| Summary: | A novel sensing methodology using two-axis Hall-effect sensors is proposed, where
the absolute positioning of a device atop any magnet matrix is possible. This methodology
has the capability of micrometer-order positioning resolution as well as unrestricted translational
and rotational range in planar 3-DOF (degree-of-freedom) motions, with potential
capability of measuring all 6-DOF motions. This research presents the methodology and
preliminary experimental results of 3-DOF planar motion measurements atop a Halbach
magnet matrix using two sets of two-axis Hall-effect sensors. Analysis of the Halbach
magnet matrix is presented to understand the generated magnetic field. The algorithm
uses the Gaussian least squares differential correction (GLSDC) algorithm to estimate the
relative position and orientation from the Hall-effect sensor measurements. A recursive
discrete-time Kalman filter (DKF) is used in combination with the GLSDC to obtain optimal
estimates of position and orientation, as well as additional estimates of velocity and
angular velocity, which we can use to design a multivariable controller.
The sensor and its algorithm is implemented to a magnetic levitation (maglev) stage
positioned atop a Halbach magnet matrix. Preliminary experimental results show its position
resolution capability of less than 10 µm and capable of sensing large rotations. Controllers
were designed to close the control loop for the three planar degrees of freedom
motion using the GLSDC outputs at a sampling frequency of 800 Hz on a Pentek 4284 digital
signal processor (DSP). Calibration was done by comparing the laser interferometers and the GLSDCÂs outputs to improve the positioning accuracy.
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