Bearingless Motors: Modeling and Control

Maksim Sokolov

Research output: ThesisDoctoral ThesisCollection of Articles


Bearingless motors integrate the functions of an active magnetic bearing (AMB) and an electric motor in the same magnetic circuit, which is utilized both for driving the motor and for maintaining active levitation. This research focuses on two types of bearingless machines: rotating synchronous reluctance machines (SyRM) and linear flux-switching permanent-magnet (FSPM) machines. The complex nature of these devices results in non-trivial control challenges, which require accurate modeling of the magnetic behavior and of the force production of these machines. Particular attention in modeling is given to the effects of magnetic saturation and air gap variation. Both effects can result in degraded control performance or even instability if not accounted for. For bearingless SyRMs, an explicit-function-based magnetic model including cross-saturation is proposed. The model is able to predict radial forces even in a saturated machine. Furthermore, based on the textbook model of bearingless SyRMs, an improved model is developed that includes a more precise inverse air-gap approximation. The improved model has better accuracy in the predicted variation of forces and inductances due to eccentricity. For bearingless FSPM linear machines, a dynamic model based on an equivalent magnetic circuit is proposed, taking into account the effects of the saturation, the air gap variation, and the attraction force due to the permanent-magnet (PM) leakage flux. An analysis and characterization of the studied machines is conducted using the finite-element method (FEM). The proposed dynamic models are utilized as a basis for the development of model-based control systems. Classical state feedback control with direct pole placement is applied to bearingless machines. However, traditional current controllers cannot guarantee consistent performance in the presence of saturation and cross-coupling effects. These effects are automatically taken into account by the proposed state-space flux-linkage controller. A digital implementation of the controller is provided and robustness against the system parameter inaccuracies is analyzed. For levitation control, an observer-based state-space levitation controller is designed. Analytical tuning rules for each proposed controller are presented. Furthermore, feedback linearization is used for accurate calculation of current references based on the requested forces and torque. The applicability of the developed modeling and control methods is demonstrated with experimental results from three prototype bearingless machines including levitation, rotation, and propulsion tests.
Translated title of the contributionBearingless Motors: Modeling and Control
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Hinkkanen, Marko, Supervising Professor
  • Saarakkala, Seppo, Thesis Advisor
Print ISBNs978-952-64-0650-3
Electronic ISBNs978-952-64-0651-0
Publication statusPublished - 2021
MoE publication typeG5 Doctoral dissertation (article)


  • bearingless motor
  • magnetic model
  • magnetic saturation
  • eccentricity
  • inductance
  • radial force
  • unbalanced magnetic pull
  • flux-switching permanent-magnet (FSPM) machine
  • synchronous reluctance machine (SyRM)
  • linear motor
  • magnetic levitation
  • model-based state-space control
  • flux-linkage controller
  • combined winding


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