Systematic Hysteresis Compensator Design based on Extended Unparallel Prandtl-Ishlinskii Model for SPM Imaging Rectification

Abstract

Scanning probe microscopy (SPM) technology plays the irreplaceable role in investigating micro/nano world, which has been bringing tremendous development opportunities to various fields. To enhance maneuverability, SPM can be modified into a nanomanipulation system with its scanning probe as the end-effector. The probe is commonly mounted on smart material based actuators to generate precise motion with nanometer level resolution. However, instinctive hysteretic characteristics ubiquitously exist in smart material actuators, which degrade their arbitrary positioning precision. To effectively represent and further reduce complex hysteretic effects, this paper proposes to utilize the modified Prandtl-Ishlinskii (PI) model: extended unparallel PI (EUPI) model, which possesses advantages such as the flexible modeling capability (compared to the prevalently implemented modified PI models) and the easy-to-use property for construction and identification (compared to the well known Preisach model and the Generalized PI (GPI) model). To effectively reduce complex hysteresis, the EUPI model based compensator (IMUPI compensator) is required to be flexible and precise. To efficiently design such a compensator satisfying stability requirement, this study proposes a systematic approach, including stabilizing gain selection and analytical calculation of boundary gains of the EUPI irreversible component. As a demonstration, satisfactorily precise IMUPI compensator was established according to this systematic design approach and tested through simulations on rectifying Atomic Force Microscopy (AFM, one special SPM) imaging process distorted by complex hysteresis.