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Inverse of the rate-dependent Prandtl-Ishlinskii model is proposed to compensate rate-dependent hysteresis effects in smart actuators. The rate-dependent hysteresis properties of a piezoceramic actuator were characterized using the rate-dependent play operators and a dynamic density function. The inverse model is subsequently obtained analytically from the rate-dependent play operators and a dynamic density function. The effectiveness of the analytical inverse is demonstrated by its implementation as a feed-forward compensator to mitigate the rate-dependent hysteresis effects over a wide frequency range of actuator input. The proposed model resulted in exact inversion and thus could be quite attractive for compensating the hysteresis effects of smart actuators in real-time applications.