Exact inversion of discrete Preisach model for compensating complex hysteresis in AFM based nanomanipulator

Atomic Force microscopy (AFM) is a powerful technology for observing and developing the micro/nano world, which has been bringing tremendous revolution opportunities to various fields. An AFM's maneuverability can be enhanced via modification into a nanorobotic system with its scanning probe working as the end-effector. The probe's spatial precision can easily reach to nanometer level, which is commonly actuated by smart materials, typically the piezoceramics. However, instinctive hysteretic characteristics ubiquitously exist in smart material actuators, which degrade their controllable positioning accuracy, especially for the open-loop cases. As common phenomena, input-output hysteretic relations of integrated AFM systems are generally complicated, caused by actuators' specific characteristics. Since the AFM based nanomanipulation requires slow operations to prevent damage from samples and the sharp probe itself, commonly only hysteresis at low frequency (typically less than 10Hz) need to be reduced. To precisely represent and further reduce generalized hysteretic effects at low frequency, this paper proposes the equivalent representation of the classical Preisach model with analytical inversion. The contributions of this paper are: it is the first time that the exact inversion is established for the Preisach model with generalized discrete representation; furthermore, while maintaining modeling accuracy, the new discrete Preisach model significantly reduces model complexity compared to the traditional Preisach model. Numerical verification was conducted to demonstrate the effectiveness of the proposed discrete Preisach model and its analytical inversion.