Abstract:
This dissertation considers the application of recent robust linear control techniques to rotors with active magnetic bearings. Rotors suspended with electromagnetic bearings are inherently unstable; therefore feedback control is an essential part of their operation. The purpose of the study is to design, analyze and compare the performance of various stabilizing robust controllers for a model of horizontal rotor with active magnetic bearings. Particular emphasis is placed on the study of time varying and parameter varying linear systems, due to the parameter (rotational speed) dependent structure of rotor dynamics. Despite the nonlinear form of the actuator (electromagnetic bearing) dynamics, the controlled system is linear and time invariant at constant speed. Control inputs from the actuators are linearized using a constant bias current in order to synthesize a linear stabilizing controller. Main sources of uncertainty in the system stem from the changing spring stiffness (due to different operating conditions) of the electromagnetic bearings, and changing rotor dynamics at different rotational speeds due to gyroscopic effects. Several H∞ controllers with nominal performance are designed. Simulations are carried out on the actual nonlinear system at speeds as high as 6000 rpm. Robust stability of the system with H∞ control using an appropriate uncertainty structure is tested and the limits of uncertainty for the uncertain parameters are established. In order to reduce the uncertainty in the system model and to enhance the operation speed with robust stability, a LPV controller is designed with H∞ performance via scheduling by the rotor speed on-line. Finally, to enhance the performance of controller with respect to possible transients during the operation, a multi-objective LPV controller is designed with generalized H2 performance, trading-off robustness against performance.
