Modeling of Hysteresis for Piezo-driven Stages using a Rate-dependent Krasnosel’skii-Pokrovskii Model

To describe the rate-dependent hysteresis of piezo-driven stages, a modified rate-dependent Krasnosel'skii-Pokrovskii (RDKP) model is proposed in this paper. In this method, both the differential of the output displacement and rate-dependent parameters are introduced into the classical Krasnosel'skii-Pokrovskii (CKP) model. Then the interior point algorithm and bat search optimization algorithm are used to obtain the density function and rate-dependent parameters of the RDKP model respectively. Moreover, the relationship between the obtained rate-dependent parameters and input voltage frequency is produced to an exponential function. Simulation results show that the RDKP model with the rate-dependent exponential function can describe the rate-dependent hysteresis of piezo-driven stages with a higher modeling precision compared with the CKP model.