A Multivariable Controller for an Electromagnetic Bearing / Shaft System

A Multivariable Control System is designed for an Electromagnetic Bearing and Rotating Shaft System. The Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) methodology is used to design a robust Model Based Compensator (MBC). The electromagnetic bearing consists of an electromagnetic actuator, operated in magnetic "attractive" force mode, with permanent magnet biased coils. The permanent magnet bias serves to linearize the actuator force application. The magnetic bearing operated in the attractive mode produces unstable system poles. The rotating member consists of a flexible shaft with an off center rotor. A simplified, scaled, infinitely stiff shaft model is used for the control system design. However robustness testing is done with a flexible shaft / rotor model. The thesis is concerned with the radial control of the combined system which is represented by a 4-input, 4-output plant model. A pair of magnetic bearings, each with orthogonal force capability, comprise the plant inputs, while shaft position within the bearings X-Y plane comprise the four outputs. Integral action is required to meet disturbance rejection specifications and is accomplished using state augmentation techniques. Nonlinear simulations are performed to complete the documentation of the design. Limitations of the compensator designed using the simplified model are discussed. A Model Based Compensator is also designed using the full order model of the flexible shaft. This compensator is combined with a flexible shaft model and system performance is compared to the baseline design. Thesis Advisor: Professor Lena Valavani Boeing Assistant Professor of Aeronautics and Astronautics