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系統識別號 U0002-2401200723144800
中文論文名稱 正多項式方法之低階控制器設計: 縱向自動駕駛設計
英文論文名稱 Low Order Controller Design via Positive Polynomials: A Longitudinal Auto-Pilot Design
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 95
學期 1
出版年 96
研究生中文姓名 吳振炘
研究生英文姓名 Chen-Hsin Wu
學號 693370834
學位類別 碩士
語文別 英文
口試日期 2006-12-28
論文頁數 46頁
口試委員 指導教授-蕭照焜
委員-葉哲勝
委員-馬德明
委員-蕭照焜
中文關鍵字 正多項式  低階控制器 
英文關鍵字 LMI region  fix-order control  pole-clustering 
學科別分類 學科別應用科學航空太空
中文摘要 本論文討論以矩陣型式表示多樣的複數平面圖形區域,以及正多項的低階控制器設計。本文中所討論穩定區域的圖形包含一維度、二維度以及多維度的組合圖形如:平移平面、圓形、橢圓、拋物線及其任意組成之區域圖形。在多項式方法的控制器設計中,我們以設定的區域為閉迴路極點放置的目標,並給定我們所想要的控制器階數以求解一組符合的控制器。最後我們以淡江大學航太系UAV實驗室所設計的無人飛行載具為例,做縱向運動之高度及姿態保持控制設計。
英文摘要 This thesis discusses the matrix representations of various complex stability regions and the designs of fixed-order controllers using positive polynomials. Stability regions presented in this thesis include one dimensional, two dimensional and their combinations. Regions such as shifted half plane, circle, ellipse, parabola, and union of regions are narrated and collated. A stabilizing control problem with low-order controller to satisfy additional constraints on the closed-loop pole location is explored in the thesis. A H-infinity control problem using positive polynomial concepts is also investigated. The longitudinal auto-pilot designs for a low-speed uninhabited experimental aircraft are presented to illustrate the fixed-order controller design using positive polynomials.
論文目次 Contents
List of Figures v
List of Tables vii
Chapter 1 Introduction 1
I. Norm 2
II. Kroncker product 3
III. Lyapunov stability for Linear system 4
Chapter 2 Stability region 6
I. Normal asymptotic stable 7
II. Circle region 8
III. Parabola region 9
IV. Elliptical region 11
V. Union region 12
VI. Rotated and shifted region 14
Chapter 3 Stabilizing controller 16
I. Stabilizing problem formulation 17
II. Numerical Example 21
Chapter 4 H-inifity controller 26
I. H-infinity problem formulation 26
II. Numerical Example 29
Chapter 5 Illustration 33
Chapter 6 Conclusion 44
Reference 45
List of Figures
Figure 1.1 H-inifity block diagram 3
Figure 2.1 Unit feedback diagram 7
Figure 2.2 Left half plane region 8
Figure 2.3 Circle centered on origin 8
Figure 2.4 Circle centered on (-5,0) 9
Figure 2.5 Parabolic region 10
Figure 2.6 Fat ellipse 11
Figure 2.7 Tall ellipse 12
Figure 2.8 Union region composed of circle and ellipse 13
Figure 2.9 Union region composed of circle and parabola 13
Figure 2.10 Union region composed of circles 14
Figure 2.11 Rotated ellipsoid 15
Figure 3.1 D-Region 23
Figure 3.2 Step response of feedback system. 24
Figure 3.3 Pole-zero map of the feedback system 24
Figure 4.1 control model 26
Figure 4.2 in bode plot 27
Figure 4.3 Unit feedback diagram 30
Figure 4.4 Initial design closed-loop step response 30
Figure 4.5 Closed-loop step response (a zero added) 31
Figure 4.6 Closed-loop step response(root-locus initial guess) 32
Figure 4.7 Closed-loop step response (redesigned) 32
Figure 5.1 Experimental aircraft developed by Tamkang University 33
Figure 5.2 Dynamic of the wing 34
Figure 5.3 Unit feedback diagram 36
Figure 5.4 Response without controller 36
Figure 5.5 Closed-loop with initial controller 37
Figure 5.6 Closed-loop with redesigned controller 37
Figure 5.7 Simulink of plant 38
Figure 5.8 Elevator input 38
Figure 5.9 Height of aircraft 39
Figure 5.10 Response of pitch angle 39
Figure 5.11 Response of angle of attack 40
Figure 5.12 Pitch hold 40
Figure 5.13 Unit feedback diagram 41
Figure 5.14 Initial step response 41
Figure 5.15 step response 42
Figure 5.16 Initial step response 43
Figure 5.17 step response 43
List of Tables
Table 5.1 Aero dynamic parameters 35



參考文獻 [1] D. Henrion, M. Sebek, “New robust control functions for the polynomial toolbox 3.0” LAAS-CNRS Research Report No. 02493, October 2002.
