Axial flux permanent magnet (AFPM) motors are rendered susceptible to axial forces during operation, by which air gap fluctuations and parameter variations are induced. Consequently, issues such as diminished speed stability and inadequate disturbance rejection capabilities are precipitated. To address these challenges, a composite control strategy integrating an extended Kalman filter (EKF) with adaptive tube model predictive control (Tube-MPC) was proposed. The motor states and parameters were estimated online utilizing the EKF. Concurrently, the disturbance boundaries and tube radii were adjusted in real-time by the adaptive Tube-MPC based on dynamic minimal robust positively invariant (mRPI) sets, ensuring that the state trajectories are maintained within the robust feasible region. It is demonstrated by simulation results that high tracking accuracy and stability are sustained under conditions of abrupt parameter changes and external disturbances, whereby the adaptability and robustness of the system are significantly enhanced.