臺灣博碩士論文加值系統

在多輸入多輸出(MIMO)的多變數控制系統設計中，強健(Robust)控制系統設計已具重要性。所謂強健控制系統是指在受控體(Plant)具參數擾動或不確定性系統(Uncertainty)之強健控制器設計，強健控制問題主要在於設計控制器使補償後之系統維持穩定性，而仍能進行設計使其滿足系統需求。
此設計問題可利用迴路轉移函數回復（Loop Transfer Recovery,LTR）的觀念，以進行強健多變數控制器設計。此觀念的控制器設計方法，為線性二次高斯調制器及迴路轉移函數回復（LQG/LTR ）設計法。LQG 控制器中有兩個可以調整的的增益矩陣－狀態回授增益矩陣與Kalman Filter增益矩陣。這二個增益矩陣皆是由解二個不同的Riccati 方程式得來。而在這二個Riccati 方程式中，分別有兩個可以調整的矩陣，使得能調整二個增益矩陣。LTR步驟是利用其中一個增益矩陣來控制迴路轉移矩陣，而在另一增益矩陣使用高增益來確保受控體一端的強健性。
本論文以MIMO的飛行器系統為對象，將非線性物理結構引入模型中，並經由適當的控制器設計，讓系統能應用於高性能的機器上。飛機系統是相當複雜的控制系統。一般的方法是忽略某些特性，將系統分為數個單變數（SISO）的子系統，分別對子系統設計控制器。如此作法固然可降低控制器設計的困難度，但誤差亦隨之增大。為避免此情況，即以多變數設計的控制方式設計，先將非線性系統對不同的操作平衡點分別線性化，再依據線性化的模型利用LQG/LTR這種多變數設計法進行控制器設計，然後將設計出之控制器系統進行模擬，來討論此設計法之應用。

Robust control design is very important in the multi-variable control system design of the MIMO system. Robust control means the design under a plant with parameter stirring or uncertainty. The main problem is how to maintain the stability through compensating, and we can make it satisfy the system requirement.
We can make use of Loop Transfer Recovery(LTR) concept to design multi-variables controller. The method is combined by Linear Quadratic Gaussian (LQG) regulator and Loop Transer Recovery(LTR). LQG controller has a couple of adjustment gain matrices─state feedback gain matrix and Kalman Filter gain matrix. They are solved by two different Riccati equations. And each Riccati equation has two different adjustment matrices. The step of LTR method uses one gain matrix to control feedback loop transfer matrix, and the other high gain matrix is used to ensure the robustness of the operating plant.
The object of the thesis is to design a MIMO flying system. By proper modeling the nonlinear physics construction then go through suitable controller design, let the whole system work on the machine of high performance. Flight vehicle system is a very sophisticated control system. The conventional method usually is simplified by neglecting certain characteristic. Decompose the system into several sub-system of SISO, then designs a separate controller for each sub-system. This method is somehow easier but error augmented, In order to avoid this situation, we should design by multi-variable method. First for different operating points or equilibrium points of a nonlinear system go through linearization separately, further using the linerized model go through the LQG/LTR design methodology to design the suitable controller. Finally we simulate the design and discuss the theory behind this methodology and the application trend.

誌謝----------------------------------------------------------i
中文摘要-----------------------------------------------------ii
英文摘要-----------------------------------------------------iv
目錄---------------------------------------------------------vi
符號表-----------------------------------------------------viii
圖目錄--------------------------------------------------------x
第1章 緒論----------------------------------------------------1
第2章 基本理論------------------------------------------------3
2.1 穩定性問題-------------------------------------------3
2.2 常態性能---------------------------------------------6
2.3 強健穩定性-------------------------------------------8
2.4 迴路成型--------------------------------------------10
2.5 LQR(Linear Quadratic Regulator)理論----------------13
2.6 Kalman Filter理論----------------------------------16
2.7 LQG(Linear Quadratic Gaussian)理論-----------------18
2.8 LQG/LTR理論----------------------------------------21
第3章 系統描述-----------------------------------------------24
3.1 六自由度的飛行器模型--------------------------------24
3.2 空氣動力係數----------------------------------------28
3.3 線性化----------------------------------------------31
3.4 飛行器模型狀態表示式--------------------------------35
第4章 強健性能控制器設計-------------------------------------37
4.1 設計體模型------------------------------------------37
4.2 目標回授迴路之設計----------------------------------38
4.3 LQG/LTR 控制器設計----------------------------------41
第5章 模擬結果分析-------------------------------------------43
5.1 設計的規格描述--------------------------------------43
5.2 模擬結果--------------------------------------------44
5.3 結果分析--------------------------------------------53
第6章 結論與未來展望-----------------------------------------55
參考文獻-----------------------------------------------------57

