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To achieve natural and mutually engaging rhythmic human-robot handshaking, the movements of the human and robot should be synchronized. However, the intended movements of the human, namely the frequency components and amplitudes of the periodic motion, are largely unknown. In this paper, a robot controller has been developed to reach the goal of natural handshake. The control system for the robot consists of two parts. One part is the reactive control which was implemented to attain safe human-robot interaction and to overcome random instantaneous disturbances. The other part is a predictive controller, which is a feedforward loop designed to overcome steady-state uncertain disturbances. The effectiveness of the control system is validated by the simulation of mutual interaction between the robot arm and the human arm. Despite the lack of knowledge of the human intended movements, tracking of the human desired trajectory is achieved and predicted effectively. These findings will be appealing to researchers interested in attaining synchronous motion between human and robot.