Robust Performance Analysis of Uncertain Magnetic Bearings

Abstract

This paper deals with uncertain model structures, model validation and robust performance analysis of active magnetic bearing systems. The dynamics of active magnetic bearing systems are characterized by their instability and complex dynamics of rotor and electromagnets. One of the most critical problems of AMBs is a description of a complex behavior of the dynamics of electromagnets and their forces. The exact description of them is almost hopeless, some approximations and assumptions must be employed, and consequently a discrepancy between the real physical system and the nominal design model cannot be avoided. This discrepancy of the magnetic bearing systems is a serious problem of stability and performance. Hence feedback control is indispensable to stabilize the system, further the closed-loop systems of AMBs should have robustness for stability and performance against model uncertainties. First we derive a nominal mathematical model of AMBs as a linear state-space model under some assumption and idealization, then we consider the discrepancy between the real physical systems and the obtained nominal design model. This discrepancy can be expressed as the structured uncertainties by Linear Fractional Transformation. These uncertainties include linearization error, parametric uncertainties, unmodeled dynamics, and gyroscopic effect. Then we set the interconnection structure which contains the above structurally represented uncertainties. Next we design a robust controller which achieves robust performance condition. Finally, we validate the interconnection structure with the nominal model and uncertainties, and analyze the robustness of stability and performance of the closed-loop system via the mixed structured singular value.