軸流壓縮機不穩定現象之控制

Abstract

本論文探討軸流壓縮機系統之穩定性分析及控制設計。除了以數值分析的方式對系統作穩定性分析，並提出三種控制設計法則以有效穩定系統〝激喘〞(surge) 現象。 首先，應用輸入-輸出線性化法則設計系統之穩定控制器。針對實際系統在壓縮機特徵函數上具有不可避免的不確定性，我們建立系統Lyapunov 函數以達到強健控制設計。然而，此方法需要知道系統確切的工作點。因此，我們應用washout filter來延遲或消除系統因參數改變所造成不穩定現象之發生。其優點為不需要知道系統之工作點，且可自動追蹤系統實際之操作點。最後，藉由數值模擬驗證，所提出控制設計確實達成預期之成效。

In this thesis, we study the stability of an axial flow compression system via numerical analysis and propose three different control schemes to control the post-surge dynamics. Based on Moore and Greitzer's model (1986), the surge behavior is found to be attributed to the appearance of Hopf bifurcation. The input-output linearization scheme is first employed to globally stabilize the surge inception operating point via either throttle or close-coupled valve control. A Lyapunov function based control is then proposed to provide the asymptotic stability of the post-surge operating point for the compressor with uncertain axisymmetric characteristic. Though the robust stabilization can be achieved by Lyapunov function based design, however, such an approach strongly relies on the exact knowledge of the operating point. A washout filter type controller is hence proposed to delay the occurrence of Hopf bifurcation in compressor dynamics, which does not require the knowledge of system equilibria. Numerical results are given to demonstrate the effectiveness of the proposed designs.