Multi-Degree-of-Freedom Precision Position Sensing and Motion Control Using Two-Axis Hall-Effect Sensors

[+] Author and Article Information
Yusuke Kawato

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@tamu.edu


Corresponding author.

J. Dyn. Sys., Meas., Control 128(4), 980-988 (Mar 06, 2006) (9 pages) doi:10.1115/1.2363201 History: Received May 11, 2005; Revised March 06, 2006

This paper presents a novel precision position-sensing methodology using two-axis Hall-effect sensors, where the absolute multi-degree-of-freedom (DOF) positioning of a device above any magnet matrix is possible. Magnet matrices have a periodic magnetic field about each of its orthogonal axes, which can be modeled using Fourier series. This position-sensing methodology was implemented on a Halbach-magnet-matrix-based magnetic-levitation (maglev) stage. It enables unrestricted translational and rotational ranges in planar motions with a potential 6-DOF motion-measuring capability. A Gaussian least-squares differential-correction (GLSDC) algorithm was developed and implemented to estimate the maglev stage’s position and orientation in three planar DOFs from raw Hall-effect-sensor measurements. Experimental results show its position resolution of better than 10μm in translation and 100μrad in rotation. The maximum rotational range achieved so far is 16deg, a factor of 100 improvement of a typical laser interferometers’ rotational range of a few milliradians. Classical lead-lag compensators were designed and implemented on a digital signal processor (DSP) to close the control loop at a sampling frequency of 800Hz for the three planar DOFs using the GLSDC outputs. Calibration was performed by comparing the Hall-effect sensors’ outputs against the laser-interferometer readings, which improved the positioning accuracy by correcting the GLSDC error. The experimental results exhibit better than a micrometer repeatability. This multi-DOF sensing mechanism is an excellent cost-effective solution to planar micro-positioning applications with unrestricted three-axis travel ranges.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Analytical results of the magnetic flux density generated by the Halbach magnet matrix at an air gap of Z0=3mm. (a) BX, (b) BY, and (c) BZ.

Grahic Jump Location
Figure 2

Experimental setup with three sets of 2D-VH-11SO 2-axis Hall-effect sensors. The coordinate-axis definition for the experimental setup with the indication of the three two-axis Hall-effect sensors’ locations is also given. The actual locations of the three Hall-effect sensors are indicated with arrows. The white triangular Delrin frame is the moving platen. Beneath the mirror-finished aluminum plate is the Halbach magnet matrix. (b) Schematic diagram of the sensing circuit with a 2D-VH-11SO two-axis Hall-effect sensor.

Grahic Jump Location
Figure 3

Batch least-squares results of the magnetic-flux-density measurement. (a) Sensor output ã, (b) curve-fitted model for the sensor output ã, and (c) modeling error from curve-fitting.

Grahic Jump Location
Figure 4

Flowchart of the modified GLSDC algorithm

Grahic Jump Location
Figure 5

Experimental results of 2-DOF positioning in X and Y following a zigzag trajectory. (a) Commanded trajectory, (b) measured trajectory from the Hall-effect sensors, (c) measured trajectory from the laser interferometers used for Hall-effect-sensor calibration purpose, and (d) error between the two measured values.

Grahic Jump Location
Figure 6

Laser interferometer readings from a 4mm step response (a) before calibration and (b) after calibration and error correction. (c) GLSDC output after calibration and error correction.

Grahic Jump Location
Figure 7

Experimental results of positioning the platen in 3 DOFs using the proposed sensing methodology for (a) 10μm consecutive steps in Y and (b) 100μrad consecutive steps in θz

Grahic Jump Location
Figure 8

Large-rotation ramp response in θz with (a) clockwise (−θz) and (b) counter-clockwise (+θz) motions




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In