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研究生：	蘇布穆 Shoeb Moon Ali
論文名稱：	動態彈性指標的有效量化計算方法及其在製程改善中之應用 Effective Quantification of Dynamic Flexibility Index and its Application for Process Improvement
指導教授：	張珏庭 Chang, Chuei-Tin
共同指導教授:	張嘉修 Chang, Jo-Shu
學位類別：	博士 Doctor
系所名稱：	工學院 - 化學工程學系 Department of Chemical Engineering
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	105
中文關鍵詞：	動態彈性指標、非穩態過程、頂點法、遺傳算法、程序改善、回饋迴路、PID調諧
外文關鍵詞：	dynamic flexibility index, unsteady process, vertex method, genetic algorithm, process improvement, feedback loop, PID tuning
相關次數：	點閱：80 下載：6
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儘管化學程序傳統上是在指定的正常條件下根據經濟標准進行評估，但仍然有必要確保給定程序設計在偏離標準水平的條件下的實際操作可行性。本研究的目的是減少彈性指標(〖FI〗_d) 的計算時間，並提高動態彈性分析的實用性。在這項研究中，我們採用兩種不同的解決策略來處理計算彈性指數的雙層最適化問題。下層最大化計算是使用確定性求解器執行的，而上層最小化則是使用元啟發式算法(即基因演算法)。為了簡化並加快所提出的計算方法的實施，我們將操縱變量視為時間的分段常數函數。通過兩個數值案例研究獲得的計算結果及其與現有技術的比較，可以得到令人滿意的驗證。
在能夠以上述方法有效率的獲得給定程序的精確動態彈性指標後，這些〖 FI〗_d 值可用於改進程序系統的物理設計。為了使系統在預期不確定偏差的整個時間範圍內可行，〖FI〗_d 值應大於或等於 1。利用這一事實，我們開發了一個系統化的步驟，利用動態彈性分析來改進給定流程的設計。另外也通過第三、第四兩個案例研究闡明，彈性指標可以有效地引導流程設計，以確保在實際應用中的可操作性。另外，我們在本研究中也提出有效方法應用於閉環動態系統，以決定最佳控制器參數。具體而言，我們將動態彈性指數與誤差平方積分 (ISE) 皆視為評量控制系統的標準。通過同時計算前述兩種指標的數值（〖FI〗_d 與ISE），開發出了一種定量方法，以確保給定的控制系統在整個時間範圍內都可以運行，並且在運行期間仍然可以實現令人滿意的控制性能。從最後兩個案例研究可以看出，彈性指標可以有效地輔助傳統程序控制參數調諧方法，確保在實際應用中的可操作性。
關鍵詞：動態彈性指標，非穩態過程，頂點法，遺傳算法，程序改善，回饋迴路，PID調諧

Although chemical processes are traditionally evaluated according to economic criteria under the designated normal conditions, it is still necessary to ensure operational feasibility of a given design if, in realistic environment, the process conditions stray away from the nominal levels. The purpose of the current study is to improve the computation efficiency of dynamic flexibility index (〖FI〗_d) and also demonstrate its practical applicability. The two-level optimization problem for computing flexibility index has been handled with two different solution strategies in this work. The lower-level maximization is performed with a deterministic solver whereas the upper-level minimization a metaheuristic algorithm. To expedite implementation of the proposed methodology, the manipulated variables are treated as piecewise-constant functions of time. The obtained computation results have been compared and validated with those solved by the state-of-the-art numerical methods in two case studies. Subsequently, the dynamic flexibility indices of a given process may then be utilized for improving its physical design. It has been shown through another two case studies that the flexibility index can effectively guide process design to ensure operability in practical applications. Additionally, the flexibility analysis is also applied to the closed-loop dynamic systems to determine reliable controller tuning parameters. Specifically, the dynamic flexibility index is used as an additional design criterion along with the well-established integrated square of error (ISE) for selecting suitable controllers. Via simultaneous evaluation of these two measures (i.e., 〖FI〗_d and ISE), a quantitative approach is developed to ensure that the given control system performs satisfactorily and is operable throughout the entire time horizon. It has been shown in the last two case studies that the flexibility analysis can effectively complement feedback control to ensure both operability and control performance in practical applications.
Keywords: dynamic flexibility index, unsteady process, vertex method, genetic algorithm, process improvement, feedback loop, PID tuning

Abstract 	                 ii
Abstract (Mandarin)	iv
Acknowledgement	vi
Table of Contents	viii
List of Tables	xi
List of Figures	xii
	
1  Introduction	1
    1.1  Background	1
    1.2  Literature Review	2
    1.3  Motivation	4
    1.4  Objectives	5
    1.5  Thesis Organization	6
	
2  Review of Available Solution Methods	8
    2.1  Vertex Enumeration Based Strategy	9
    2.2  Active Set Based Strategy	11
    2.3  Dynamic Flexibility Index	12
    2.4  Extended Vertex Method	15
    2.5  Extended Active Set Method	15
    	
3  Genetic Algorithm assisted Vertex Enumeration Methodology 	20
   (GAVE) for FId Evaluation	
    3.1  Auxiliary Constraints	21
    3.2  Vertex Based Strategy using Genetic Algorithm	23
    3.3  A Generalized Computation Procedure	26
    3.4  Numerical Examples	28
           3.4.1  A Buffer Tank System	28
           3.4.2  An Alcoholic Fermentation System	33
    3.5  Additional Discussions on Computational Results	39
    3.6  Concluding Remarks	41
	
4  Application of Dynamic Flexibility Index for Process Design   	43
   Improvement	
    4.1  Flexibility Analysis Based Design Improvement Procedure	43
    4.2  Numerical Examples	45
           4.2.1  A Two-Tank Buffer System	45
           4.2.2  A Photobioreactor System	50
    4.3  Importance of Flexibility Analysis in Process Design	54
    4.5  Concluding Remarks	55
	
5  Application of Dynamic Flexibility Index for Evaluating 	58
   Process Control System Design	
    5.1  Flexibility Analysis Based Process Control System Design	59
    5.2  Numerical Examples	61
           5.2.1  A Mixing Tank System	62
           5.2.2  A Semi-Batch Reactor System	66
    5.3  Significance of Flexibility Analysis in Controller Tuning	71
    5.4  Concluding Remarks	73
	
6  Conclusions and Future Directions	76
    6.1  Final Conclusions and Achievements	76
    6.2  Research Articles and Conference Talks	77
    6.3  Plausible Future Directions	78
	
References	82
Appendix A  Discretization of Dynamic Model	87
Appendix B  An Overview of Genetic Algorithm	91
Appendix C  GA-assisted Vertex Enumeration Technique Code Listing	94
            C.1 MATLAB Listing for Genetic Algorithm	94
            C.2 GAMS Listing for Numerical Example 3.4.1	102
                                    

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