Compared　to　control　bandwidth,　low-frequency　uncertainties　or　disturbances　like　step　signals　can　be　well　rejected　by　many　methods　having　two-degree-of-freedom　(2-DOF).　Due　to　robustness　constraint,　technically　more　challenging　is　the　rejection　of　medium　frequencies,　especially　for　bandwidth-limited　systems.　Here,　the　equivalent-input-disturbance　(EID)　approach　is　extended　to　deal　with　the　main　medium-frequency　oscillation　of　a　pantograph-catenary　system.　First,　a　general　EID　estimator　is　developed　with　a　low-frequency　estimator　as　a　special　case.　Then,　a　fair　comparison　is　conducted　to　clarify　the　essential　differences　between　the　conventional　1-DOF-based　and　the　developed　2-DOF-based　control　systems.　Furthermore,　a　robust　stability　condition　is　derived　for　the　2-DOF-based　closed-loop　control　system.　A　design　algorithm　together　with　design　guidelines　is　provided,　where　the　frequency　characteristics　of　the　uncertainties　are　utilized　in　the　parameter　design.　Finally,　simulations　are　carried　out　to　validate　the　developed　2-DOF-based　method　for　the　pantograph-catenary　system　in　realistic　environment.