“…For example, these applications include the Atomic Force Microscopy (AFM) [2,3], manipulator applications [4,5,6], piezoelectrically actuated hydraulic valves [7], diesel injectors [8], medical microrobots [9]. Different hysteresis models have been used to characterize the voltage-to-displacement hysteresis nonlinearities in piezoelectric material-based actuators over different operating conditions have been presented in a number of recent studies, see for example [10,11,12,13,14]. In [10], the both rate-independent and rate-dependent hysteresis in piezoelectric actuators were modeled using a Takagi-Sugeno fuzzy system.…”