A disturbance-cancellation system and method is provided that facilitates the adaptive cancellation of periodic disturbances. The disturbance-cancellation system and method includes a pair of control moment gyroscopes (CMGs) arranged together as a scissored pair. The scissored pair of CMGs is used to create a periodic torque with a controllable amplitude and frequency. The periodic torque created by the CMGs is adaptively controlled to cancel out periodic disturbances in the system. The system and method creates a periodic torque with a controllable amplitude and frequency by rotating the inner-gimbal assemblies of the CMGs in opposite directions at substantially equal phase and angular velocity. Amplitude matching can be achieved by adjusting the rotor spin rate. The steady-state constant motion results in a periodic torque along the output axis of the scissored pair, while components of torque along axes orthogonal to this one cancel out.