thus　affecting　the　processing　accuracy　of　the　spindle.　To　solve　the　problem　of　unbalanced　vibration　of　the　spindle,　a　new　type　of　controllable　radial　aerostatic　bearing　is　designed　by　combining　piezoelectric　ceramics,　which　use　the　inverse　piezoelectric　effect　of　piezoelectric　ceramics　to　squeeze　the　air　film　to　produce　corresponding　control　force,　and　the　radial　unbalanced　vibration　of　the　spindle　is　suppressed.　A　bearing–rotor–piezoelectric　ceramic　coupling　model　was　established,　and　the　control　method　of　feedforward　combined　with　feedback　was　used　to　reduce　the　hysteresis　characteristics　of　piezoelectric　ceramics.　On　this　basis,　the　sliding　mode　controller　of　the　entire　system,　and　through　research,　it　is　found　that　the　sliding　mode　controller　based　on　the　extended　observer　has　the　best　vibration　suppression　effect　compared　with　other　sliding　mode　controllers　in　the　article;　this　research　results　can　improve　the　rotation　accuracy　of　the　spindle　system　and　the　machining　accuracy　of　ultra-precision　machine　tools.　©　The　Author(s)　2023.