Piezoelectric actuators （PEAs） are smart drivers that are widely employed in precision instruments to achieve high-speed， high-precision positioning. However， the nonlinear properties of PEAs， such as creep and， particularly， hysteresis， seriously affect their control precision. This paper proposes a multiple delay-input Prandtl–Ishlinskii （MDPI） model to solve the offset and rate-dependent issues encountered during modeling. Notably， the MDPI model has a set of rate-dependent dynamic factors， and offset coefficients are added to improve the asymmetry of the model. Next， experimental data of 1 V sinusoidal signals ranging from 1 to 100 Hz are collected on the piezoelectric micro-motion platform， and the accuracy of the model is compared with that of rate-dependent and dynamic delay PI models. The experimental results indicate that the MDPI model describes the dynamic and hysteresis characteristics of PEAs more accurately than the other two dynamic PI models. For input signal frequencies of 50 and 100 Hz， the maximum absolute errors of the MDPI model are 0.0815 and 0.1429 μm， and the root mean square errors （RMSEs） are 0.009 5 and 0.011 9 μm， respectively. Compared with the RMSE accuracies of the other two models， that of the MDPI model is improved by 72.46% and 64.21%， respectively.