系統鑑別經常受到未知初始狀態和負載擾動的影響，導致不正確的鑑別模型。代數鑑別法能將這兩種未知情況轉變成狄拉克函數形式，然後乘以適當的候選函數，即可將這些不利影響消除。現有代數鑑別法常以簡單的步階或脈波函數作為輸入訊號，訊號的單調性使得較複雜的模型難以鑑別，另外其基礎演算法對模型不匹配和量測雜訊相當敏感。
本論文提出改良式代數鑑別法，使用多重脈波函數作為輸入測試訊號，所產生的輸出量測包含系統相關的豐富訊息，因此增加了複雜模型鑑別的可行性。多重脈波訊號可在開環實驗中以制動器產生，亦能在閉環實驗中透過替續器產生。所提鑑別演算法保留傳統方法面對初始狀態與負載擾動之消除能力，將多重脈波輸入鑑別問題分解成多個獨立的步階輸入鑑別問題，每個問題皆存在著須消除之未知初始狀態和負載擾動。所提鑑別法可分為三個階段來實施。第一階段利用鑑別矩陣輔以奇異值分解來求取時延之最佳估測；第二與第三階段透過最小平方法來分別獲得系統輸出和輸入參數。當採用閉環實驗數據時，所提鑑別演算法可加入替續器產生之頻率響應訊息，以增加鑑別的準確性與強健性。
模擬結果顯示，本代數鑑別法在量測雜訊存在的情況下，可根據開環或閉環實驗準確地鑑別出複雜程序模型，在假設的模型階次比實際值小的情況下，可獲得有效的簡化程序模型。

System identification is usually affected by unknown initial states and load disturbances, leading to incorrect identified models. The algebraic identification method can transform these two unknown situations into Dirac delta functions, and then multiply them by an appropriate candidate function to eliminate these adverse effects. Available algebraic identification methods often use simple step or pulse functions as input signals. The monotonicity of such input signals makes it difficult to identify more complicated models. In addition, their underlying algorithms are very sensitive to model mismatch and measurement noise.

This thesis proposes an improved algebraic identification method, which employs multiple-pulse functions as input signals. The output measurement induced contains rich information about the system, thus increasing the feasibility of identification for complicated models. A multiple-pulse signal can be generated with an actuator in an open-loop experiment, or by the relay in a closed-loop experiment. The proposed identification algorithm retains the conventional method's ability to eliminate initial states and load disturbances, and decomposes the identification problem based on a multiple-pulse input into several independent identification problems based on step inputs. Each problem consists of unknown initial states and load disturbances to be eliminated. The proposed identification method can be implemented in three stages. The first stage uses the identification matrix in conjunction with singular value decomposition to obtain the best estimation of the time delay; the second and third stages use the least square method to obtain the system’s output and input parameters respectively. When closed-loop experimental data are employed, the proposed identification algorithm could incorporate the frequency response information generated by the relay to increase the accuracy and robustness of identification.

The simulation results show that this algebraic identification method can accurately identify complicated process models based on open-loop or closed-loop experiments in the presence of measurement noise. When the assumed model order is smaller than the actual value, the method can yield an effective reduced process model.

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