This paper proposes a method for the compensation of harmonic disturbances with parametrically varying frequencies for linear time-invariant (LTI) plants. Torsional oscillations arising from cyclic irregularity is an inherent problem of the internal combustion engine (ICE) powered automotive powertrains. The ICE due to its cyclic combustion process generates periodic disturbances whose frequency varies with its operating speed. Furthermore, the amplitude of the oscillatory torque depends on the demanded set-point torque and the speed of operation. The objective of the controller is to reduce the effect of disturbances resulting in a reduction of oscillatory motion quantities using external actuation. The proposed scheme uses a harmonic controller to command input of the compensating actuators. Torsional vibration systems are studied, in which the effect of disturbance torques resulting in speed oscillations are reduced using the commanded compensation torque. The developed controller is evaluated using simulations and validated with experiments using a two-cylinder gasoline engine at a powerpack test bench.