An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

Abstract

Active magnetic bearing (AMB) systems are intrinsically unstable but stabilized by feedback control. In order to evaluate objectively the stability, a standard criterion is necessary. One of the indices for stability evaluation is a maximum gain of sensitivity functions. Radial positions of the rotor are regulated by four-axis control, that is, a radial system needs to be treated as a multi-input multi-output (MIMO) system. One of general criteria for evaluating the stability of a MIMO system is a maximum singular value of a sensitivity function matrix, which needs 16 matrix elements for calculation. It is, however, easier to regard each control axis as an independent single-input single-output (SISO) system and it can be evaluated by just four sensitivity functions. ISO/DIS 14839-3 will employ this concept. This paper discusses the stability evaluation as a SISO system with parallel/conical mode separation or side-by-side treatment, and a MIMO system using maximum singular value, also these differences. In addition to this, a conversion from the usual x,y-axis form to forward/backward form is proposed and the stability is evaluated for the system in the converted form. For experimental evaluation, a test rig diverted from a high-speed turbo compressor rated at 180kW was used. The transfer functions were measured by exciting the system with swept signals at rotor standstill and at 30,000r/min rotational speed. For stability limit evaluation, the control loop gain was increased or a phase lag was inserted in the control loop to lead the system to be nearby unstable intentionally. Using these test results, the differences among the evaluation manners are discussed.