Ph.D. Thesis Summary

Real-Time Control and Characterization of a Variable Reluctance Spherical Motor

Zhi Zhou

The demand for dexterous robotic manipulation has motivated researchers to direct their efforts towards designing unusual actuators. Among the developments is a ball-joint-like multiple degree-of-freedom (DOF) variable-reluctance (VR) spherical motor that is capable of providing smooth and isotropic three dimensional motion in a single joint. The innovative VR spherical motor has advantages over conventional mechanisms including its relatively simple and compact structure and large range of continuous motion with uniform resolution. These attractive features offer the multi-DOF device significant  potential in applications such as coordinate measuring, high-speed plasma, and laser  cutting where orientation must be achieved rapidly and continuously in all directions. Although previous research has demonstrated the basic principle and design  methodology of the VR spherical motor, many fundamental (theoretical and practical)  issues remain to be further investigated. This thesis develops unique concepts, theories  and experimental methods for characterization and design optimization of multi-DOF  actuators, investigates new control schemes and bearing support mechanisms to enhance the performance characteristics, and to design and implement practical techniques  (hardware and software) for real-time control applications. 

The ability to characterize specifications of an innovative actuator is essential in design and control strategy development, since the characteristic specifications will serve as constraints in controller design. The unique features of a VR spherical motor make its characterization significantly different from and more difficult than one DOF actuators. A maximum torque formula is derived in this thesis to serve as a basis for characterization and design optimization of the multi-DOF VR spherical motor. The formula is used effectively to predict the torque output capacity of the device. A torque-to-power ratio defined on the basis of the maximum torque formula provides a more desirable objective function for design optimization. New concepts and observations developed from the formulation and derivation of the maximum torque formula are presented. Typical specifications of the VR spherical motor prototype critical to practical applications are characterized to illustrate the application of the maximum torque formula. Results of this investigation lay an essential analytical and engineering basis for integrated design and characterization of a wide variety of multi-DOF actuators. 

A resultant magnetic force model is derived which, along with the torque model, competes the dynamic modeling of the electromagnetic interaction of the VR spherical motor. Six degrees of freedom of the VR spherical motor is conceptualized by allowing the rotor to translate. The concept development allows a reaction-free control strategy be designed to magnetically levitate the rotor so that a non-contact support mechanism is established without additional system complication. As a result of the implementation of the reaction-free control strategy, high performance motion is achieved through the substantial reduction of the internal friction inherent to most existing driving mechanisms. The conceptualization of virtual translation of the VR spherical motor leads to a new concept of permeance model with variable airgap that is a function of both rotor orientation and translation. Experimental and analytical methods used to determine the permeance model are presented in the thesis due to its important role in implementation of the reaction-free control strategy. 

Practical implementation techniques and associated hardware and software are developed for real-time control applications. An equivalent angle-axis based control is designed and implemented along with a load compensation mechanism. The control strategy designed requires only limited knowledge of load dynamics, and is physically intuitive and practically useful. An analytical path planning algorithm is devised to facilitate the control strategy for the prototype VR spherical motor. Two approaches, a linearized near optimum algorithm and a look-up table based on-line nonlinear optimization scheme, are taken to address practical implementation issues in control input optimization. A typical look-up table is generated and implemented along with the generalized reduced gradient (GRG) optimization algorithm. Various motion control experiments are performed and results analyzed. Experimental results verify the control strategies and demonstrate the motion capability of the multi-DOF VR spherical motor. While the experiments illustrate the motion ability of the multi-DOF device, they also reveal constraints and limitations of the prototype design and provide insights for future design of the VR spherical motors. 

Major contributions of this thesis research include: (1) methodology and new concept development for characterization and design optimization of multi-DOF actuators, and illustrative characterization (specification determination) of the VR spherical motor prototype, (2) conceptualization of six degrees of freedom, permeance model with variable airgap, and design of reaction-free control strategy and magnetic levitation, and (3) efficient and practical experimentation of the control strategies and the development of the hardware and software implementation tools. The concepts, principles, methodologies, and experimental techniques developed and presented in the thesis establish an essential analytical and engineering basis for characterization, design optimization, and real-time control of a spectrum of multi-DOF robotic actuators, especially the variable reluctance spherical motors.