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A driver's body functions as a pathway that transmits vehicle motion and inertia forces to the vehicle's manual control interface, producing unintended commands and degrading driver/vehicle performance. In this paper, we apply a model-based cancellation controller to mitigate this effect, called biodynamic feedthrough. Using measurements of vehicle acceleration and hand/interface interaction force, we first construct a model of the body transmittance. In operation, the controller processes vehicle acceleration measurements through a regression model of the biodynamic transmittance and a motor imposes the result as a torque on the manual interface. We tested individually fit cancellation controllers by quantifying the tracking performance of 12 human subjects using a joystick to control displacements of a single-axis motion platform. The addition of the cancellation controller reduced the root mean square tracking error by 45%, significantly reduced spectral energy in the 1-7 Hz band, and had a marked effect on the ability of the driver to reject exogenous disturbances.