This dissertation presents the design, control, and implementation of a compact highprecision
multidimensional positioner. This precision-positioning system consists of a
novel concentrated-field magnet matrix and a triangular single-moving part that carries
three 3-phase permanent-magnet planar-levitation-motor armatures. Since only a single
levitated moving part, namely the platen, generates all required fine and coarse motions,
this positioning system is reliable and potentially cost-effective. The three planar
levitation motors based on the Lorentz-force law not only produce the vertical force to
levitate the triangular platen but also control the platen's position and orientation in the
horizontal plane. Three laser distance sensors are used to measure vertical, x-, and yrotation
motions. Three 2-axis Hall-effect sensors are used to determine lateral motions
and rotation motion about the z-axis by measuring the magnetic flux density generated by
the magnet matrix.
This positioning system has a total mass of 1.52 kg, which is the minimized mass to
produce better dynamic performance. In order to reduce the mass of the moving platen, it is made of Delrin with a mass density of 1.54 g/cm3 by Computer Numerical Controlled
(CNC) machining. The platen can be regarded a pure mass, and the spring and damping
effects are neglected except for the vertical dynamic. Single-input single-output (SISO)
digital lead-lag controllers and a multivariable Linear Quadratic Gaussian (LQG)
controller were designed and implemented. Real-time control was performed with the
Linux-Ubuntu operating system OS. Real Time Application Interface (RTAI) for Linux
works with Comedi and Comedi libraries and enables closed-loop real-time control.
One of the key advantages of this positioning stage with Hall-effect sensors is the
extended travel range and rotation angle in the horizontal mode. The maximum travel
ranges of 220 mm in x and 200 mm in y were achieved experimentally. Since the magnet
matrix generates periodical sinusoidal flux densities in the x-y plane, the travel range can
be extended by increasing the number of magnet pitches. The rotation angle of 12 degrees was
achieved in rotation around z. The angular velocities of 0.2094 rad/s and 4.74 rad/s were
produced by a 200-mm-diameter circular motion and a 30-mm-diameter spiral motion,
respectively. The maximum velocity of 16.25 mm/s was acquired from over one pitch
motion. The maximum velocity of 17.5 mm/s in a 8-mm scanning motion was achieved
with the acceleration of 72.4 m/s2. Step responses demonstrated a 10-um resolution and
6-um rms position noise in the translational mode. For the vertical mode, step responses
of 5 um in z, 0.001 degrees in roation around x, and 0.001 degrees in rotation around y were achieved.
This compact single-moving-part positioner has potential applications for precisionpositioning
systems in semiconductor- manufacturing
