Loop Shaping Based H^∞ Robust Control of a Horizontal Shaft Magnetic Bearing

Abstract

This paper is concerned with H^∞ control design of a magnetic bearing from the point of view of loop shaping. Feedback control is indispensable for a magnetic bearing, since it is essentially an unstable system. For feedback control, a mathematical model is required; however, it does not always express the exact behavior of the system. Hence the model has various uncertainties such as the errors of parameters, neglected nonlinearities, or unmodeled dynamics. The controller is needed to guarantee robustness for both stability and performance against these uncertainties on the model.
Firstly, based on some assumptions, a linear state space model of a magnetic bearing is shown. Secondly, the experimental machine and the surroundings of its controller are introduced. The experimental machine is a 4-axis controlled horizontal shaft magnetic bearing. The controller consists of a Digital Signal Processor with fast A/D converters and D/A converters. Thirdly, the control system is designed using normalized coprime factor plant descriptions. Selecting shaping functions in this procedure called “The Loop Shaping Design Procedure (LSDP)”, we can shape the open loop transfer function and the transfer functions of the closed loop system. Finally, several experiments are carried out according to the above designed controller.