修正式雙紐線軌跡結合自適應積分終端滑動模態控制與逆模型遲滯補償實現壓電平台精確追蹤

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姓名

許廷魁(Ting-Kuei Hsu) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

修正式雙紐線軌跡結合自適應積分終端滑動模態控制與逆模型遲滯補償實現壓電平台精確追蹤
(Modified Lemniscate Trajectory with Adaptive Integral Terminal Sliding Mode Control and Inversion-Based Hysteresis Compensation for Piezoelectric Stage Precise Tracking)

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至系統瀏覽論文 (2028-7-1以後開放)

摘要(中)

一般精密量測系統為了達成微/奈米尺度的三維結構掃描，在掃描器的XY軸會給予一個預先決定追蹤的掃描軌跡，並輔以所量測到的高度資訊來建構出樣本三維尺寸與形貌。然而，傳統精密量測系統的掃描路徑使用柵欄式軌跡，使用此掃描軌跡在高速追蹤時容易造成機械共振問題，導致高速掃描結果大幅失真。另外，壓電平台由於其本身材質的特性，會有遲滯與蠕變等非線性現象，間接造成軌跡輸出的位移不符預期，此錯誤的位移也會導致掃描結果失真，對於三維樣本表面精確的建構，會產生很大的負面影響。
從上述兩點問題切入，本論文將提出一個修正式雙紐線掃描軌跡，它不需要搭配步階函數即能夠達成路徑的連續掃描。該軌跡具有平滑特性，所以能夠改善傳統掃描方式容易造成機械共振的問題，同時也保留柵欄式掃描軌跡的直線路徑，因此相較於目前存在的平滑式軌跡，我們能獲得更小的映射誤差，以達到提高掃描影像精確度之要求。其次，為了消除非線性現象並達成軌跡精確追蹤控制，本論文結合逆模型前饋遲滯補償與自適應積分終端滑模控制，它的使用可以大幅地減緩壓電平台非線性問題，使其達成軌跡精確追蹤之要求。最後，我們藉由一系列模擬與實驗來驗證所提出的軌跡與控制器之效能。

摘要(英)

In general, in order to achieve micro-/nanoscale three-dimensional scanning in high-precision measurement systems, the XY-axis scanner is used to track a pre-determined trajectory and then combine the measured height information to construct a 3D topography of the scanned sample. However, traditional raster scanning easily leads to mechanical resonance of the scanner, resulting in image distortion. Additionally, the piezoelectric stage used in measurement is subjected to nonlinear phenomena such as hysteresis and creep, leading to unexpected output displacement. Incorrect displacement will distort the scanning result, greatly and negatively affecting sample topography interpretation.
In order to effectively address the abovementioned issues, this thesis proposes a modified lemniscate trajectory that can achieve sequential scanning without needing a step function. The proposed trajectory can mitigate mechanical resonance and incorporate its smooth characteristics while retaining the linear portion of the raster trajectory to reduce unwanted mapping error. To eliminate nonlinearities and achieve high-precision tracking control, we combine inversion-based feedforward hysteresis compensation with adaptive integral terminal sliding mode control as the control system to significantly alleviate the piezoelectric stage’s nonlinear impact. Finally, the tracking performance of the proposed controller is verified through a series of simulations and experiments.

關鍵字(中)

★ 精密量測系統
★ 壓電平台
★ 修正式雙紐線軌跡
★ 滑動模態控制
★ 逆遲滯模型

關鍵字(英)

★ High-precision measurement system
★ piezoelectric stage
★ modified lemniscate trajectory
★ sliding mode control
★ inversion-based hysteresis model

論文目次

摘要 i
ABSTRACT iii
誌謝 v
Table of Content vi
List of Figures viii
List of Tables xi
Explanation of Symbols xii
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Literature Review 3
1.2.1 Selection of Scanning Trajectory 3
1.2.2 Control Methods of Piezoelectric Scanner 11
1.3 Contribution 18
1.4 Thesis Organization 19
Chapter 2 Preliminaries 21
2.1 Characteristics of Piezoelectric Actuation 21
2.1.1 Piezoelectric Effect 21
2.1.2 Hysteresis Phenomenon 22
2.1.3 Creep Effect 24
2.2 Feedforward Control 25
2.3 Sliding Mode Control (SMC) 26
Chapter 3 Modified Lemniscate Scanning Trajectory 29
3.1 Lemniscate Algorithm 29
3.1.1 Conventional Raster Scan Trajectory 29
3.1.2 Sequential Lemniscate Scan Trajectory 31
3.2 Comparison of Mapping Methods 44
Chapter 4 Controller Design 47
4.1 Scanning Trajectory of XY-axis Scanner 47
4.2 AITSMC with Inversion-Based Hysteresis Compensation 48
4.2.1 Problem Formulation 48
4.2.2 Control Algorithm 53
4.2.3 Stability Analysis 56
Chapter 5 Simulation Results 60
5.1 Simulation Setting 60
5.2 Simulation Result of Hysteresis Compensation 63
5.3 Lemniscate Trajectory Tracking Results 68
5.4 Spiral Trajectory Tracking Result 92
5.5 Triangular Wave Tracking Result 99
Chapter 6 Experimental Results 106
6.1 Experimental Setup 106
6.2 Lemniscate Trajectory Tracking Results 108
Chapter 7 Conclusions 111
Reference 112

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指導教授

吳俊緯(Jim-Wei Wu)

審核日期

2023-8-14

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