正多項式方法之低階控制器設計:
縱向自動駕駛設計

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。

關鍵字

正多項式；低階控制器

並列摘要

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.

並列關鍵字

LMI region ； fix-order control ； pole-clustering

參考文獻

[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

[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

國際替代計量

正多項式方法之低階控制器設計: 縱向自動駕駛設計

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