[en] This paper presents a modified rate-dependent Prandtl–Ishlinskii (MRPI) model for the description and compensation of the rate-dependent asymmetric hysteresis in piezoelectric actuators. Different from the commonly used approach with dynamic weights or dynamic thresholds, the MRPI model is formulated by employing dynamic envelope functions into the play operators, while the weights and thresholds of the play operators are still static. By this way, the developed MRPI model has a relatively simple mathematic format with fewer parameters and easier parameter identification process. The benefit for the developed MRPI model also lies in the fact that the existing control approaches can be directly adopted with the MRPI model for hysteresis compensation in real-time applications. To validate the proposed model, an open-loop tracking controller and a closed-loop tracking controller are developed based on a dynamic hysteresis compensator, which is directly constructed with the MRPI model. Comparative experiments are carried out on a piezo-actuated nanopositioning stage. The experimental results demonstrate the effectiveness and superiority of the controllers based on the developed MRPI model compared to the controllers based on the rate-independent P–I model and the rate-dependent P–I model with dynamic weighting functions. (paper)