A　sensorless　vector　active　disturbance　rejection　control　(ADRC)　method　for　permanent　magnet　synchronous　motors　(PMSM)　utilizing　a　Luenberger　observer　is　presented.　This　method　aims　to　address　the　challenges　associated　with　weak　active　disturbances,　substantial　steady-state　speed　amplitude　fluctuations,　and　difficulty　in　achieving　a　balance　between　overshoot　and　speed　control　in　the　sensorless　PMSM　control　system.　Mathematical　models　of　the　Luenberger　observer　and　the　ADRC　were　analyzed,　leading　to　the　proposal　of　a　second-order　ADRC　control　method　based　on　the　Luenberger　observer.　A　mathematical　model　of　the　permanent　PMSM　has　been　introduced.　Additionally,　the　necessary　conditions　for　the　convergence　of　the　Luenberger　observer　were　derived　and　examined.　The　allowable　range　of　error　feedback　gain　values　was　determined,　and　rotor　position　data　were　acquired　using　a　phase-locked　loop.　The　principle　of　the　ADRC　was　analyzed,　and　the　ADRC　simulation　results,　along　with　the　PI　simulation　results,　were　detailed.　When　the　target　speed　is　1000　r/min,　the　steady-state　error　and　load　disturbance　resistance　of　the　ADRC　control　method　outperform　those　of　the　PI　control　method.　Finally,　the　control　method　was　experimentally　tested　on　an　STM32F4　chip,　demonstrating　the　advantages　of　small　steady-state　error　and　strong　active　disturbance　ability.