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For an attitude control and energy storage flywheel (ACESF), not only does the speed of the rotor must be high but also the position of the rotor must be controlled accurately. To research the relationship between superconducting magnetic bearings (SMBs) and active magnetic bearings (AMBs) in this presented superconducting ACESF, the rotor model is established, the force of SMBs and AMBs is simplified by linearization, and the radial translation and tilting movement of the rotor suspended by only SMBs, SMBs with equivalent permanent-magnet bearings, and SMBs and AMBs with proportional-derivative-type control are researched, respectively. For the disklike rigid rotor with large inertia and high speed, simulation and experimental results proved that the gyroscopic effect of the rotor is prominent, the rotor model including gyroscopic couples can describe its behaviors, and the linearization of force for SMBs and AMBs are reasonable. The AMB can suppress the nutation and precession of the rotor effectively by a cross-feedback control method or other modern control methods; the SMB, together with the AMB, can make the rotor in ACESF be stable and the amplitude of the vibration of rotor be small.