本論文提出一種新式間接型的數位再設計方法，適用於串聯和動態輸出迴授系統之多種採樣控制器。這些類比控制器往往用來預測可用的頻率特性，像是頻寬，自然角頻率等等。然而數位控制器比類比控制器優點在於實現較為可取。由於只有輸入輸出訊號可量測時，使用一種理想狀態重建演算法去獲得原始連續系統多種採樣時間的離散狀態。基於切比雪夫正交法則，根據不同採樣時間而使用不同閉迴路系統，使用多種採樣時間串聯和輸出迴授數位控制器的增益來算出連續時間部分。因此，高頻和低頻特性類比控制器可以用來實現相對應的高數率採樣和低數率採樣時間數位控制器。不同於傳統方法的直接雙線性變換，是一種開迴路的數位控制器。本論文所提出的數位控制器有考慮到狀態匹配相對於原始的連續閉迴路系統和數位再設計取樣閉迴路系統。而為了進一步提高狀態匹配的特性，一種改良型的數位再設計方法也被提出來。範例說明，以證明方法的有效性。

In this thesis, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analog controllers are often predesigned based on desirable frequency specification, such as the bandwidth, the natural angular frequency, etc. To take advantages of the digital controller over the analog controller, digital implementations of these analog controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilized to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analog controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.

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