臺灣博碩士論文加值系統

本論文主要為創新一個狀態補償反覆學習控制（SCILC）法則，應用於一個壓電致動器循跡追蹤控制系統，其間進行相關理論探討和控制器設計規劃，以期達到最佳循跡追蹤效能，研究過程並進行一系列該系統測試，以為創新理論與實作之驗證。本論文所提出SCILC控制器，具有二個主要特色：狀態補償和誤差濾波。狀態補償機制融入反覆學習控制（ILC）法則，為本研究針對非線性系統控制一項新穎的設計。狀態補償主要針對連續二次ILC學習週期之系統狀態變動先行補償，藉由預先補償系統狀態變動，輔助SCILC控制器精準地進行學習控制機能。同時，本研究將誤差濾波技巧融入ILC控制法則，其濾波功能可免除ILC反覆學習過程中雜訊累積，得以確保追蹤誤差穩定收斂至最小極限。
本研究首先介紹基本連續時域ILC控制法則和其收斂分析，其後提出一泛用型離散時域回授輔助反覆學習控制（FB-ILC）法則，並完成FB-ILC控制法則收斂分析之理論證明。由於SCILC控制法則可視為FB-ILC控制法則的一個特例，FB-ILC的收斂分析結果佐證SCILC控制法則收斂特性之理論基礎。
本研究進一步於頻域對ILC控制法則進行收斂分析，因此提出創新ILC收斂頻寬理論公式，並針對主要ILC濾波器進行深入探討。其後，本研究採用訊號分析技術Wigner-Ville distribution (WVD)，對ILC系統追蹤誤差之頻譜特性進行分析探討。緣是，本研究提出一嶄新ILC濾波器設計法，運用追蹤誤差的WVD分析和ILC系統的收斂頻寬分析，得以設計適當ILC濾波器和ILC控制器而提升循跡追蹤效能。
綜言之，本研究根據基本理論基礎與創新方法設計SCILC控制器與相關ILC濾波器，並將SCILC控制器和傳統ILC控制器實作應用於壓電致動器循跡追蹤而進行性能比對。實驗結果顯示，在任採同一種濾波器條件下，SCILC控制器追蹤性能都顯著優於傳統ILC控制器。本研究對SCILC控制器進行一系列廣泛深入實作驗證，針對壓電致動器位移軌跡，調變動其設定軌跡頻率和振幅，後由SCILC控制器進行追蹤控制。實驗證明，SCILC控制器在任採一種濾波器情況下，追蹤各種不同頻率和振幅的軌跡，皆具有極佳且相似的追蹤結果。綜上結論，本論文確認所創新SCILC控制法則具有優異反覆學習控制性能，本論文對ILC理論研究與非線性系統應用都著有貢獻。

This dissertation presents a research on trajectory tracking of a piezoelectric actuator using a state compensated iterative learning control (SCILC) scheme. The SCILC scheme has two main features: a novel design of state compensation for iterative learning control (ILC), and an enhancement of ILC using error filtering. In the SCILC scheme, a state compensation is designed to compensate for the change in states from one iteration to the next. Due to the state compensation, the SCILC scheme can yield more precise tracking control in comparison to conventional ILC schemes. The adoption of error filtering in the SCILC scheme is intended to prevent noise accumulation in iterative learning and ensure long-term stability in executing the scheme. In this dissertation, a fundamental ILC theory is introduced and a general feedback assisted ILC (FB-ILC) scheme is presented. Convergence analysis of the FB-ILC scheme is uniquely performed, and thus convergency of the SCILC scheme is established accordingly. In-depth studies into ILC error filtering are undertaken. Convergence bandwidth of an ILC system is novelly addressed. Essential ILC filters are discussed extensively. Analysis of ILC tracking errors using the Wigner-Ville distribution (WVD) is introduced. A methodology for ILC filter design is proposed by utilizing the WVD and the convergence bandwidth analyses associated with an ILC system. SCILC controllers using essential filters are designed and applied to a tracking task with extensive tracking experiments on a piezoelectric actuator. Results of the extensive experiments confirm the efficacy and robustness of the innovative SCILC scheme in tracking control of the piezoelectric actuator.

Abstract
Table of Contents
List of Figures
Nomenclature
Chapter 1 Introduction
1.1 Motivation and Related Researches
1.2 Overview of Iterative Learning Control
1.3 Contributions of the Dissertation
1.4 Organization of the Dissertation
Chapter 2 Basic Iterative Learning Control
2.1 D-Type Iterative Learning Control
2.2 Convergence Analysis for Linear Systems
2.3 Convergence Analysis for Nonlinear Systems
2.4 Summary
Chapter 3 Feedback Assisted Iterative Learning Control
3.1 High-Order Feedback Assisted Iterative Learning Control
3.2 Problem Formulation
3.3 Convergence Analysis
3.4 First-Order Feedback Assisted Iterative Learning Control
3.5 State Compensated Iterative Learning Control
3.6 Summary
Chapter 4 Iterative Learning Control with Error Filtering
4.1 Convergence Bandwidth of ILC with Error Filtering
4.2 ILC with FIR Filtering
4.3 ILC with Wavelet Transform Filtering
4.4 ILC with B-Spline Network Filtering
4.5 Wigner-Ville Distribution of Tracking Errors
4.6 ILC Filter Design
4.7 Summary
Chapter 5 Tracking Experiments of a Piezoelectric Actuator Using Iterative Learning Control
5.1 Experimental Setup
5.2 Iterative Learning Controller Design
5.2.1 Design of Learning Operators
5.2.2 Wigner-Ville Distribution
5.2.3 FIR Filter Design
5.2.4 Wavelet Transform Filter Design
5.2.5 B-Spline Network Filter Design
5.3 Tracking Experiments Using ILC with FIR Filtering 5.4 Tracking Experiments Using ILC with Wavelet Transform Filtering
5.5 Tracking Experiments Using ILC with B-Spline Network Filtering
5.6 Summary
Chapter 6 Conclusions
References
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