Modeling And Motion Control Of Magnetically Levitated Planar Motors

Planar motor is a new kind of motor which can generate planar motions directly. Itgets the features of simple structure, high accuracy, and quick response speed. Thisdissertation addresses the motion control of a magnetically levitated planar motor. Theelectromagnetic force and moment modeling is carried out on a current loop in themagnetic field of a permanent magnet array. A current distribution method which canrealize the decoupling of the thrust components in the horizontal directions is proposedbased on the analysis of one-dimensional coil array’s force characteristic. The forcesand moments acting on the platen are modeled, and the decomposition algorithms of thethrust components in the horizontal directions and in the vertical directions are given,respectively. A decoupling model for the six-degree-of-freedom motion control of theplanar motor is built. Controller design and parameter optimization are accomplishedfor the motion control of each degree of freedom. Simulations and experiments arecarried out respectively to validate the effectiveness of the overall control scheme.Firstly, the force condition of finite current elements is studied based on the firstharmonic model of the permanent magnet array’s magnetic flux density distribution,utilizing Lorentz Force Law. A descriptive model of the electromagnetic force is built,suitable for all the current loops getting a form of geometric symmetry, and placedleveled in the magnetic field of a Halbach type permanent magnet array. A parametricanalytical model of the electromagnetic force and moment is built, through a fewappropriate geometric simplifications, with which the influence of a coil’s keydimensions on the coil array’s thrust constant is studied. The operation mechanism of amagnetic levitated planar motor is illustrated. A decomposition algorithm of the thrustcomponents is proposed, which will ensure the equilibrium working state of each coilarray. Based on the research of current distribution methods for two and three-phasequadrature coil arrays, the criterion and a current distribution method for a quadraturecoil array are given. Along with the current distribution method, the couplingcharacteristic of electromagnetic forces and moments is studied for a three-phasequadrature coil array, and a compensation method to eliminate the influence ofadditional torques is proposed. Secondly, the physical model of the platen is built to study the system’s couplingcharacteristic between the input currents and the output forces and torques. Adecoupling control model is acquired by the means of precision linearization based onthe dynamic model of the platen. SISO controllers are designed with PID feedbackcontrol for the six-degree-of-freedom motions of the planar motor. The influence ofelectromagnetic force and moment’s exponential decay characteristic in the verticaldirection on the system’s control performance is studied, using Euler’s formula. Theplaten has the form of a magnetic spring system in the vertical direction, and a gravitycompensation strategy is proposed.Thirdly, the thrust constant of the planar motor and the damping coefficient in thevertical direction are acquired through open-loop parameter identification. A simulationmodel describing the motion in the vertical direction of the platen is built underSimulink, and the experimental results are compared with those from simulation. Theparameter design of the six-degree-of-freedom motion controller is accomplishedthrough trial and error. The unstable equilibrium characteristic of the platen undermagnetic levitated condition is studied. A current distribution method suitable forthree-phase non-quadrature coil arrays is proposed to let out the accuracy ofmanufacturing and assembling. The6-DOF motion control of a magnetic levitatedplanar motor system is realized.