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TECHNICAL BRIEFS

# 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

1

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

## Abstract

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.

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## Figures

Figure 8

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

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.

Figure 4

Flowchart of the modified GLSDC algorithm

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.

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.

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

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.

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.

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