傳統上，程序設計大多都是依據經濟效益作為評量標準，但在現實應用中存在不確定隨機變化的外界干擾，設計過程中採用的參數值可能會在極端狀況下改變，以致使系統無法操作，因此在設計過程中除了考慮成本以外，還需要確保操作的可行性。此外，一般認為程序設計與控制應在製程開發初期就同時考慮，以獲得同時具有操作彈性與經濟效益的實際系統。在過去的研究中，雖然已有學者利用動態與暫態彈性指標分析在參數不確定影響情況下動態系統的操作彈性，使設計者能夠以此性能指標作為設計衡量依據，但大多針對單元設計與配置對系統彈性的影響，對於實際操作情形下，藉由調整操作變數消除程序參數變動對彈性影響的議題未有廣泛的討論，且在閉環路控制系統中，PID控制器參數之設定亦未曾考慮系統操作上不等式限制以及干擾的特性。因此在本研究中，我們將探討開環路系統中操作變數的限制對操作彈性可能帶來的影響，以及發展閉環路系統中以彈性指標為PID控制器參數設定和控制手段選擇依據之方法。

The chemical processes, designed according to the nominal operating conditions and parameters, have traditionally been evaluated with economic criteria. This approach often ends up with an inoperable plant if some of the conditions/parameters significantly deviate from their nominal values. Thus, in addition to the capital and operating costs, it is important to consider operational flexibility in a design. Furthermore, it is also beneficial to address the design and control issues simultaneously in early stage of process development.
The dynamic and temporal flexibility indices are performance indices for characterizing the operational flexibility of open-loop unsteady processes. The previous analyses focused primarily on the effects of adjusting design parameters, while ignored the roles of control variables. In addition, since one is free to adjust these control variables at will in computing the above indices, there are incentives to impose additional constraints to produce assessments that are more realistic. Therefore, the aim of this study is to develop an improved vertex method for computing the dynamic flexibility index in order to circumvent the aforementioned drawbacks.
Since the control variable is a function of the online measurement in a closed-loop system, this work also proposes a tuning method to determine the PID controller parameters according to the dynamic flexibility index. From the simulation results obtained in the single- and double-tank buffer systems, we found that this approach yields the best controller under specified disturbances. Furthermore, from the simulation results obtained in the SMDDS (Solar Membrane Distillation Desalination System) example, one can also conclude that the proposed design strategy is effective for PID controller tuning in periodic or dynamic processes.

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