聚羥基丁酸酯〈Poly(β-hydroxybutyrate), PHB〉是一種微生物的生物高分子，它藉由微生物生產出來。PHB的生成條件是藉由氮源限制使微生物開始生產產物，所以饋料批次是最適合來生產PHB的發酵槽，然後再遵循最佳的進料方式來生產。在真實程序中都會受到一些無法量測與預測的干擾，所以程序必定需要受到控制，使產物濃度遵循最佳狀態的軌跡。本研究主旨是找出一組精簡的數學模式來模擬PHB生長過程，數學模式中參數估測的方法是使用基因演算法〈Genetic Algorithms, GA〉。接下來再使用最佳的數學模式進行最適化操作方式尋找出最大產率以及最小進料流率段數，進料流率、進料濃度、進料段數的尋找方法是使用基因演算法。最後在饋料批次程序的控制設計上採用適應性控制策略，藉由基質的進料流率將產物濃度維持在最佳狀態。

Poly(β-hydroxybutyrate), PHB, is a microbial biopolymer produced by bacteria. PHB produced by nitrogen source limited in microbe, so PHB can be suitably produced by fed-batch bioreactor, and production methods allow the optimization of feeding profiles. In the plants, they have several disturbances, which are not measured and predicted, so the plants need to be controlled, however, production concentration profiles abide by the optimum state. In this work, to develop a process model simulating the PHB production, parameters of model were obtained using Genetic Algorithms, GA. Next work, dynamic optimization is applied to maximize PHB productivity and minimum feeding stages. Feeding rate, concentration, stages are optimized by GA. Final, control design of this process use adaptive control, the objective is production concentration, which can maintain the best state.

[中文]
[1] 林勳棟，「整合醱酵與分離程序的最適化設計研究」，博士論文，國立中正大學，嘉義(2008)。
[2] 林東信，「以β-Parato預測法解決不確定因素下之多目標最佳化」，碩士論文，成功大學，台南(2009)
[3] 許智凱，「研發乳酸連續發酵製程」，碩士論文，國立台灣科技大學，台北(2010)。
[4] 陳嘉明，「酒精共醱酵程序之最適化策略」，碩士論文，國立中正大學，嘉義(2010)。
[5] 黃有任，「最適化設計聚羥基丁酸酯製成養分濃度與操作時間」，碩士論文，國立台灣科技大學，台北(2010)。
[6] 蔣寬和、鍾秀菊，「模糊多目標線性規劃在地區農業生產決策之應用」，修平學報，私立修平科技大學，台中(2007)。
[7] 蘇浩仁，「生物高分子(PHB)發酵系統最適化規劃與控制」，碩士論文，國立台灣科技大學，台北(2006)。
[英文]
[1] Aidan, O., Handbook of PI and PID controller tuning rules., second edition, 2006.
[2] Andrews, J.F., A mathematical model for the continuous culture of microorgranisms utilizing inhibiting substrates., Biotechnology and Bioengineering. 1968, 10, 707-723.
[3] Astrom, K. J., Wittenmark, B. (1989) Adaptive Control. Addison-Wesley Publishing Company.
[4] Banga, J.R., Irizarry-Rivera, R., Seider, W.D., Stochastic optimization for optimal and model-predictive control, Computers and Chemical Engineering. 1998, 22, 603-612.
[5] Bastin, G., Dochain, D. (1990) On-line Estimation and Adaptive Control of Bioreactors. Elsevier Science Publishing Company, New York.
[6] Bindlish, R., Model order selection for process identification applied to an industrial ethylene furnace., Journal of Process Control, 2003,13,569-577.
[7] Dias, J.M.L, Serafim, L.S., Lemos, P.C., Reis, M.A.M., Oliveira, R. Mathematical modelling of a mixed culture cultivation process for the production of polyhydroxybutyrate, Biotechnology and Bioengineering, 2005, 92, 209-222.
