Modeling of Hysteresis Nonlinearity in Piezoelectric Ceramic Micro-Positioning Platform based on Generalized Rate-Dependent Prandtl-Ishlinskii Model

Piezoelectric ceramic micro-positioning platform has been widely used in micro-positioning, vibration control, and manufacturing applications as a core component of precision manufacturing equipment. However, the main drawback of the piezoelectric ceramic micro-positioning platform is the inherent hysteresis nonlinearity, which affects the positioning accuracy because of its non-memoryless as well as multi-valuedness. In this paper, we propose a generalized rate-dependent Prandtl-Ishlinskii (GRPI) model with rate-dependent asymmetric properties by introducing dynamic envelope functions into the play operators and polynomial input function. Then, the parameters of the proposed model are identified by optimization toolbox of MATLAB based on the measured data of piezoelectric ceramic micro-positioning platform. Finally, different frequencies signals are adopted to test the effectiveness of GRPI model. Compared with the Prandtl-Ishlinskii (PI) model, the simulation results verify that the hysteresis nonlinearity of the piezoelectric ceramic micro-positioning platform can be described accurately by the proposed GRPI model.