本文旨在設計高速五軸磁浮軸承系統的頻率整型順滑控制器設計。由電磁致動器之動態，轉軸之匹配推導整體磁浮軸承系統之運動方程式作為控制器設計之依據。基於線性二次式、最佳投影、頻率整型等原理，從頻域的觀點設計頻率整型順滑控制器，對主軸高階模態加以抑制，以避免激勵高階響應，且能保證系統參數在有界的各種參數不確定和捨去建模誤差下，系統仍能維持穩定。由於磁浮軸承為隨轉速時變系統，故本文應用Kharitonov’s Theorem判斷回授系統相對於轉速變動之穩定度，並分析所設計的等效控制力對轉速變動之強健穩定性。本文所提出之頻率整型順滑控制策略，除推導與證明外，所有電腦模擬之結果均展現設計之控制器具有優越的性能，足以於短時間內節制主軸的偏移於微米範圍以內。

The Frequency-Shaping Sliding Mode Control (FSSMC) for high-speed active magnetic bearing (AMB) is synthesized. The controller is designed on the basis of the equation of motion of the magnetic bearing system, which composed the dynamics of the electrical sub-system and mechanical sub-system. By linear quadratic, optimal projection and frequency shaping methodology, FSSMC is proved to be asymptotica-lly stable as long as the uncertainties of system parameters are bounded. The main purpose of frequency-shaping design is to avoid excitation of high-order dynamics of the rotating spindle so that the effect of a low-pass filter is presented. For the AMB is Linear Parameter Varying (LPV) system, the Kharitonov’s Theorem is employed to examine the stability under variation of rotational speed. It is proved that the equivalent control for the speed-dependent AMB system is robust. The simulation results show that FSSMC performs rapid response to regulate the deviation of high-speed spindle within 1 um .

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