利用替續器產生之有限迴圈現象來取得程序動態訊息的鑑別技術已經在工業界獲得廣泛的應用。Kaya和Atherton (2001)利用埃氏有限迴圈軌跡理論提出二階時延模式(不含零點)的鑑別方法，此法具有實際應用的困難，因為輸出量測的微小偏差即可造成錯誤的鑑別結果。
本論文沿用埃氏有限迴圈軌跡理論來發展兩種較Kaya法更適合實際應用的鑑別方法。第一種方法以頻率加權的方式將軌跡理論產生之輸出方程式作積分處理，可處理鑑別實驗時靜態負載擾動存在的問題。第二種方法則利用輸出方程式進行多區域之面積積分並與量測結果作比較。除了二階不含零點模式之應用，此兩種方法亦被擴展至二階含零點模式之鑑別。經模擬研究與實驗印證，本文所提之兩種鑑別方法均較Kaya法更具有實用的價值。

Identification techniques based on relay-induced limit cycles have found wide applications in the industry to acquire information about process dynamics. Kaya and Atherton (2001) proposed the use of the A-locus limit-cycle theory to identify second-order plus delay models (without zeros). However, their method is not feasible because slight variations in the output measurement could cause erroneous identification results.
This thesis presents two identification methods based on the A-locus limit-cycle theory, which are superior to Kaya’s method in applications. The first method integrates the output equation obtained by the A-locus theory in a frequency-weighted manner, which can deal with the problem of static load disturbances. The second method utilizes the output equation to generate multiple area integrals, which are compared with the measured results. In addition to the application of second-order without zero models, the two methods are extended to identification of second-order with zero models. Extensive simulation study and an experimental work demonstrate that the proposed methods are indeed much more feasible than Kaya’s method.

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