Enhanced Complex Space Vector Modeling and Control System Design of Multiphase Magnetically Levitated Rotary–Linear Machines

Rotary-linear electric machines can perform coupled rotary and linear motion. In addition, they can have magnetic bearings (MBs) integrated and magnetically coupled with the rotary, linear, or rotary-linear machine operation. Since rotary-linear machines with MBs have not been thoroughly analyzed in the literature, the models that provide understanding of their operation and give basis for the control system implementation are not entirely covered. Hence, in this article, an enhanced complex space vector-based model of the rotary-linear machine with MBs is derived and expressions for the torque, thrust force, and MB force are given. The rotary-linear machine complex space vector of the voltage, current, or flux linkage is defined using the proposed transformation with two complex frames: one related to the rotation and MBs and another to the linear motion. This results in complex space vectors with two complex units; however, the techniques used for a conventional complex space vector calculation can also be applied to the proposed complex space vector description. This is also experimentally validated on a hardware prototype of a magnetically levitated linear tubular actuator (MALTA), whose position control system is designed and implemented based on the enhanced space vector modeling approach, with the dynamic operation of the MALTA, including linear motor operation with an axial stroke of 10mm and a mechanical frequency of 17Hz.