在本論文中，針對具有直接傳輸項與已知系統干擾之離散系統，我們提出廣義線性二次式數位追蹤器的設計方法，並且將其應用於一些控制問題上，以便達到設計目標。然而，為了應付這類非方形非極小相位離散系統，我們結合了古典控制方法與廣義線性二次式數位追蹤器設計，使得這類非方形非極小相位離散系統對於一個具有劇烈變化的任意參考軌跡能夠擁有一個期望且類似於極小相位的追蹤性能。另外，當有未知外部干擾發生於受控系統的輸入端時，那麼我們先使用離散比例加積分觀測器來建構一個狀態與干擾估測器。然後再直接應用廣義線性二次式數位追蹤器，設計一個基於比例加積分觀測器的線性二次式數位追蹤器，使得受控系統在這樣的情況下仍然能夠擁有一個期望的追蹤性能。此外，針對具有直接傳輸項、未知程序干擾以及未知量測雜訊之離散反覆系統，我們也提出疊代學習線性二次式數位追蹤器並且含有輸入飽和功能的設計方法。對於一個期望的追蹤性能，經由所提議的初始化，它能夠在一個回合就收斂。除此之外，我們同時也提出一種簡單並且相當有效的方法來應付這類具有直接傳輸項、未知程序干擾以及未知量測雜訊之離散系統。最後，我們以一些數值範例來驗證所提方法的有效性。

In this thesis, a generalized linear quadratic digital tracker (LQDT) for the more general discrete-time system, which has a direct-feedthrough term and the known system disturbances, has been presented, and it will be applied in some control problems to achieve design goals. In order to deal with the non-square non-minimum phase discrete-time system, we blend the classical control methodology and the generalized LQDT design such that the non-square non-minimum phase discrete-time system has a desired minimum-phase-like tracking performance for a given arbitrary reference trajectory with drastic variations. In addition, we construct a state and disturbance estimator using discrete-time proportional plus integral observer to estimate both the system state and the unknown external disturbance for the discrete-time systems with an unknown external disturbance. Then, by applying the generalized LQDT design, design a proportional plus integral observer-based LQDT with a high-gain property to have a desired tracking performance. A new iterative learning LQDT with input constraint for the discrete-time repetitive system with a direct-feedthrough term, unknown process disturbance, and unknown measurement noise, has been presented. By the initialization of the proposed iterative learning control (ILC), it can converge in one epoch for a desired tracking performance. Besides, we also present a simple and effective method to deal with the more general discrete-time system which has a direct-feedthrough term, unknown process disturbance, and unknown measurement noise.

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