| dc.description.abstract | Magnetic levitated planar motors employ electromagnetic force to levitate and manipulate the movers. They have the characteristics of multi-degrees-of-freedom motion, contactless operation, high precision and high acceleration. They have shown great potential in the area of flexible manufacturing, material transportation and photolithography. Maglev Microrobotics Laboratory at the University of Waterloo has proposed a novel electromagnetic design with stationary square coil arrays and a 2D Halbach array mover. With this electromagnetic design, two platforms are fabricated and tetsed, the maglev test bench and the maglev floor. The maglev test bench is a 64-coil platform with a levitation area of 0.6 m by 0.6 m, which is a pilot project of the maglev floor. The maglev floor is a 768-coil platform, whose levitation area is 2.4 m by 1.8 m. The maglev floor allows the tests to be closer to real-life manufacturing. The contributions of this thesis include the mover design, force and torque modeling between the mover and the coils, system integration, levitation implementation and advanced control for mover path tracking.
This thesis proposes a novel lookup-table-free data-driven method to model the force and torque on a 2D Halbach array when the magnet array is above a stationary coil. One critical contribution is the rapid and accurate force and torque modeling when the coil is located near the edge of the 2D magnet array. First, the area under the 2D Halbach array is divided into a central region, edge regions, and corner regions. Then, nonlinear force and torque components are identified and modeled with a modified third-order Fourier series for force and torque modeling. The proposed model is implemented on an industrial server, and the average computation time is measured to be 2.3 μs. This model is universal for symmetric coils, verified through experimental measurements with circular and square coils of different sizes. The measurement result agrees well with the proposed modeling method, showing that the proposed method is suitable for real-time control of the maglev planar motor.
With accurate force and torque modeling, a new 2D Halbach mover is designed and fabricated. The coil dimensions are identified by the Fabry Factor, optimizing its magnetic flux density over the working area. For the mover, instead of directly aligning a magnetic pole with the coil center, a study area is identified to represent the entire levitation area. Then, the mover dimensions are identified through the analysis of energy efficiency, load-carrying ability and maximum horizontal force. A lightweight mover case with a cross feature on the top is designed to control the mover deformation down to 0.02 mm. Vicon visual markers are attached to the mover for the camera to measure the mover’s location. The modular test bench, including current amplifiers, coils, programmable logic controller and Vicon motion cameras, is then integrated and tested for levitation. A direct wrench and active coil selection method is used to decouple the force and torque and determine the coil currents. With the force and torque model and the active coil selection method, the mover can move across different sets of active coils for long-stroke movement. Lastly, experimental validation results are presented. On the magelv test bench, the motion range is ±120 mm in the horizontal directions. The platform is validated to have a full 360° range of yaw motion. The motion precision reaches 0.01 mm for the translational directions. The motion precision for the roll and pitch is 5 mdeg, and for yaw is 2 mdeg. Experiments are also conducted on the maglev floor. The mover’s motion range is validated to be 2000 mm by 700 mm in the horizontal plane with a full yaw rotation range. The motion precision is 0.03 mm for the translational directions and 10 mdeg for the rotational directions. The maximum speed on both platforms are validated to be 500 mm/s for the translational motion and 75 deg/s for the yaw motion.
A novel predictor-based model predictive control is proposed to improve the tracking performance of the maglev planar motor. A Kalman filter and finite spectrum assignment based on an augmented system model are employed to forecast mover’s location by compensating for the system delay due to data transmission and processing. The predicted location is fed back to model predictive control for control optimization under the limit of coil currents. Hildreth’s quadratic algorithm is then applied to solve for the optimal control effort within the constraints. Comparative experiments demonstrate the effectiveness of the proposed control strategy, the total tracking error of which is much smaller than the result of a proportional-integral-derivative controller and standard model predictive control in all tests. Additionally, experimental results show that the proposed predictor-based model predictive control can tolerate higher speeds of the mover while retaining mover’s steadiness. The experimental results suggest the proposed predictor-based model predictive control is an effective path-tracking strategy for magnetic levitated planar motors subject to delays. | en |