[8] Dochain, D., State and parameter estimation in chemical and biochemical processes: A tutorial, Journal of Process Control, 2003, 13, 801-808.
[9] Grothe, E., Chisti,Y., Poly(beta-hydroxybutyric acid) thermoplastic production by Alcaligenes latus: Behavior of fed-batch cultures, Bioprocess Engineering.,2000, 22, 441-449.
[10] Haas, R., Jin, B., Zepf, F. T., Production of poly(3-hydroxybutyrate)from waste potato starch., Bioscience, Biotechnology, and Biochemistry, 2008, 72, 253-256.
[11]Hunt, K.J., Sbarbaro, D., Zbikowski, R., Gawthrop, P.J., Neural networks for control systems - A survey, Automatica, 1992, 28, 1083-1112.
[12] Johnson, K., Kleerebezem, R., van Loosdrecht, M.C.M., Influence of the C/N ratio on the performance of polyhydroxybutyrate (PHB) producing sequencing batch reactors at short SRTs, Water Research, 2010, 44, 2141-2152.
[13] Johnson, K., Kleerebezem, R., Van Loosdrecht, M.C.M., Model-based data evaluation of polyhydroxybutyrate producing mixed microbial cultures in aerobic sequencing batch and fed-batch reactors, Biotechnology and Bioengineering, 2009, 104, 50-67.
[14] Khanna, S., Srivastava , A. K., A Simple structured mathematical model for biopolymer (PHB) production., Biotechnology Progress., 2005, 21, 830-838.
[15] Khanna, S., Srivastava , A. K., Computer simulated fed-batch cultivation for over production of PHB: A comparison of simultaneous and alternate feeding of carbon and nitrogen., Biochemical Engineering Journal , 2006(a), 27, 197–203.
[16] Khanna, S., Srivastava , A. K., Optimization of nutrient feed concentration and addition time for production of poly(b-hydroxybutyrate).,Enzyme and Microbial Technology, 2006(b), 39, 1145–1151.
[17] Khanna, S., Srivastava , A. K., Productivity enhancement of Poly-(b-hydroxybutyrate) by fed-batch cultivation of nutrients using variable (decreasing) nutrient rate by Wautersia eutropha., Chemical Engineering Communications, 2008, 195, 1424–1436.
[18] Lai, Y.-J., Hierarchical optimization: A satisfactory solution., Fuzzy Sets and Systems, 1996, 77, 321–335.
[19] Lin, H.-T., Wang, F.-S., Fuzzy optimization of extractive fermentation processes including cell recycle for lactic acid production, Chemical Engineering and Technology, 2008, 31, 249-257.
[20] Lopez, J. A, Bucala, V., Villar, M. A, Application of dynamic optimization techniques for poly(β-hydroxybutyrate) production in a fed-batch bioreactor., Ind. Eng. Chem. Res., 2010, 49, 1762-1769.
[21] Luyben, W. L., Fed-batch reactor temperature control using lag compensation and gain scheduling, Industry & Engineering Chemistry Research, 2004, 43, 4242-4252
[22] Mahadevan, R., Agrawal, S.K., Doyle III, F.J., Differential flatness based nonlinear predictive control of fed-batch bioreactors, Control Engineering Practice, 2001, 9, 889-899
[23] Miettinen, K. M., Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, 1998.
[24] Mulchandani, A., Luong, J. H. T., Groom, C., Substrate inhibition kinetics for microbial growth and synthesis of PHB by Alcaligenes eutrophus ATCC 17697. Applied Microbiology and Biotechnology, 1989, 30, 11-17.
[25] Ochoa, S., Lyubenova, V., Repke, J.-U., Ignatova, M., Wozny, G., Adaptive control of the Simultaneous Saccharification-Fermentation Process from Starch to Ethanol. Computer Aided Chemical Engineering, 2008, 25, 489-494.
