The vibration control of speed-dependent flexible rotor/magnetic bearing systems using linear matrix inequality gain-scheduled H ∞ design

Abstract

The dynamics of rotor/magnetic bearing systems are speed dependent due to gyroscopic effects and other aerodynamic influences. This paper introduces a linear matrix inequality (LMI)-based design method that enables the speed dependence to be embedded within robust gain-scheduled controllers. By utilizing an augmented plant that closely resembles the physical system, it allows for the formulation of multiple design objectives in a unified framework. In particular, a control design for minimized rotor displacements or bearing transmitted forces is considered and the importance of achieving performance over the whole speed range is addressed. If speed dependence is ignored in the controller design, system instability may occur at particular rotational speeds. However, the LMI-based gain-scheduling approach is shown to maintain closed-loop stability over the full speed range. The results are demonstrated using a system model and through measurements taken from a flexible rotor/magnetic bearing facility.

Keywords

LMI gain-scheduling linear parameter dependent system gyroscopic effects

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