A Modified Prandtl-Ishlinskii Model for Rate-dependent Hysteresis Nonlinearity Using <i>m</i>th-power Velocity Damping Mechanism

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., Λ i . 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.