使用估測-遞迴之方法分析飛行器之分叉現象

Abstract

數值分析對非線性系統來說是非常重要的，原因是大部分的非線性系 統都是非常複雜的。其中最重要的平衡點的問題，在非線性系統中佔有相 當重要的地位。以往在分析非線性平衡點的問題時，皆以牛頓法解之。而 傳統牛頓法存在著只能對單一平衡點計算的缺點。本文將研究一牛頓法之 修正方法，解決傳統牛頓法之缺陷，以利於我們分析非線性平衡點分叉的 現象。我們將上述牛頓修正法使用於分析三階飛行器中平衡點變化的現象 。由分析可以得知平衡點穩定的情形，並藉由最佳化控制中LQR設計，以 控制平衡點的穩定性。 Numerical analysis is very important for non-linear system. Because most non-linear system is very complex. The problem of determining the equilibria play an important role in the non- linear system. In traditional, We solve the equilibria of the nonlinear system by using Newton's method.However, the main disadvantage of Newton's method is that it can not deal with the system with more than one equilibria point. In this thesis, we develop a new method to analyze the bifurcated phenomenon of equilibria in order to solve the disadvantage of the traditional Newton's method. We will use the new method to analyze the equilibria change situation of third order model of the F-8 aircraft. By this way, we could know the stability of the equilibria and through the LQR design of Optimal control to control the stability of equilibria.