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.

Cascaded Position-Flux Controller for an AMB System Operating at Zero Bias

“…The undershoot increases the settling time of the current controller. The measured output sensitivity function accesses the AMB system stability [19]. The measured output sensitivities of system at standstill and at 11, 000 rpm are presented in Figures 7 and 8.…”

Case study comparison of linear H<inf>∞</inf> loop-shaping design and signal-based H<inf>∞</inf> control

“…The evaluation of a general performance and stability of AMB systems is typically based on the output sensitivity functions [16]. When considering the closed-loop systems for the non-perturbed plant with the first three bending modes, the both controllers result in similar sensitivity functions as presented in Fig.…”

Stability analysis and imbalance compensation for active magnetic bearing with gyroscopic effects

“…Dynamic models of the AMB system can be divided to the translation system (7) and the rotation system (8). As can be seen, the static imbalance …”

“…In [7], gyroscopic effects can be reduced by placing proper poles and eigenstructure in the second-order systems with the damped gyroscopic matrix. In [8], the transfer functions to the forward/backward are converted to decouple the mixed peaks caused by the gyroscopic effects. However, all these works require intensive computational effort, and it is difficult to analyze and design the stability and parameters of the controllers.…”