微生物醱酵是生物製程中一個重要的程序，而程序模式中的比生長速率一般採用非結構模式描述。但此模式以建立基質與比生長速率之間的關係為主，多因子模式的討論較少且公式複雜。本研究分析程序之基質、產物、酸鹼度、溫度與溶氧等因子對微生物生長之效應，發現比生長速率可由這些物理參數以多因子二階模式描述，並利用回應曲面法來識別模式。因此，所有模式參數只需搭配二水準因子設計與中心混成設計實驗即可獲得。考慮基質與溶氧兩個參數的程序，在化學恆定 (chemostat) 操作下取得回應曲面法實驗設計之回應值。為維持連續操作部分在不穩定區進行，故需施以回饋控制。識別出的多因子二階模式與程序的比生長速率，在實驗識別區域內相較相當吻合。以此二階模式替代非結構模型比生長速率來設計及控制饋料批次操作，其結果經模擬證明有很好的成效。

Microbial fermentation is an important process in bioprocess and, the specific growth rate of the process is depicted by unstructured model. These models are almost always based on the sole relationship between the substrate and the specific growth rate. It is rare, in the open literature, to have the multi-factorial models. In this work, we found the specific growth rate can be depicted by multi-factorial second order model in terms of almost all factors in process, i.e., the substrate concentration, product concentration, pH, temperature and dissolved oxygen. Using response surface methodology (RSM) to identify process model, all the parameters can be obtained by combining the methodology of two level factorial design and central composite design (CCD). The illustration of a process with two factors,(i.e., substrate and dissolved oxygen), using RSM experimental design under chemostat operation was demonstrated. In order to maintain the continuous operation in the unstable region, feedback controller is needed to overcome this problem. The second-order model obtained by RSM matches well with the process inside the identified region. Replacing the original unstructured model in process with this second-order model, it is found that effective control can still achieved for a fed-batch bioprocess via computer simulation.

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