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In this paper, control strategies for an active stabilizer dedicated to beating heart coronary artery bypass grafting are investigated. The active stabilizer, which consists of a piezoactuated compliant mechanism, has to be controlled to compensate for the displacements induced by the beating heart in order to provide the surgeon with a locally motionless myocardium surface. Three controllers, including different levels of prior knowledge about the heart motion, are presented. Their performance with respect to modeling uncertainties, arising unknown interactions of the stabilizer with its positioning mechanism, and the heart, is studied through simulations, as well as laboratory and in vivo experiments. Finally, the selection of the most adequate control scheme and the performance of the device from a clinical point of view are discussed.