雙驅動系統之線性二次追跡結合路徑規劃控制器設計｜國立臺灣科技大學博碩士論文系統

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研究生：	周雅貞 Ya-Zhen Zhou
論文名稱：	雙驅動系統之線性二次追跡結合路徑規劃控制器設計 Linear Quadratic Tracking Controller with Path Planning Design for Dual Stage Actuator system
指導教授：	張以全 I-Tsyuen Chang
口試委員:	梁國淦 Kuo-Kan Liang 林紀穎 Chi-Ying Lin
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	91
中文關鍵詞：	雙驅動系統、最佳控制、線性二次追跡、路徑規劃、飽和問題
外文關鍵詞：	DSA system, Optimal control, LQT, Path Planning design, Saturation problem
相關次數：	點閱：388 下載：3
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上一筆

本文主要探討雙驅動系統的線性二次追跡(Linear Quadratic Tracking)結合路徑規劃(Path Planning)的控制器設計，使其達到長行程高精度的定位需求並且避免飽和問題的產生。本文首先推導雙驅動系統(Dual-Stage Actuator system)之數學模型，接著將本文之數學模型以Smith-McMillan Form表示，並討論雙驅動系統之特性。根據所討論之模型，利用最佳控制方法中之線性二次追跡，使雙驅動系統達到期望之點到點(Point to Point)追蹤軌跡。然而雙驅動系統之間的耦合問題及其不同響應特性可能會造成其產生飽和問題(Saturation problem)，故本文利用路徑規劃設計，以限制雙驅動器間之最大相對距離，由此，可同時達到追跡之需求並且避免飽和問題之產生。本文以模擬結果驗證所提出之控制器設計方法的有效性，並且提供結論與討論未來研究之方向。

This thesis mainly discusses the controller design of Linear Quadratic Tracking (LQT) and the path planning for a Dual Stage Actuator (DSA) system. With the proposed method, it allows the DSA system to achieve long stroke precision positioning. Besides, it prevents the saturation problem. First, the mathematical model derivation of the DSA system is presented. Next, apply the Smith-McMillan form on the DSA model to analyze the characteristics of the DSA system. After that, according to the analyzed DSA system model, design the LQT state feedback controller to track the point to point reference trajectory. However, the couple effect and the different characteristics between the two actuators may cause the saturation problem. Therefore, this thesis applies the path planning design to restrict the relative distance between the two actuators. With the proposed method, the trajectory tracking and the prevention of the saturation problem can be achieved simultaneously.This thesis proves the proposed method with the simulation results, and provides the conclusions and the future works.

Abstract in Chinese.................................. I
Abstract in English .................................. II Acknowledgements.................................. III Contents........................................ IV
List of Figures..................................... VII
List of Tables ..................................... XI
List of abbreviation .................................. XII
Introduction.................................... 1
1 Introduction to Dual Stage Actuator .................... 1
2 Background................................. 3
3 Literature Review.............................. 5
4 Optimal control............................... 10
4.1 Cost Function............................ 11
4.2 Positive Definite (PD) and Positive Semi-definite (PSD) . . . . . 12
4.3 Hamiltonian............................. 13
4.4 Boundary Conditions for Different System . . . . . . . . . . . . 14
4.5 Backstepping............................ 15
4.6 Linear Quadratic Regulator (LQR)................. 16
4.7 Linear Quadratic Tracking (LQT) ................. 18
DSA System Modeling .............................. 21
1 Mathematical Model Derivation ...................... 21
2 The Explanation of Transfer Functions................... 25
3 DSA Parameter Analysis .......................... 26
4 Poles and Zeros of DSA Model....................... 31
Feedback Controller Design............................ 35
1 Feedback Control Scheme of DSA System................. 35
2 Linear Quadratic Tracking Feedback controller . . . . . . . . . . . . . . 36
2.1 Hamiltonian............................. 37
2.2 Open-Loop Optimal Control, State System and Co-State System . 37
2.3 Boundary Condition ........................ 39
2.4 Riccati Equation and Vector Equation . . . . . . . . . . . . . . . 39
2.5 Closed-Loop Optimal control and Optimal State . . . . . . . . . 41
3 Reference Path Planning .......................... 41
Simulation Results................................. 43
1 Parameters of DSA System......................... 43
2 Parameters of LQT Feedback Controller.................. 44
3 LQT Feedback controller Without Path Planning Design . . . . . . . . . 45
4 LQT Feedback controller With Path Planning Design . . . . . . . . . . . 50
5 A Different Original Reference trajectory for LQT Feedback controller Without Path Planning Design ....................... 53
6 A Different Original Reference for LQT Feedback controller With Path Planning Design............................... 58
7 Stability of LQT Feedback Controller ................... 61
Conclusion and Future Work ........................... 63
1 Conclusion ................................. 63
2 Future Work................................. 64 References....................................... 65
Appendix A:DSA Model s-domain Derivation ................... 68
Appendix B:DSA Model State Space Form Derivation . . . . . . . . . . . . . . . 71 Appendix C:Smith-McMillan Form ......................... 73
                                

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