This research is motivated by the need for actuators capable of delivering precise multiple degrees of freedom (DOF) motion with structure and energy efficiency in numerous applications. Permanent magnet spherical motors (PMSMs) are typical examples that can provide continuous and precise 3 dimensional (3D) rotational motion about a ball joint. The result of this research demonstrates a unique PMSM capable of 3D rotational motion control with high accuracy and bandwidth.

A Kalman filter (KF) sensor fusion method is developed to implement full state estimation of 3-DOF angular displacement and velocity in real time for a PMSM by simultaneously measuring the existing magnetic flux density (MFD) field and the back-electromotive-force (EMF) as inputs to the sensor fusion algorithm. More specifically, the bijective property between the orientation and measured MFD field is numerically demonstrated, which provides the basis to implement the measurement model through an artificial neural network (ANN) trained with a Levenberg-Marquardt algorithm. A mathematical model presenting the angular velocity and back-EMF measurements is formulated in quaternion representation, simplifying the computations required to implement the sensor fusion system while providing a reliable and accurate estimation of both the orientation and its angular velocity. The rotor dynamics are modeled and represented with time-varying nonlinear differential equations. The system uncertainties due to parameter inaccuracies of the cascaded system and the changes of the loads are analyzed. A sliding mode control (SMC) system is developed to precisely and robustly control the typical nonlinear system of the PMSM regardless of the system uncertainties. The capabilities of chatter suppression and error convergence of the proposed control law are investigated. A PMSM prototype fabricated using additive manufacturing is developed to experimentally demonstrate the facilitation of the motor design and effectiveness/accuracy of the entire 3D orientation feedback control system.


Min Li

Committee Member

Pavan Karra

Committee Member

Vincent Winstead

Date of Degree




Document Type



Master of Science (MS)

Program of Study

Mechanical Engineering


Mechanical and Civil Engineering


Science, Engineering and Technology

Available for download on Tuesday, May 07, 2024



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