Multivariable Control and Optimization of a Compact 6-DOF Precision Positioner With Hybrid ${\cal H}_{2}/{\cal H}_{\infty}$ and Digital Filtering

In this paper, we present multivariable controller design and implementation of a high-precision 6-DOF magnetically levitated (maglev) positioner. To achieve high-precision positioning, two discrete-time integrator-augmented controllers based on the linear quadratic Gaussian multivariable control are applied. A novel discrete hybrid H
₂
/H
_∞
filter is used as the observer to obtain the optimal estimates of position and orientation, as well as additional estimates of linear and angular velocities for all six axes. The positioner has a single moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. The positioner moves over a Halbach magnet matrix using three sets of two-axis Hall-effect sensors to measure the planar motion and three laser distance sensors for the vertical motion. The Hall-effect sensor signals are found to generate a considerable amount of noise and are centered at 50 Hz. A second-order digital notch filter is implemented to optimize the sensor readings and attenuate the noise. Experimental results show a position resolution, which is the smallest noticeable step of 1.5 μm with a position noise of 0.545 μm rms in the x- and y-directions, and a position resolution of 110 nm with a position noise of 49.3 nm rms in the z-direction.