本論文提出一種新型比例-積分最佳線性二次狀態估測追蹤器。基於在時域性能指標函數中頻域塑型法的發展，頻域的設計概念得以融入時域的最佳方法論;首先，針對具有未知外部干擾的非隨機連續/離散系統，我們分別推導廣義最佳線性二次類比/數位追蹤器，接著，相對應新的估測狀態器設計程序也在本論文呈現，基於比例-積分-微分濾波器塑型法的方法，發展出一種新的比例-積分最佳線性二次狀態估測器，其適用於非方陣、非最小相位多輸入多輸出的連續/離散系統；最後，此論文提出足以達到類似最小相位系統之追蹤性能的新型最佳濾波器塑型比例–積分狀態回授二次狀態估測追蹤器，用以解決非方陣、非最小相位多變數系統，其系統含有不可量測的狀態和劇烈變化的時變指令輸入。在本論文中，以多種範例驗證所提方法的有效性。

New proportional-plus-integral (PI) optimal linear quadratic state-estimate trackers are proposed in this dissertation. With the development of the frequency-domain shaping on the time-domain performance index function, the frequency-domain design concept can be merged into the optimization methodology in the time domain. First, generalized optimal linear quadratic analog and digital trackers are derived for the deterministic continuous-time and discrete-time general systems with disturbances models, respectively. Secondly, this dissertation presents corresponding new procedures for the continuous-time and discrete-time state estimator designs. Based on the proportional-integral-derivative (PID) filter shaping approach, new PI optimal linear quadratic state estimator (LQSE) for the continuous-time/discrete-time non-square and non-minimum phase (NMP) multi-input-multi-output (MIMO) systems is developed. Finally, the proposed LQSE-based tracker is able to optimally achieve satisfactory minimum phase-like tracking performances for a non-square NMP multivariable system with unmeasurable states and time-varying command inputs with drastic variations. Illustrative examples are demonstrated in this dissertation to shows the effectiveness of the proposed design methodology.

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