A generalized Prandtl-Ishlinskii model for characterizing the rate-independent and rate-dependent hysteresis of piezoelectric actuators

• Published in: Review of scientific instruments 2016-03, Vol.87 (3), p.035002-035002
• Main Authors: Gan, Jinqiang, Zhang, Xianmin, Wu, Heng
• Format: Article
• Language: English
• Subjects: Computer simulation; Hysteresis models; Mathematical models; Parameter identification; Particle swarm optimization; Piezoelectric actuators; Piezoelectricity; Scientific apparatus & instruments
• ISSN: 0034-6748; 1089-7623
• DOI: 10.1063/1.4941941

In this paper, a generalized hysteresis model is developed to describe both rate-independent and rate-dependent hysteresis in piezoelectric actuators. Based on the classical Prandtl-Ishlinskii (P-I) model, the developed model adds a quadratic polynomial and makes other small changes. When it is used to describe rate-independent hysteresis, the parameters of the model are constants, which can be identified by self-adaptive particle swarm optimization. The effectiveness of this rate-independent modified P-I model is demonstrated by comparing simulation results of the developed model and the classic Prandtl-Ishlinskii model. Simulation results suggest that the rate-independent modified P-I model can describe hysteresis more precisely. Compared with the classical P-I model, the rate-independent modified P-I model reduces modeling error by more than 50%. When it is used to describe rate-independent hysteresis, a one-side operator is adopted and the parameters are functions with input frequency. The results of the experiments and simulations have shown that the proposed models can accurately describe both rate-independent and rate-dependent hysteresis in piezoelectric actuators.