(A) study on the determination of accurate inverse kinematics in a high precision magnetic levitation system

Abstract

The high precision systems have been developed in various fields. Especially, high precision system with high performance is demanded for the semiconductor manufacturing. As a vacuum compatible precision stages are demanded, a high precision magnetic levitation system has developed. In order to control the magnetic levitation system, an inverse kinematics which connects forces and currents should be found. A basic method for finding the inverse kinematics is mathematical modeling. With the mathematical modeling, however, an inaccurate inverse kinematics is obtained due to the complexity of the inverse kinematics, manufacturing errors, and assembly errors. The inaccurate inverse kinematics is a main cause of coupling the force from the controller and the actual force, leading to low performances. Especially, rotational motion errors caused by the force coupling are key factors for low speed. Therefore, an accurate inverse kinematics should be found for the high performances and the high speed. In this dissertation, a new method for obtaining the accurate inverse kinematics is proposed. The method does not utilize the mathematical modeling. Instead, the method obtains an accurate inverse kinematics with experiments. The sequence of the proposed method was established and the effectiveness of the method was verified with a simulation. The various conditions for the method were chosen with consideration of properties of the magnetic levitation system and an accurate inverse kinematics was determined by the proposed method. In order for verifying the accuracy of the inverse kinematics, performances when the previously found inverse kinematics was used and when the inverse kinematics from the proposed method was used were compared. The better performances were obtained with the inverse kinematics obtained from the proposed method in terms of velocity and decoupled force. In conclusion, the fact that the proposed method can find more accurate inverse kinematics was validated by the comparison.