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Hysteresis of piezoelectric actuators is rate-dependent at high frequencies, but most of the hysteresis models are rate-independent and cannot describe the rate-dependent hysteresis nonlinearity independently. In this paper, a modified Prandtl-Ishlinskii (P-I) model is proposed to characterize the rate-dependent hysteresis of piezoelectric actuators under sinusoidal excitation. This model is formulated by a mth-power velocity damping model in conjunction with the rate-independent P-I model. The parameter identification of this model is divided into two steps using different experimental data and algorithms. The particle swarm optimization is introduced first to identify the rate-independent parameters, and the nonlinear least square method is adopted afterwards to identify the rate-dependent parameters which are functions of the excitation frequency. Moreover, the proposed P-I model is developed to describe hysteresis nonlinearity under triangular excitation by introducing weighted functions, i.e., Λi. Finally, the model results attained under the sinusoidal and triangular inputs at different frequencies are compared with the corresponding experimental data. The comparisons demonstrate that the proposed P-I model can well describe hysteresis nonlinearity under sinusoidal excitation up to 1,500 Hz and triangular excitation up to 250 Hz, respectively

A Modified Prandtl-Ishlinskii Model for Rate-dependent Hysteresis Nonlinearity Using mth-power Velocity Damping Mechanism