本論文主要在設計立式四軸主動磁浮軸承(Active Magnetic Bearing, AMB)系統的H-inf強健控制器。 藉著H-inf強健控制器使閉迴路系統具有強健穩定性及良好的響應性能，且能有效抑制參數不確定性(Parametric Uncertainty)及轉軸的陀螺儀效應(Gyroscopic Effect)對輸出的影響。 此外，引用Kharitonov定理對H-inf閉迴路系統作強健穩定性分析，利用參數變異區間(Interval)的極值(Extremal Value)找出克利托諾夫多項式(Kharitonov Polynomials)及克利托諾夫多項式(Kharitonov Segments)，並挑選有限個此類呈參數極值的閉迴路特徵多項式，並藉之判定它們的穩定性。 亦可藉此求得可容忍的主軸轉速範圍，且可預知閉迴路能承受多少陀螺儀效應。 最後，引用改良型的奈氏穩定準則 (Nyquist Stability Criterion)分析二輸入二輸出系統的閉迴路穩定性，並經由模擬以確認其性能。

　This thesis principally designs H-inf robust controller of vertical active magnetic bearing (AMB) system, which has four degree of freedom. The closed-loop system has robust stability and fine response performance by H-inf robust controller, and it is able to reduce the influence of the output on parametric uncertainty and on gyroscopic effect of rotor. Furthermore, Kharitonov theory is applied to analysis robust stability in H-inf closed-loop system. It utilizes extremal value of parametric variation interval to find Kharitonov Polynomials and Kharitonov Segments out, and determines the stability of them, which are chosen finite number closed-loop characteristic polynomials with Parametric Extremal Value. By this way, it gets the endurable range of rotational speed of spindle, and forecasts that the closed-loop system can bear how much gyroscopic effect. Finally, modified Nyquist Stability Criterion is applied to analysis the closed-loop stability of two outputs and two inputs system. And it confirmed it’s performance by simulation.

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