本文旨在探討立式撓性轉軸於承受軸向壓力下之系統動態與穩定性分析，並整合磁浮軸承技術以及順滑/模糊順滑控制器之設計，使磁浮撓性轉軸維持漸進穩穩定。當撓性轉軸承受軸向壓力高速運轉時，撓性轉軸會產生挫曲與迴動現象效應。因此考量撓性轉軸之轉動慣量與陀螺效應因素，基於雷立夫樑理論建構轉軸運動方程式，根據迴動頻率方程式與模態振型對撓性轉軸系統動態與穩定性加以分析，並獲得轉軸系統挫曲與迴動之臨界轉速與臨界負載。撓性轉軸匹配磁浮軸承之數學模型可推導出磁浮撓性轉軸系統之宰制方程式，因系統具有奇異擾動之特性，藉由奇異擾動理論可將系統轉換成降階模型，以作為控制器設計之依據。為了使磁浮轉軸系統能克服參數變異以及減低轉軸質量偏心對系統之影響，故本文於控制器設計部份分別採用順滑控制策略以及模糊順滑控制策略。由電腦模擬之結果均展現出設計之順滑控制器與模糊順滑控制器皆具有優越的性能，使系統滿足使用者預先規劃之響應規格。

The analysis of the dynamics and stability of vertical flexible rotors under axial forces is studied in this thesis. In order to keep flexible rotors asymptotically stable, the technology of magnetic bearing and design of sliding mode control/fuzzy sliding mode control loop are incorporated to practically stabilize flexible rotors. The two phenomena, buckling and whirling, are caused as the rotor is spinning at high speed. Take the rotary inertia and gyroscope effect into account, the motion of the flexible rotors is analyzed on the basis of the Rayleigh beam theory. Depending on the whirling frequency equation and mode shape of the flexible rotors, the dynamics and stability of the flexible rotors is investigated, and the critical speed and critical load of the buckling and whirling of rotors system can be obtained. The governing equation of the maglev rotors is derived via the mathematical model of the magnetic bearing and the motion of the flexible rotors. By singular perturbation technology, the system model can be transformed into reduced order model which is the basis of the controller design. For overcoming the uncertainty of system parameter and reducing the effect due to mass eccentricity, the fuzzy sliding mode controller (FSMC) is employed in this thesis. The simulation results show that FSMC has good performance, satisfying the specification of the system response which is designated what users normally expect.

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