Managed Pressure Drilling (MPD) in oil-gas industry remains a challenge problem. As the annulus is completely clogged, upstream choke pressure measurement can be used to control the well downhole pressure. To reinforce the tunnel face, MPD becomes difficult as the annulus is totally open. In this paper, we propose a finite dimensional model to all fluid phenomena between the main pump till the fluid outlet through the annulus. The translational dynamic of the sonic-head carrying the drillstring is coupled to mud dynamics. We construct a stabilizing observer-based controller to the bottomhole pressure in analyzing all the system variables. From the perturbation theory, we show that the perturbed system is stable at the origin. The theoretical results are supported by simulation.
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