隨著壓電材料的發現與應用，原子力顯微鏡(AFM)開始利用壓電材料作為平台的驅動器，以壓電平台的方式來做高精密的軌跡掃描定位，利用軌跡定位之結果來建構出一張奈米尺度的三維(3D)影像。然而，壓電平台本身具有高度非線性特性，例如: 磁滯效應、蠕變效應等，會導致AFM掃描成像的失真問題；另外，傳統AFM的掃描路徑為柵欄式掃描軌跡，它是以週期式三角波與連續步階軌跡所建構而成，但三角波軌跡是由無限奇次諧波所組成，所以在追蹤該軌跡時容易引發壓電平台的機械共振問題，導致在高速掃描下會無法準確依照預定軌跡移動。 為了有效地解決上述問題，本論文從軌跡著手以及控制器設計來改善。首先，我們開發出一種新型雙紐線掃描軌跡，它具有平滑軌跡的特性可以減緩壓電平台的機構共振，同時也保留了傳統柵欄式軌跡的直線部分，可以將掃描點的圖像映射失真問題最小化。另外，本論文首次結合模型預測控制(MPC)與長短期記憶(LSTM)來作為壓電平台的控制器，該控制器可以大幅消除磁滯與蠕變等非線性特性，並且提升追蹤軌跡的掃描速度。最後，我們藉由大量模擬證實所設計之控制方法的追蹤誤差，明顯低於比例積分微分控制(PID)及模型預測控制，並且在追蹤雙紐線軌跡的直線部分也有不錯的表現。 ;With the discovery of piezoelectric material, atomic force microscopy (AFM) uses the piezoelectric material to design the piezo-stage for high precision positioning of nanometer scale. However, the piezo-stage has inherent shortcomings like hysteresis and creep effects that inevitably cause unwanted distortion in the AFM scanned results. In addition, the traditional scan trajectory is the raster scan, which is constructed with a period triangular waveform and continuous steps. However, since the triangular waveform is a signal with infinite odd frequency, it will easily excite the mechanical resonance of the piezo-stage while tracking the trajectory, resulting in inaccurate movements according to the predetermined trajectory at a high-frequency scanning speed requirement. This thesis focuses on trajectory improvement and controller design to effectively deal with the abovementioned problems. First, we design a novel smooth lemniscate scan trajectory to reduce resonant vibration of the piezo-stage. Furthermore, the proposed trajectory preserves the straight part of the triangular waveform to minimize the mapping distortion of scanning points. Second, this work is the first to combine model predictive control (MPC) and long short-term memory (LSTM) control methods for use in the piezo-stage. The proposed controller can not only mitigate the nonlinear property like hysteresis and creep effect but also increase the scanning rate and the tracking accuracy of the lemniscate scan trajectory. Simulation results show that the tracking error of our proposed controller is smaller than those of the PID and MPC, and it also has an excellent performance in tracking the straight part of the lemniscate scan trajectory.
