For the permanent magnet eddy-current coupler speed control system with external disturbances, consideration is given to achieving anti-disturbance objectives through disturbance compensation. Utilizing partial information of disturbance dynamics, it is convenient to design a disturbance interval observer (DIO), generating upper and lower bounds covering each element of the external disturbances, where the positive system theory ensures non-negativity of errors. Then, based on the DIO, disturbance reconstruction is performed for feedforward compensation, while feedback control is employed for tracking and stabilization, eliminating control chattering generated by the sliding mode. The controller is presented in a parameterized form to obtain the designed closed-loop system, allowing for easy handling of additional performance requirements. Finally, numerical simulations validate the superiority and benefit of the estimation and control scheme.