在本篇研究中，本文針對具有結構化不確定的多輸入多輸出線性非時變系統，設計μ-H∞控制器，讓系統足以應付非結構化及結構化的不確定項。為了使μ-H∞控制器可達預定之性能規格，本文發展了一套 μ-H∞/LTR的設計程序，透過設定之權重函數，使系統的靈敏度矩陣、互補靈敏度矩陣及控制能量矩陣之奇異值具有良好的形狀，以達到預設系統性能之設定；使閉迴路系統擁有良好的強健性、追蹤性能及排除雜訊的能力，本研究使用 H∞/LTR的設計概念來推導μ-H∞/LTR理論。並使用能排除正交性假設之H∞控制器，使所設計的控制器更能廣泛地應用在各種系統上。接著，利用H∞控制理論來壓縮µ值，以快速求得μ-H∞控制器，最後，對於系統之狀態迴授作迴路整型，並對系統之輸出迴授作迴路函數回復，透過一連串的設計步驟使得輸出迴授控制器回復到設定的目標迴路，使系統的性能可以滿足預設的設計規格，以達到性能強健的目的。電腦模擬結果顯示，本文所設計之μ-H∞/LTR控制器，確定能在具有不確定之系統中，達到預設之系統性能。

　　This research focuses on designing an μ-H∞ controller for multi-input multi-output linear time-invariant systems with structured or unstructured uncertainties. In order to achieve the prescribed performance specifications of a system, the loop transfer recovery (LTR) technique is used and then the μ-H∞/LTR design methodology is developed in this research. By adjusting the weighting matrices of the control problem, the sensitivity, complementary and the power-transfer function matrices of the system can be shaped well so that the system performance may easily achieved under the presence of uncertainties or disturbances. To meet the prescribed specifications, the singular value plot of the open loop transfer function matrix is loop-shaped to match the target loop so as to achieve the desired performance and then the LTR technique is used to ensure that the performances are able to be guaranteed for the output-feedback cases. Computer simulation results recall that the system performance can be achieved by using the proposed μ-H∞/LTR control methodology even in the presence of system uncertainties and disturbances.

【1】Dahleh, M., and Doyle, J.C., “Overview of robust stability and performance methods of systems with structured mixed perturbations,” Proceedings of the 31st IEEE Conference, vol.4, pp. 3158 -3162, 1992.
【2】Doyle, J.C., “Analysis of Feedback System with Structured Uncertainty,” proceedings of IEE, part D,vol.129,pp.242-250,1982.
【3】Doyle, J.C., “Structured Uncertainty in Control System Design,” proc. IEEE conf., Fort Lauderdale, vol.3, pp.160-265, 1985.
【4】Doyle, J.C., and Gunter, S., “Robustness with Observers,” IEEE Transaction on Automatic Control, Vol.24, No. 4, pp.607-611, 1979.
【5】Doyle, J.C., and Packard, A., and Zhou, K., “Review of LFTs, LMIs, and ,’’ Proceedings of the 29th IEEE Conference on Dscision and Control, vol.2, pp.1227-1232, 1992.
【6】Glover, J., and Sefton, D.C., “A Tutorial on Loop Shaping using
Robust Stabilization,” Transaction of the institute of Measurement and Control, vol.12, No.2, pp.157-168, 1992.
【7】Hwang, C.N., “Formulation of and Optimal Control Problems-A Variational Approach,” Journal of the Chinese institute of engineerings, vol. 16, No. 6, pp.853-866, 1993.
【8】Kwakernaak, H., and Sivan, R., “Linear optimal control systems,” John Wiley & Sons,1972.
【9】Limebeer, D.J., “Linear Robust Control,” Prentice Hall, Paramount Communications Company, 1995.
【10】Maciejowski, J.M.., “Multivariable Feedback Design,” Addison
Wesley Book Store ,1989.
【11】Rawson, J.L., Yeh, H.H. and Hsu, C.H., “ /LTR: A loop shaping method for output feedback problem compensator design,” Proceedings of American Control Conf.., vol20, pp.2196-2201 ,1991.
【12】Stevens, B.L., and Frank, L. Lewis, “Aircraft control and simulation
,’’ John Wiley & Sons ,1992.
【13】Stein, G., and Athans, M., “ The LQG/LTR Procedure for
Multivariable Feedback Control Design ,”IEEE trans. Aut. Control , vol Ac-32, pp. 105-114 ,1987.
【14】Stoustrup, J., and Niemann, H. H., “Loop Transfer Recovery with an
Optimality Criterion,” Proceedings of American Control ,vol.5, pp2196-2201,1991.
【15】Zhou, K., and Doyle J.C., “Essentials of Robust Control,” Prentice
Hall ,1998.
【16】黃正能，陳冠良，"狀態空間 -控制器之迴路整型及其在船
上的應用"，國立成功大學造船暨船舶機械工程研究所碩士論文， 1997。
【17】黃正能，羅章才，"模基 -控制補償器之設計及其在船上的應用", 國立成功大學造船暨船舶機械工程研究所碩士論文，1998。
【18】黃正能，詹國琴，"非線性系統之 -控制器設計及迴路整型
"，國立成功大學造船暨船舶機械工程研究所碩士論文，1999。
【19】黃正能，梁益彰，"強健 控制器之µ綜合設計法"，國立成功
大學造船暨船舶機械工程研究所碩士論文， 2002。
【20】楊憲東，葉芳柏，“線性與非線性 控制理論’’，全華科技
圖書股份公司，1997.
【21】楊憲東,“ 控制理論與應用’’ ,全華科技圖書股份公司，1997.