具未知擾動線性非時變系統之順滑模態觀測器設計

Abstract

本論文主要在設計對未知擾動具有強健性之順滑模態觀測器，當線性非時變系統遭受外來雜訊干擾時，此順滑模態觀測器能有效降低雜訊干擾，且準確估測無法量測之系統狀態。除了估測理論之探討外，本論文以雙水槽液面調控之非線性系統為例，模擬驗證所設計之順滑模態觀測器，並與Yang and Wilde 所提出之線性觀測器相比較。從模擬結果可得知，在系統遭受到外來雜訊干擾的影響下，兩者皆能正確、精準估測系統的狀態，達到所預設之估測目的。但以設計的角度而言，線性觀測器必須滿足較為繁瑣的條件，再經過複雜的計算後，才能取得觀測器所需之參數，而本論文所提出之順滑模態觀測器僅利用簡單的二次平方式，及李亞普諾夫的收斂條件，即可將觀測器設計完成，明顯的具有簡易設計的優勢，不過線性觀測器不受雜訊大小的影響，但是順滑模態觀測器必須事先規劃雜訊的最大值，一旦雜訊大小超出規劃值，可能造成估測誤差不準度的提升。

This thesis presents a robust sliding mode observer for linear time-invariant systems with unknown disturbance. The sliding mode observer can effectively and accurately estimate the unmeasurable state variables, even under the effect of external undesirable perturbation. In addition to the theoretical investigation of observers , this thesis applies the propose sliding mode observer to a two-tanked hydraulic system for water level regulation problem. When compare the sliding mode observer and the linear observer designed by Yang and Wilde, their numerical simulation results demonstrate that both can accurately estimate the system state under the effect of external unknown disturbance. However, viewing from the design procedure, unlike the linear observer whose design is based on some complicated conditions and computation, the sliding mode observer is easier since it is designed in the sense of Lyapunov theory by choosing a simple quadratic equation. The only restriction is the bound of disturbance which is required before the design of the proposed sliding mode observer.