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Piezomicropositioning actuators, which are widely used in micropositioning applications, exhibit strong rate-dependent hysteresis nonlinearities that affect the accuracy of these micropositioning systems when used in open-loop control systems, and may also even lead to system instability of closed-loop control systems. Feedback control techniques could compensate for the rate-dependent hysteresis in piezomicropositioning actuators. However, accurate sensors over a wide range of excitation frequencies and the feedback control techniques inserted in the closed-loop control systems may limit the use of the piezomicropositioning and nanopositioning systems in different micropositioning and nanopositioning applications. We show that open-loop control techniques, also called feedforward techniques, can compensate for rate-dependent hysteresis nonlinearities over different excitation frequencies. An inverse rate-dependent Prandtl-Ishlinskii model is utilized for feedforward compensation of the rate-dependent hysteresis nonlinearities in a piezomicropositioning stage. The exact inversion of the rate-dependent model holds under the condition that the distances between the thresholds do not decrease in time. The inverse of the rate-dependent model is applied as a feedforward compensator to compensate for the rate-dependent hysteresis nonlinearities of a piezomicropositioning actuator at a range of different excitation frequencies between 0.05-100 Hz. The results show that the inverse compensator suppresses the rate-dependent hysteresis nonlinearities, and the maximum positioning error in the output displacement at different excitation frequencies.