本文對原子力顯微鏡探針作動態分析與控制系統設計，期望原子力顯微鏡探針達到精確且快速定位的目標。首先透過動力學得到系統的動能和位能，依據漢米頓原理(Hamilton’s principle)求得到系統的運動方程式及相關邊界條件，經由拉普拉斯轉換(Laplace transform)得到系統的開迴路轉移函數，具有無窮多個極點和零點，利用模態疊加法取得精確度足以描述系統之模態數，以根軌跡法和Martin理論分析系統穩定度並進行控制器之設計。最後對所設計出來的比例微分控制器、相位領先補償器和專家比例-微分-積分控制器進行時間響應模擬，其中專家比例-微分-積分控制器能減少系統的安定時間且能有效抑制系統振盪是最為理想與實用的控制器。

The objective of this thesis is to discuss the dynamic analysis and controlling system design for atomic force microscopy, with the aim to enhance the system stability and achieve accuracy and precision in positioning. First, the kinetic and potential energy of system are obtained based on the theory of dynamics. The dynamic equations and related boundary conditions of atomic force microscopy are derived from Hamilton’s principle. Then, the open-loop transfer function is derived from the Laplace transform. Since the transfer function has an infinite number of poles and zeros, mode summation method can be used to obtain modes with precision that is sufficient to describe the system. The system stabilization and controller design are analyzed by using the root-locus method and Martin’s theorem. Finally, time response simulation is conducted on the proportional-derivative (PD) controller, phase-lead compensator, and expert PID controller developed by this study. Among which, the expert PID controller is proved to improve the effect of the vibration suppression and reduce the settling time. Therefore, it is an ideal and practical controller to solve the problem of vibration suppressions for high-speed precision positioning.

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