[1] A. A. Rodriguez and M. Athans,” Multivariable Control of Twin Lift Helicopter System Using, The LQG/LTR Design Methodology,” American Control Conference, pp. 1325-1332, 1986.
[2] Athans, M.,”A Tutorial on the LQG/LTR Method,” Proc. American Control Conf., pp. 1289-1296, 1986.
[3] B. Shahian and M. Hassul,”Control system design using Matlab,” Prentice Hall, 1993.
[4] B.D.O. Anderson and J.B. More,”Linear Optimal Control,” Prentice Hall, 1990.
[5] Blakelock, John H.,”Automatic control of aircraft and missiles,” Wiley, 1991.
[6] Brian L. Stevens and Frank L. Lewis,”Aircraft Control and Simulation,” Wiley , 1992.
[7] Burl. Jeffrey B.,” Linear optimal control,” Addison Wesley Longman., 1999.
[8] Ching-Fang Lin,” Advanced Control Systems Design,” Prentice Hall, 1990.
[9] Collinson, R. P. G.,”Introduction to avionics,” Chapman & Hall, 1996.
[10] G. Stein, M. Athans.,”The LQG/LTR procedure for multivariable feedback control design, IEEE conference on decision and control, Honolulu, pp.1835-1840, 1990.
[11] Gibson, John E.,”Nonlinear automatic Control,” McGraw Hill, 1963.
[12] H. Kwakernaak and R. Sivan.,”Linear Optimal Control Systems,” Wiley Interscience, 1972.
[13] Hedrick J. K. and Gopalswamy S.,” Nonlinear Flight Control Design via Sliding Methods,” Journal of Guidance, Vo1. 13, pp.850-858, 1990.
[14] Huang J.,Lin C.G., Cloutier J.R., Evers J.H. and D’ Souza C.,” Robust Feedback Linearization Approach to Autopilot Design,” IEEE Conference Control Application, Vo1.1,pp.220-225, 1992.
[15] J. Cloutier and J. Evers,”Missile Autopilot Design Using a Generalized Hamiltonian Formulation,” Proceedings of the first IEEE Conference on Aerospace Control System, pp. 715-723, 1993.
[16] J. M. Maciejowski,”Multivariable Feedback Design,” Addison Wesley, 1989.
[17] John C. Doyle,”Essentials of Robust Control,” Prentice HALL , 1998.
[18] Jose Ragot, Didier Maquin, Adiallah KONDO,” Control design for loop transfer recovery,” IEEE Trans,pp.2653-2657 , 1994.
[19] Kailath, T.,”Linear Systems,” Prentice Hall, Englewood Cliffs, N.J., 1980.
[20] Kazerooni, H. etal.,”An Approach to Loop Transfer Recovery Using Eigenstructure Assignment,” Proc. A.C.C., 1985.
[21] Khalil H.K.,”Nonlinear Systems,” Prentice Hall, 1996.
[22] Krstic, Miroslav,”Nonlinear and Adaptive Control Design,” Wiley, 1995.
[23] L. L. Frank,”Applied Optimal Control and Estimation,” Prentice Hall , 1992.
[24] M. Tadjine, A. Tayebi, and A. Rachid,” On robust LQG/LTR control design,” IEEE Trans, pp.4772-4773, 1996.
[26] M. Vidyasagar,”Nonlinear Systems Analysis,” Prentice Hall, 1993.
[27] Perkins, C. D., and R. E. Hage,”Airplane Performance Stability and Control,” Wiley, 1949.
[28] Richard J. Vaccaro,”Digital Control A State-Space Approach,” McGraw Hill, 1995.
[29] Ridegly D.B. et.al.,”Linear-Quadratic-Gaussian with Loop-Transfer-Recovery Methodology for Unmanned Aircraft,” J. Guidance, pp. 82-89, Jan.-Feb. 1987.
[30] Slotine J-J.E. and Li W.,”Applied Nonlinear Control,” Prentice Hall, 1991.
[31] Xu Gang and Cao Guangzhong,” On the LQG and LQG/LTR Methodology,” IEEE Trans, pp.210-213, 2000.