殘留振動的存在，影響了撓性機件傳輸運動之精度定位，增加達成工作目標所需要的時間。減少殘留振動的方法有閉迴路設計的回授控制以及開迴路設計的輸入修正法。輸入修正能有效地縮短安定時間及抑制殘留振動，但若存在外在干擾或本身具參數不確定性，可能造成殘留振動無法完全消除；回授控制具有抵抗干擾以及提供系統強健性之能力，但往往需與系統妥協而影響了控制系統性能表現。於本文中，我們拓展輸入修正法的運用面至反覆式切換定位減振，並考慮到輸入修正法的開回路限制，成功的將輸入修正結合簡單的回授控制系統進行定位減振，並以實驗實現於具Duffing非線性特性雙鉗樑系統。在控制器的選擇上，考慮到整體系統為非線性系統，致動器具電磁力的非線性特性，當氣隙增加，可能造成電磁力參數的不確定性，因此我們選用了具參數強健性的滑動模態控制器結合回饋線性化方法對系統進行定位分析，並探討了控制器參數對系統整體性能之影響。最後，我們整合了輸入修正及滑動模態態控制的減振優點，利用輸入修正達到快速定位，而滑動模態則用來抵抗外在干擾，對於純動態之軌跡定位，則可由滑動模態控制器進行定位實現。

Magnetic servo levitation(MSL) is currently being investigated as an alternative to drive fast-tool servo systems. Due to the strongly nonlinear system dynamics, system performance is easily affected by parameter uncertainties and external disturbances. This thesis concerns the precision positioning and vibration suppression of an electromagnetically driven duffing nonlinear system using both open-loop command shaping and closed-loop robust control approaches. Command shaping is an effective technique for suppressing motion-induced residual vibration of lightly damped systems. However, due to its open-loop feature, the steady state behavior may not be well controlled due to the influences of external disturbances. An other suppression method is closed-loop control. In the first part of this thesis, a scheme to integrate the command shaping with feedback control is proposed. By command shaping, systems can fast reach their target positions while the feedback control ensures the robustness against environment disturbance. This scheme is verified using an electromagnetically driven fixed-fixed beam. The experimental results indicate that the proposed scheme can effectively reduce the rising time and suppress the residual vibration excited by external disturbance, but the system performance may be influenced by system parameters uncertainties. In the second part of this thesis, we applied three schemes including command shaping, sliding control and a scheme to integrate the command shaping with sliding control on tracking an electromagnetically driven duffing nonlinear system. The sliding controller consists of two parts：the nominal control part that linearizes the nonlinear dynamics, and the robust control part that provides robust performance against the system uncertainties. For the command shaping and sliding control integration scheme, by command shaping, systems can fast reach their target positions while the sliding control ensures the robustness against environment disturbance and system uncertainties. The simulation and experimental results indicates that the proposed scheme can successfully reduce the rising time and suppress the residual vibration excited by system uncertainties and external disturbance. In the future, the proposed method can be applied not only on electromagnetically driven fast-tool servo systems but also on the next generation magnetic bearing suspended wafer scanner for lithography process. Or, by system analogy, it can also be applied to electrostatically actuated MEMS structures.

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