[26] Pareto, V., Manuel d'Economic Politique. Girard, 2 ed, 1927.
[27] Patwardhan, P. R., Srivastava, A.K., Model-based fed-batch cultivation of R. eutropha for enhanced biopolymer production., Biochemical Engineering Journal, 2004, 20, 21–28.
[28] Patwardhan, P., Srivastava, A.K., Fed-batch cultivation of Wautersia eutropha, Bioresource Technology., 2008, 99, 1787–1792.
[29] Penloglou, G., Roussos, A., Chatzidoukas, C., Kiparissides, C., A combined metabolic/polymerization kinetic model on the microbial production of poly(3-hydroxybutyrate), New Biotechnology, 2010, 27, 358–367.
[30] Rawlings, J.B., Tutorial overview of model predictive control, IEEE Control Systems Magazine, 2000, 20, 38–52.
[31] Rusendi, D., Sheppard, J.D., Hydrolysis of potato processing waste for the production of poly-beta-hydroxybutyrate., Bioresource Technology., 1995, 54, 191-196.
[32] Ryu, H.W., Hahn, S.K., Chang, Y.K, Chang, H.N., Production of Poly(3-hydroxybutyrate) by high cell density fed-batch culture of Alcaligenes eutrophus with phosphate limitation., Biotechnology and bioengineering, 1996, 55, 28-32.
[33] Raje ,P., Srivastava, A.K., Updated mathematical model and fed-batch strategies for poly-beta-hydroxybutyrate (PHB) production by Alcaligenes eutrophus., Bioresource Technology, 1998, 64, 185-192.
[34] Roeva, O., Tzonkov, S., Modelling of Escherichia coli cultivations: acetate inhibition in a fed-batch culture., Bioautomation, 2006,4,1-11.
[35] Serafim, L.S., Lemos, P.C., Oliveira, R., Reis, M.A.M., Optimization of polyhydroxybutyrate production by mixed cultures submitted to aerobic dynamic feeding conditions., Biotechnology and Bioengineering, 2004,87,145-160.
[36] Shang, L., Fan, D.D., Kim, M.I.J., Choi, D.R., Chang, H.N., Modeling of poly(3-hydroxybutyrate) production by high cell density fed-batch culture of Ralstonia eutropha., Biotechnology and Bioprocess Engineering, 2007, 12, 417-423.
[37] Shang, L., Jiang, M., Chang, H.N., Poly(3-hydroxybutyrate) synthesis in fed-batch culture of Ralstonia eutropha with phosphate limitation under different glucose concentrations., Biotechnology Letters, 2003, 25, 1415–1419.
[38] Shahhosseini, S., Simulation and optimisation of PHB production in fed-batch culture of Ralstonia eutropha., Process Biochemistry, 2004, 39, 963–969.
[39] Shih, H.-S., Lai, Y.-J., Lee, E.S., Fuzzy approach for multi-level programming problems., Computers and Operations Research, 1996, 23, 73–91.
[40] Smith, C. A., Corripio, A. B. (1985) Principles and Practice of Automatic Process Control. Wiley.
[41]Van Aalst-Van Leeuwen, M.A., Pot, M.A., Van Loosdrecht, M.C.M., Heijnen, J.J., Kinetic modeling of poly(β-hydroxybutyrate) production and consumption by Paracoccus pantotrophus under dynamic substrate supply, Biotechnology and Bioengineering, 1997, 55, 773–782.
[42] Voit, E. O. (2000) Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists. Cambridge University Press.
[43] Yeo, J.S., Park, J.Y., Yeom, S.H., Yoo, Y.J., Enhancement of poly-3-hydroxybutyrate (PHB) productivity by the two-stage supplementation of carbon sources and continuous feeding of NH4Cl, Biotechnology and Bioprocess Engineering, 2008, 13, 14–24.
[44] Zeleny, M. Compromise programming, University of South Carolina Press, 1973.