Modeling and control of magnetically-levitated rotating shafts with active magnetic bearings and self-bearing motors

This thesis covers aspects of modeling, control, and design of magnetically-levitated rotating shafts. This topic is subdivided into two discrete but related problems.;In the second problem we consider a shaft that is simultaneously levitated and rotated by a self-bearing motor (SBM). Whereas AMBs achieve levitation on the well-known basis of reluctance force, the type of SBM considered in this thesis, namely the toothless self-bearing servomotor (TSBS), creates levitation using the less common Lorentz force. The operating principle of the TSBS is studied and nonlinear expressions for levitation force and torque are derived from first principles. Insight from force and torque characterization leads to a more general dynamic model that introduces previously unused control variables. Based on our dynamic model a control system is designed which extends the physical operating range of the TSBS relative to the established control approach and resolves the conflict between the levitation and rotation subsystems in the presence of input saturation. Performance improvements are confirmed on an experimental TSBS. Finally, exploiting all control variables of the TSBS motivates redesign of the TSBS itself. A new operating principle, dynamic model, and control system are proposed and experimentally validated which reduces the device's power electronic requirements.;Keywords: magnetic levitation, active magnetic bearings, self-bearing motors, nonlinear control, nonlinear observers.;In the first problem we consider trajectory tracking of a shaft that is levitated by active magnetic bearings (AMBs) and rotated by a conventional motor. Trajectory tracking involves control of the AMBs such that the rotating shaft follows a prescribed path with minimal vibration. Trajectory tracking and vibration minimization are addressed in a common control framework incorporating the ideas of differential flatness and nonlinear observers. Furthermore, the nonlinear and overactuated nature of AMBs are studied through a comparison of control approaches.