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研究生： 陳重光
Chen, Chung-Kuang
論文名稱： 不確定系統之QFT/H∞控制器設計
Design of QFT/H∞ Composite Controller for Uncertain Systems
指導教授： 黃正能
Huang, Cheng-Neng
學位類別： 碩士
Master
系所名稱： 工學院 - 系統及船舶機電工程學系
Department of Systems and Naval Mechatronic Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 英文
論文頁數： 100
中文關鍵詞： H∞控制理論 、Popov穩定性準則 、量化回授理論
外文關鍵詞： H∞ control theory, Popov stability criterion, Quantitative Feedback Theory (QFT)
相關次數： 點閱：138  下載：12 
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    • 數學模型化之複雜受控系統，具有因外部干擾而造成的參數不確定性，其不僅導致了控制性能低落，更可能造成系統不穩定的情形發生。為此，本文結合量化回授理論(Quantitative Feedback Theory; QFT)來選取H∞控制問題之權重函數，以確保系統在不確定項干擾下，仍可維持穩定，以提高控制器的強健性並達成所預設之指標。
    在本文中，首先將落後領先補償器及伺服補償器擴增至受控系統，以使得預設性能可以被滿足，並達到完美追蹤的目標。進一步以QFT選取H∞綜合控制器的權重函數。過程係將參數不確定之受控系統於頻域中進行分析，以求得上述所需之權重函數，並擴增此系統為H∞標準控制問題，以求取H∞最佳控制增益。如此得以抑制外界輸入(其包含系統干擾及量測雜訊)所造成的不良影響，同時壓縮控制能量到最低，從而提升系統強健性，以獲得最佳的控制效果。此外，尚未消除的非線性及不確定項，本研究則透過Popov穩定性準則進行驗證，確保系統可達強健穩定。
    最後，本文針對含不確定項的數個系統進行電腦模擬，結果顯示該綜合控制器皆有良好之追蹤效果。在系統不確定參數和外部干擾下皆可保有其強健性，且預設性能皆可被滿足。

    For the complicated systems, the plant parameter uncertainties and external disturbances will lead to unfavorable performance or system instability. For this reason, the Quantitative Feedback Theory (QFT) is explored in this research to offer optimal weighting functions to the standard H∞ control problem so that the system robustness and performance can be maintained.
    The lag-lead compensator and the servo-compensator will first be formulated into the system so that the desired specifications and perfect tracking can be achieved by adjusting the control parameters in the lag-lead control component. Furthermore, the weighting functions, which ensure the closed-loop stability under plant uncertainties, are then augmented to the system to form the standard H∞ control problem in order to get the H∞ optimal control gains. To select weighting functions, the sensitivity function S(s) and the complementary function T_1 (s) under plant parameter variation are analyzed in the frequency spectrum such that the satisfaction of the set of inequalities proposed in this research will guarantee the system robustness. Moreover, the optimal H∞ controller will eliminate the harmful influence of the exogenous inputs (i.e., disturbances and noises) on the controlled outputs (i.e., tracking errors and the control energy) so as to improve the robustness and tracking performance of the system. As for the uncancelled nonlinearities and uncertainties in the plant, the Popov stability criterion is then utilized to ensure the closed-loop stability.
    Finally, two examples with uncertainties are simulated to illustrate the achievement of tracking performance of the systems. The computer simulation results show that these systems can meet their desired specifications even though these systems encounter external disturbances and parameter uncertainties.

    摘要 I Abstract II 致謝 IV Contents V List of Tables VIII List of Figures VIII Chapter 1: Introduction 1 1.1 Motivation 1 1.2 Literature Reviews 1 1.3 Thesis Outline 3 Chapter 2: H_∞ Control System 4 2.1 Control Theory 4 2.2 Norm and Singular value 4 2.2.1 Definition of norm 4 2.2.2 The norms of a signal 5 2.2.3 The norms of a system 6 2.2.4 The norms of a transfer function 6 2.3 Loop Shaping 9 2.3.1 Sensitivity matrix S(s) 9 2.3.2 Power transfer matrix R(s) 10 2.3.3 Complementary function matrix T(s) 11 2.4 Augmented system matrix 14 2.5 H_∞ state feedback controller 16 2.5.1 State-Space Method 17 2.5.2 Variational Approach 20 Chapter 3: QFT and Nonlinear Stability Criterion 24 3.1 Quantitative Feedback Theory; QFT 24 3.2 Transformation of specifications 25 3.2.1 Percentage overshoot 25 3.2.2 Rise time 25 3.2.3 Settling time 26 3.2.4 The prototype 2nd order closed-loop system 26 3.3 Example for preceding QFT design procedure 27 3.4 Nonlinear stability criterion 31 3.4.1 Lur’e type system 31 3.4.2 Circle criterion 33 3.4.3 Popov criterion 37 Chapter 4: Design of QFT/H_∞ Composite Controller 41 4.1 Description of system 41 4.2 Controller structure 41 4.3 Design of Lag-Lead Compensator P_l (s) 42 4.3.1 Design procedure of lead compensator P_1 (s) 42 4.3.2 Design procedure of lag compensator P_2 (s) 43 4.3.3 Lag-lead compensator P_l (s) 44 4.4 Design of Servo-Compensator S_c (s) 44 4.4.1 Servo-compensator for a SISO case 45 4.4.2 Servo-compensator for a MIMO case 45 4.5 The composite QFT/H_∞ controller 46 4.5.1 Select of sensitivity weighting function W_S (s) 47 4.5.2 Select of weighting function W_U (s) 48 4.5.3 Select of weighting function W_T (s) 49 4.5.4 Weighting function in Controllable Canonical Form (CCF) 52 4.5.5 The augmented system 53 4.6 Popov criterion for Lur’e type system 57 Chapter 5: Computer Simulation 64 5.1 Case1: A type1 system with uncertainties 64 5.1.1 Phase1: P_l=1 67 5.1.2 Phse2: Adjust P_l 76 5.1.3 Results 81 5.2 Case2: Unmanned Underwater Vehicles 85 5.2.1 Design the controller 88 5.2.2 Results 92 Chapter 6: Conclusion 97 References 98

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