Nanoscale Path Planning and Motion Control with Maglev Positioners

This paper addresses nanoscale path planning and motion control, which is essential in nanomanufacturing applications such as microstereolithography (muSTL), dip-pen-nanolithography (DPN), and scanning applications for imaging and manipulation of nanoscale surface phenomena, with the magnetic levitation (maglev) technology. We identified the motion trajectories commonly used in industrial applications along with the challenges in optimal path planning to meet the nanoscale motion-control objectives and achieve precise positioning and maximum throughput simultaneously. The key control parameters in path planning are determined, and control design methodologies, including a well-damped lead-lag controller and an optimal linear quadratic regulator are proposed to satisfy the positioning requirements. The proposed methodologies were implemented individually and collectively. The experimental results are presented in this paper to illustrate their effectiveness in planning optimal trajectories. The damped lead-lag controller exhibited the command overshoot values of as small as 0.37%, and the multivariable LQ controller reduced the dynamic coupling among the axes by 97.1% as compared with the decoupled single-input-single-output (SISO) lead-lag controllers. The position resolution of 5 nm was achieved in x and y with the errors in command tracking as small as 4.5 nm. The maglev stage demonstrated excellent performances for the chosen nanomanufacturing applications in terms of position resolution and accuracy, and speed