Low-Coupling Hybrid Parallel-Serial-Kinematic Nanopositioner with Nonorthogonal Flexure: Nonlinear Design and Control

Abstract

This article focuses on the design and high-precision control of a new dual-stage, three-axis hybrid parallel-serial-kinematic nanopositioner developed specifically for feature-tracking applications with arbitrary scanning directions. Dual-actuation is achieved by integrating a three-axis shear piezoelectric actuator into the large-range planar stage. A novel nonorthogonal compliant motion-amplifying mechanism which reorients the lateral sample-platform displacement to align with the principal directions of the input piezoactuators is used to minimize parasitic (coupling) motion. A nonlinear rigid-link model and finite element analysis (FEA) are used to optimize over the orientation parameter during the design process. A prototype stage is manufactured and tested, and the lateral and vertical travel ranges are approximately 18 × 21 and 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m, respectively, with secondary lateral actuation in the range of 1 × 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m. Coupling in the long-range stage is below -31 dB for both axes, an estimated 51 to 86% reduction compared to a traditional perpendicular-mechanism design. The measured dominant resonances for the lateral directions of the long-range stage are approximately 1.4 kHz, while short-range positioner resonances are approximately 11 and 40 kHz for the lateral and vertical directions, respectively. The design of a new feedforward-feedback controller is described, and the controller is implemented with field-programmable gate array (FPGA) hardware, where individual actuator contributions are intuitively determined by shaping the frequency response of their relative and summed displacements. An inverse hysteresis operator is used to linearize the plant behavior for effective motion control. Experimental tracking and atomic force microscopy (AFM) imaging results are presented to demonstrate the performance of the new mechanical and control system designs.