速率陀螺儀之渾沌同步與反控制

Abstract

本篇論文研究速率陀螺儀非線性系統的渾沌同步，不同相位對同步之影響與反控制。藉由一個相同於原系統但初始值不同的系統，利用六種不同的耦合項去使兩系統產生渾沌同步。並且以李亞普諾夫指數法，時間響應以及系統同步時間去驗證系統同步時的臨界耦合強度值。接著引進歐幾里得距離以研究單向耦合時同步的暫態時間，並作出一耦合強度與距離的關係圖。然後討論如果兩個相同系統初始相位值不同，會對同步發生的影響。 繼之，以外加控制項使原來之週期解改變為渾沌以達成反控制的要求。使用的反控制方法為：外加定力矩、外加週期力矩、外加週期脈衝、時間延遲控制、適應性反控制。

Chaos synchronization and anticontrol of a rate gyroscope are studied in this thesis. By generating two identical systems with different initial conditions, six different coupling terms are used to synchronize the chaotic systems. Lyapunov exponent, time response and synchronous time are used to confirm the critical coupling strength. Then Euclidean distance is used to unidirectional synchronization and plot a figure with coupling strength vs the distance. Next, it is discovered that two identical systems with different initial phase may give different effect to synchronization. Finally anticontrolling term is added to change state from regular to chaos. The anticontrolling methods such as adding of a constant torque, a periodic torque, a periodic impulse torque, time delay control, and adaptive anticontrol are used.