Wrench Model with Rotation Angles for Magnetically Levitated Actuators

Magnetic levitation actuators (MLAs) are frequently employed in photolithography, precise positioning and transportation. The actuator, which consists of racetrack coils and one-dimensional 3 Halbach arrays, has the capacity to calculate the wrench model in real time. However, the high computational demands of the high-dimensional wrench model will result in a prolonged control cycle. Based on a levitation plane composed of three groups of magnetic levitation actuators, this paper proposes a wrench model considering six dimensions to calculate the output current required by the actuator in real time. This method simplifies the expression form of the formula and directly calculates the expression of the current conversion matrix, thereby enabling the system’s computing speed to reach 3 KHz. The system’s step response and trajectory-tracking performance were simulated and compared under the models with and without angular consideration. It has been demonstrated that when rotation angles are incorporated into the magnetic levitation plane, the wrench model considering angles achieves better performance than the wrench model without rotation angles.