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TECHNICAL PAPERS

# Nanoscale Motion Control With a Compact Minimum-Actuator Magnetic Levitator

[+] Author and Article Information
Jie Gu, Shobhit Verma

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123

Won-jong Kim1

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123wjkim@mengr.tamu.edu

1

Corresponding author, Member of ASME

J. Dyn. Sys., Meas., Control 127(3), 433-442 (Aug 24, 2004) (10 pages) doi:10.1115/1.1978906 History: Received May 23, 2003; Revised August 24, 2004

## Abstract

This paper presents a novel magnetically levitated (maglev) stage developed to meet the ever-increasing precise positioning requirements in nanotechnology. This magnetic levitator has 6 independent linear actuators necessary and sufficient to generate all 6-degree-of-freedom (6-DOF) motions. This minimum-actuator design concept led to a compact, 200 g lightweight moving part and the power consumption less than of a Watt, thereby reducing the thermal-expansion error drastically. The analysis and sizing of the magnetic linear actuators and the working principle of the maglev stage are presented. We designed and implemented stabilizing controllers for 6-DOF motion control with the dynamic model based on the actuator analysis. Test results showed nanoscale step responses in all six axes with $2nmrms$ horizontal position noise. A noise propagation model and analysis identified the capacitance sensor noise and the floor vibration as the dominant noise sources in the vertical and horizontal dynamics, respectively. A comparison of noise performances with controllers closed at 25, 65, and 90 Hz crossover frequencies illustrated how the selection of the control bandwidth should be made for nanopositioning. Experimental results including a $250μm$ step response, sinusoidal and square-wave trajectories, and spherical motion generation demonstrated the three-dimensional (3D) nanoscale motion-control capability of this minimum-actuator magnetic levitator. Potential applications of this maglev stage include manufacture of nanoscale structures, atomic-level manipulation, assembly and packaging of microparts, vibration isolation for delicate instruments, and seismic motion detection.

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## Figures

Figure 1

Photograph of the maglev stage. The triangular shape in the center is the maglev single-moving platen

Figure 2

Exploded view of the mechanical setup

Figure 3

Schematic diagram of a linear magnetic actuator. A Lorentz force is generated by placing the current-carrying coil in the magnetic field produced by the magnet assembly. The optimal thickness of 3.84mm of the aluminum nonmagnetic spacer is exaggerated here for clarity.

Figure 4

(a) Definition of the axes and the numbering convention for each actuator. (b) Definition of the geometric parameters in the modal force and displacement transformations. (c) Conceptual actuator force allocation for 6-axis modal force generation.

Figure 5

Plot of payload vs current required to maintain the position

Figure 6

Control loop of the maglev system

Figure 7

Noise contributions from various sources (a) in the horizontal modes, and (b) In the vertical modes

Figure 8

Convariances of the theoretical sensor noise and disturbance, and an empirical result with respect to the crossover frequency in the horizontal modes. To find the total theoretical noise convarience, the two components (disturbance and sensor noise) should be added. Note that the magnitude is in a logarithmic scale.

Figure 9

1μm step responses in x with crossover frequencies at (a) 25Hz, (b) 65Hz, and (c) 90Hz

Figure 10

1μm step responses in X by a MATLAB simulation and an experiment

Figure 11

Step responses in all six axes with step sizes of (a) 20nm in x, (b) 20nm in y, (c) 0.2μm in z, (d) 10μrad in ψ, (e) 10μrad in θ, and (f) 1μrad in ϕ

Figure 12

Extended-range 250μm step response in x and disturbed motions in all the other axes

Figure 13

(a) 20nm amplitude square-wave motion in x. (b) 50nm amplitude sinusoidal motion in x. The dashed lines represent the commanded input to generate the motion.

Figure 14

3D spherical motion. The hemispherical shell has a radius of 50μm, and each circular motion is separated by 0.5μm in the vertical direction.

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