[2] D. Henrion, M. Sebek, V. Kucera, “Positive polynomials and robust stabilizing with fix-order controllers” IEEE Transactions on Automatic Control, 2003
[3] M. Chilali and P. Gahinet, ” design with pole placement constraints: An LMI Approach” IEEE Transactions on Automatic Control, Vol.41, No.3, pp. 358-367, 1996.
[4] D. Henrion, O. Bachelier, M. Sebek, “ -stability of polynomial matrices” LAAS-CNRS Research Report No. 99180
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[8] J.-K. Shiau, Chun-Yuan Huang, “An auto-pilot design for the longitudinal dynamics of a low-speed experimental aircraft using two-time-scale cascade decomposition”
[9] D. Peaucelle, D. Arzelier, O. Bachelier, J, Bernussou, A new robust -stablility condition for real convex polytopic uncertainty. System & control Letters 40 (2000) 21-30.
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[11] Yeong-Hwa Chang, Yuan-Yuan Wang, Min-Hsiung Hung and Pang-Chia Chen, “Regional stabilizing and control with actuator saturation using linear matrix inequalities” Journal of C.C.I.T, Vol33, No2, May, 2005.
[12] L. Lee and J.L. Chen, “Robust admissibility analysis and design for uncertain continuous descriptor systems: an LMI approach” Proceedings of 2003 ROC Automatic Control Conference, pp. 1285-1290, Mar. 2003.
[13] S. G. Wang, S. Lin, L. Shieh and J. Sunkel, “Observer-Based Controller for Robust Pole Clustering in a Vertical Strip and Disturbance Rejection in Structured Uncertain Systems” Int. J. Robust & Nonlinear Control, Vol.8, No.5, pp. 1073-1084, 1998.
[14] C. H. Kuo and L. Lee, Robust, “ -admissibility in Generalized LMI Regions for Descriptor Systems” Proceedings of the 5th Asian Control Conference, pp. 1057-1064, Jul. 2004.
[15] Yongji Wang, M. Schinkel, Tilmann Schmitt-Hartmann and Ken J.Hunt, “Pid and pid-like controller design by pole assignment within D-stable regions” Submitted to special issue of Asian Journal of control, 2001-08-24
[16] Chun-Yuan Huang, “Analysis and Design of Aircraft Longitudinal Dynamic Control Using Two-Time-Scale Cascade Decomposition” Graduate Institude of Aerospace Engineering, Tamkang University.
[17] Tsung-Li Chuang, “Coprime factors, linear matrix inequalities, and low-order controller design” Graduate Institude of Aerospace Engineering, Tamkang University.
[18] J.-K. Shiau and C.-A. Tzeng, “An H∞ Low-Order Controller Design using Coprime Factors and Linear Matrix Inequality Techniques” (366) Intelligent Systems and Control - 2002
[19] Kemin Zhou, “Essentials of robust control” 1998 by Prentice-Hall Inc.
[20] Fang-Bo Yeh, Ciann-Dong Yang, “Post modern controller theory and design” Chinese edition 1992
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