An electromagnetic synchronized switch damper integrated with the receding horizon optimal control law was developed to enhance the damping characteristics of flexible beam structures subject to dynamic loads. The damper system consists of a magnet attached to an aluminum beam and a coil placed at the bottom of the magnet. Both ends of the coil were connected to the external switching circuit, which includes an electromagnetic transducer, a capacitor, a resistor, and a switcher designed for efficient energy dissipation to reduce structural vibration. Further, a coil-based self-sensing scheme without additional measurement of the displacement and the velocity was successfully applied to the present switching scheme without performance loss. The present results show that the electromagnetic synchronized switching scheme can be successfully employed to improve the electromagnetic damping of the flexible structures, resulting in the robust vibration control regardless of changes to the circuit parameters.