針對未知資料取樣的非線性且具有輸入─輸出傳輸項的正規系統，本論文藉由數位重新設計技術提出兩個創新的控制方案：其一是以觀測器為基礎的數位重新設計追蹤器，藉由觀測器/卡爾曼濾波器鑑別為方法的狀態反饋和前饋增益所設計的高效能追蹤器，以達到良好的追蹤特性。其二是以當有輸入錯誤的主動容錯狀態空間自調式控制器，基於觀測器/卡爾曼濾波器與修飾的ARMAX模型為系統鑑別方法基礎的數位重新設計追蹤器。研究主題陳述如下：首先，針對輸出響應追蹤問題，提出應用離線的觀測器/卡爾曼濾波器鑑別方法，可以決定未知資料取樣系統的合宜(-低階)維度，以及提供較佳的初始參數為修飾的ARMAX模型系統，可顯著改善其遞歸擴展最小平方(RELS)法的收斂速度。接著，基於修飾的ARMAX模型為系統鑑別方法的基礎，針對未知資料取樣的非線性奇異系統之不可量測系統的狀態問題，提出一個相對應的適應性數位控制方案。更進一步的，為了克服介面的輸入故障的問題，容錯控制和修飾的傳統自調式控制器，也被提出。所提的方法能有效的處理部分突發式與漸進式的輸入故障問題。在本論文中，舉出一些例子，也包含一個實際的電路系統，來說明所提方法之有效性。

A singular system can be reformulated into the equivalent regular system model with an input-output direct feedthrough term from the input to the output. This dissertation proposes two new control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with the unmeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for the unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples, including a real circuit system, are given to demonstrate the effectiveness of the presented design methodologies.

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