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研究生：	楊復云 Yang, Fu-Yun
論文名稱：	鏈散射描述法求解控制器及雙自由度控制系統之強健設計 Chain-Scattering Description Approach to Control Synthesis and Robust Design of 2DOF Control Systems
指導教授：	蔡明祺 Tsai, Mi-Ching
學位類別：	博士 Doctor
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	131
中文關鍵詞：	H2控制、鏈散射式描述、動態剛性、同動控制
外文關鍵詞：	H2 control, chain-scattering description, dynamic stiffness, synchronous control
相關次數：	點閱：71 下載：7
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本論文基於鏈散射式描述(chain-scattering description, CSD)求解標準穩定及H2最佳化控制問題。該方法早期被用以求解標準H∞ 問題: 以兩組耦合之鏈散射矩陣配合其J-lossless性質，求出所有滿足成本函數之控制器集合。本研究進一步將此解題架構延伸至求解所有穩定控制器問題以及H2控制問題，整合提出一可同時處理上述三種控制問題之統一解法。在所提出之解題架構下，上述三種控制問題均可以一致化的數學結構加以描述，並只需視問題種類加以限制各鏈散射矩陣之條件，即可合成出滿足不同目標之控制器集合。利用該方法求解控制器合成的好處為過程簡潔且易懂，配合耦合鏈散射矩陣的圖形說明，提供工程背景的設計者能快速理解並應用於不同設計所需的控制器架構。
在實務應用之設計考量上，本文基於以外擾估測器概念為主的雙自由度控制器，提出混合型雙自由度控制器設計架構。該架構結合了不同的雙自由度控制器的優點，可同時達到高動態剛性以及高強健性能之優點。並以一伺服馬達為例，說明所提出架構之特性以及其設計流程。另一方面，本研究也將外擾估測器的設計概念與同動控制結合，提出一基於多輸入多輸出系統模型的解偶同動架構。實驗結果顯示，所提出之架構可有效降低系統的雙軸同動誤差，驗證了本設計之可行性及實用性。

This research utilizes the coupled chain-scattering description (CSD) framework to solve both the stabilization and H2 problems. This approach was first investigated for solving the standard H∞ problem, in which the sophisticated mathematics involved inH∞ synthesis can be easily comprehended via constructing two CSD matrices and successive J-lossless coprime factorizations. This research extends the framework to solve the stabilization problem, H2 problem, and the special standard control configuration (SCC) plants. For different constraints on the CSD matrices of each problem, this approach is then said to be a general controller synthesis method. A significant contribution of this method is its transparency and intuitive nature, which provides a systematic control theory and allows practicing control engineers to learn this approach more easily and apply it to advanced control systems. Related graphic network representations are also presented to help explain the entire concept, which will benefit engineering readers.
With respect to practical designs, a mixed type of 2DOF scheme is proposed which integrates the advantages of different frameworks. This structure can stipulate the design specifications while satisfying dynamic stiffness, and permits intuitive and independent tuning of disturbance rejection as well as tracking performance. Experimental results obtained from an illustrated servo control system are given to demonstrate the effectiveness and feasibility of the proposed control structure and design methodology. Furthermore, the concept of 2DOF design is combined with synchronous motion control. The experimental results demonstrate that the synchronous error can be significantly reduced by the proposed framework.

Introduction 	                                          1
1 Background ...........................................3
2 Contribution and organization of this dissertation...	6

Preliminaries of Chain Scattering Description    	8
1 Preliminaries.........................................8
1.1 State-space realizations............................8
1.2 Inner and co-inner systems..........................9
1.3 J-lossless and dual J-lossless systems..............10
1.4 Coprime factorization over RH-infinity..............10
1.5 Normalized coprime factorization...................	12
1.6 Algebraic Riccati Equation..........................12
1.7 State-space formulae for Normalized Coprime Factorization.............................................14
2 Linear fractional transformations and chain scattering-matrix description........................................16
2.1 Definitions and operations..........................16
2.2 Cascaded connection of two CSD matrices.............17
2.3 Transformation between LFT and two CSDs.............22
2.4 State-space formulae between CSD-matrix and LFT-matrix....................................................23

CSD Approach to Control Synthesis	                27
1 Characterization of all Stabilizing Controllers......28
1.1 Method I:Using a right CSD coupled with a left CSD.28
1.2 Method II:Using a left CSD coupled with a right CSD.30
1.3 State-Space Formulae of Stabilizing Controllers.....32
1.4 Stabilization of Special SCC Formulations...........38
2 Optimal H2 Controller.................................41
2.1 Method I:Using a right CSD coupled with a left CSD.	42
2.2 Method II:Using a left CSD coupled with a right CSD.46
3 H-infinity Controller.................................47
3.1 H-infinity control problem..........................47
3.2 Method I:Using a right CSD coupled with a left CSD.49
3.3 Method II:Using a left CSD coupled with a right CSD.50
3.4 State-Space Formulae of H-infinity Controllers......53
3.5  H-inginity Solution of Special SCC Formulations....60
4 Example of LQR controller-the state feedback control problem...................................................62
5 Summary...............................................64

Two-Degree-of-Freedom Controllers	                65
1 Two-degree-of-freedom controllers.....................65
1.1 Two-degree-of-freedom controller with DOB...........68
1.2 Two-degree-of-freedom controller with MBDA..........68
1.3 Reference feedforward two-degree-of-freedom (RFF-2DOF) controller..........................................69
1.4 Model-based RFF- 2DOF (MRFF) Controller.............70
2 Framework of mixed two-loop 2DOF controller...........72

Design of the Mixed 2DOF Controller	                77
1 System Configuration..................................77
2 Design procedure......................................79
3 Performance evaluations...............................84
4 Summary...............................................89

Synchronous Decoupled Motion Control for Power-Wheelchairs	                                                 90
1 Synchronous Controller................................90
2 Synchronous Controller Design via DOB.................93
3 Modeling of the wheelchair............................95
4 Experimental Results..................................98
5 Summary..............................................100

Conclusions	                                        101
1 Summary..............................................101
2 Suggestions for further research.....................102

Reference	                                        104

Appendix A. State-space solutions for stabilizing/H2 controller of special SCC formulations	               111
Appendix B. State-space solutions for H∞ controller of special SCC formulations	                                121


                                    

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