Internal-model Based LQG/Hinf Design of Active Noise Controllers for A One Dimensional Acoustic Duct System

本文為研究一維聲管主動噪音控制及控制實作的問題。我們首先引用許弘 毅[24]於1990年所推導的一維聲管音場模式，建立一維聲管模式之實係數 狀態空間方程式，並為了抵銷單一特定頻率的弦波噪音源輸入，引入內部 模式的觀念，考量當噪音的頻率不等於內部模式所用之音頻所造成的模式 誤差，提出了含內部模式之LQG/Hinf 控制方法，並以 LQG+IM 控制器和 LQG/Hinf+IM 控制器的比較，說明 LQG/Hinf+IM 控制器改善了 LQG+IM 控制器對內部模式頻率的靈敏度，最後並以聲管主動噪音控制實驗驗證， LQG/Hinf+IM 控制器能有效的降低聲管噪音量並且對音頻的變動確實有較 佳的強韌性。In this thesis, we study active noise control for a one- dimensional acoustic duct system. A real-state-space model of an acoustic duct system developed in [24] is used to design active noise controllers and do computer simulation. A design method of linear quadratic gaussian control with a performance bound incorporating with an internal model principle (LQG/Hinf+IM) is developed to design active noise controller to generate repetitive control signal so that noise of specific (target) frequency in the acoustic duct can be attenuated. Computer simulation shows that the designed LQG/Hinf+IM controller can achieve perfect noise rejection at the target frequency and can acquire the desired robustness property of tolerating the uncertainty in the target frequency. Experimental results also demonstrate the robust control performance and indicate the feasibility of the proposed designed method