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Automatic managed pressure drilling is an advanced pressure-control method which is intended to meet the increasingly high demands in drilling operations in the oil and gas industry. In this method, the circulating drilling fluid, which takes the cuttings out of the well, is released at the surface through a controlled choke. This choke is used for active control of the fluid pressure in the well. The corresponding automatic control system keeps the pressure at the bottom of the well at a specified setpoint despite various disturbances. One such disturbance, i.e., the vertical motion of the drill string, causes severe pressure fluctuations which need to be actively attenuated. In this paper, we present two different disturbance rejection strategies based on discretized partial differential equations for the well hydraulic system. The performance of the controllers is shown through simulations both under idealized conditions and on a high-fidelity drilling simulator.