This thesis uses Matlab/Simulink to design the composite adaptive controller and control the position of a permanent magnet synchronous motor (PMSM). Firstly, the mathematical model of a PMSM is proved to be strictly passive. A composite adaptive controller is designed to pursue both the feedforward block and the feedback block of the equivalent system with the property of passivity. The adaptive law can estimate the moment of inertia, viscous friction coefficient, and load torque of a PMSM. By using the passivity theorem instead of the Lyapunov-based approach, the overall position control system is verified to be globally stable. Finally, experimental results show that the proposed method has the better position tracking capability as well as the robustness with regard to variations of mechanical parameters of the motor and external load torque disturbances.