在與系統鑑別相關的研究中，往往要求鑑別時系統的起始狀態為恆態並且不能有負載擾動發生。這些要求雖然可以簡化鑑別理論的推導，但也造成實際應用上的困難。本論文即利用多重積分和二次最小平方演算的原理，發展出能解決此實用問題的鑑別方法。
對於任意階次的系統微分方程式而言，因為狀態的微分量難以量測，故將之積分多次而得到系統的多重積分式。由階梯信號、斜坡信號以及正弦信號，加以線性組合，便可衍生出多種常用之脈波信號。所謂「兩階段最小平方演算法」，即是將系統的脈波響應分成兩部分，分別利用多重積分與最小平方演算法來求解模式參數，即可有效排除非零起始值與未知負載擾動的影響。
最後，經由廣泛的模擬研究以及溫度控制系統實驗證實，本方法對於不同動態系統，均能有效排除負載擾動與非恆態起始狀態的影響，而得到滿意的鑑別結果。

In the researches related to system identification, it is often required that the system be at steady state initially and no load disturbance occurs during the identification test. Although simplifying the derivation of the identification theory, these requirements could cause practical difficulties in applications. In this thesis, an identification method is developed to resolve such difficulties based on multiple integrations and the two-stage least-squares algorithms.

For a system differential equation of arbitrary order, we propose the multiple-integral transform of the equation because differentials of the states are inaccessible to measurement. Combining step, ramp, or sinusoidal signals can produce commonly used pulse signals. The so-called “two-stage least-squares algorithms” could eliminate the effects of nonzero initial conditions and unknown load disturbances by dividing the output response into two stages, each of which is dealt with by multiple integrations and least-squares algorithms.

Finally, an extensive simulation and experimental study verifies that the developed method could yield satisfactory identification results for a wide variety of process dynamics and eliminate the effects of load disturbances and unsteady initial states.

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