This dissertation presents the electromagnetic design and experimental validation of a new framework for linear permanent-magnet (PM) machines with targeted applications in precision motion control. In this framework, a single forcer, which can generate two independent force components in two perpendicular directions, consists of a stationary Halbach magnet array and two Lorentz coils with a phase difference of 90? or 270?. Any number of coil pairs can be attached on the same moving frame to work with a common magnet array or matrix, forming a linear or planar PM motor. Key advantages of this framework are simple force calculation, a linear system model, and a reduced number of coils for force generation and allocation in multi-axis positioners. The proposed framework effectively allows for decoupled dynamics, simplifying the linear controller design and real-time implementation. To experimentally verify the theoretical framework proposed herein, a high-precision 6-axis magnetically levitated (maglev) stage is designed, constructed, and controlled. The development of this 6-axis positioning system is an integrated work, including magnetic-force calculation and analysis, mechanical design, fabrication, assembly, system modeling, system identification, and control system design. The mechanical components of the system include a stationary superimposed Halbach magnet matrix, which was previously built, and a moving platen with a plastic frame, four sets of 2-phase coils, and two precision mirrors. For position measurements, there are three laser interferometers for in-plane position measurements, three laser displacement sensors for out-of-plane position sensing, and two 2-channel Hall-effect sensors for the position feedback to initialize the position and expand the travel ranges of the platen in the XY plane. The positioning resolutions of 10 nm in the xy plane and in the vertical axis are demonstrated. In out-of-plane rotation about the two horizontal axes, experimental results show the unprecedented positioning resolution of 0.1 urad. The maximum travel range in X and Y with nanoscale positioning resolution is 56 mm x 35 mm, limited by the lengths of the precision mirrors attached to the platen. With the trapezoidal-velocity input shaping, achieved performance specifications include the maximum acceleration and velocity of 0.6 m/s2 and 0.06 m/s, respectively, in translations in the horizontal plane. With the platen supported by the air bearings, the maximum acceleration and speed are 1.5 m/s2 and 0.15 m/s, respectively. A load test is performed with the platen carrying a load of 0.54 kg, which is 72% of its total mass, magnetically levitated in 6- axis closed-loop control. Experimental results show the reduced coupled dynamics between different axes in magnetic levitation. This framework of 2-phase Lorentz coils and linear Halbach arrays is highly applicable in precision-positioning linear motors and multi-axis stages, steppers, scanners, nano-scale manipulation and alignment systems, and vibration isolators.
