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An omnidirectional multirotor has the maneuverability of decoupled translational and rotational motions, superseding the traditional multirotors' motion capability. Such maneuverability is achieved due to the ability of the omnidirectional multirotor to frequently alter the thrust amplitude and direction. In doing so, the rotors' settling time, which is induced by inherent rotor dynamics, significantly affects the omnidirectional multirotor's tracking performance, especially in aggressive flights. To resolve this issue, we propose a novel tracking controller that takes the rotor dynamics into account and does not require additional rotor state measurement. This is achieved by integrating a linear rotor dynamics model into the vehicle's equations of motion and designing a PD controller to compensate for the effects introduced by rotor dynamics. We prove that the proposed controller yields almost global exponential stability. The proposed controller is validated in experiments, where we demonstrate significantly improved tracking performance in multiple aggressive maneuvers compared with a baseline geometric PD controller.