Nghiên cứu sử dụng biến cường tính trong mô hình hoá, phân tích động lực và điều khiển quá trình
Main Article Content
Abstract
Mọi quá trình chuyển đổi vật chất đều tạo ra entropy như được phát biểu bởi nguyên lý thứ hai nhiệt động lực học. Đặc tính cố hữu này là nền tảng trong nghiên cứu, nó cho phép xem xét biểu thức của tốc độ phản ứng hoá học như là hàm phi tuyến của lực phản ứng hoá học được biểu diễn trên cơ sở của đại lượng cường tính (ái lực hoá học). Trên cơ sở đó, biểu thức tường minh của tốc độ phản ứng hoá học đươc rút ra và cho phép chỉ rõ nó thuộc về kiểu quan hệ tác động khối lượng tổng quát hoá. Dưới một số điều kiện vận hành, hệ phản ứng có thể hoạt động với nhiều trạng thái dừng. Từ đây, ý tưởng cho vấn đề điều khiển ổn định hoá tại trạng thái cài đặt mong muốn thông qua phương pháp Lyapunov cũng được bình luận. Một số ví dụ đề xuất cho phép minh hoạ các khái niệm và kết quả phát triển.
Từ khóa: Mô hình toán học, tốc độ phản ứng, ái lực hoá học, entropy, phương pháp Lyapunov.
References
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[2] De Groot S.R. and Mazur P. (1962). Non-equilibrium thermodynamics. Dover Pub. Inc., Amsterdam, 1st edition.
[3] Glansdorff P. and Prigogine I. (1971). Thermodynamic theory of structure, stability and fluctuations. Wiley-Interscience.
[4] Sandler S.I. (1999). Chemical and Engineering Thermodynamics. Wiley and Sons, 3rd edition.
[5] Luyben W.L. (1990). Process modeling, simulation, and control for chemical engineers. McGraw-Hill, Singapore.
[6] Aris R. (2000). Elementary Chemical Reactor Analysis. Dover Publications, Mineola, New York.
[7] Favache A. and Dochain D. (2010). Power-shaping of reaction systems : the CSTR case study. Automatica, 46(11), 1877-1883.
[8] Viel F., Jadot F. and Bastin G. (1997). Global stabilization of exothermic chemical reactors under input constraints. Automatica, 33(8), 1437-1448.
[9] Favache A., Dochain D. and Winkin J. (2011). Power-shaping control: writing the system dynamics into the Brayton-Moser form. Syst. & Cont. Let., 60(8), 618-624.
[10] Hoang H., Couenne F., Jallut C. and Le Gorrec Y. (2011). The Port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors. J. Proc. Control, 21(10), 1449-1458.
[11] Hoang H., Couenne F., Jallut C. and Le Gorrec Y. (2012). Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics. J. Proc. Control, 22(2), 412-422.
[12] Alvarez J., Alvarez-Ramírez J., Espinosa-Perez G. and Schaum A. (2011). Energy shaping plus damping injection control for a class of chemical reactors. Chem. Eng. Sci., 66(23), 6280-6286.
[13] Bruns D.D. and Bailey J.E. (1975). Process operation near an unstable steady state using nonlinear feedback control. Chem. Eng. Sci., 30, 755-762.
[14] Alvarez-Ramírez J. and Morales A. (2000). PI control of continuously stirred tank reactors: stability and performance. Chem. Eng. Sci., 55(22), 5497-5507.
[15] Antonelli R. and Astolfi A. (2003). Continuous stirred tank reactors: easy to stabilise? Automatica, 39, 1817-1827.
[16] Hoang H., Couenne F., Jallut C. and Le Gorrec Y. (2013). Thermodynamics-based stability analysis and its use for nonlinear stabilization of CSTR. Computers & Chemical Engineering, 58(11):156-177.
[17] Ydstie B.E. and Alonso A.A. (1997). Process systems and passivity via the Clausius-Planck inequality. Syst. & Contr. Let., 30(5):253-264.
[18] Alonso A.A. and Ydstie B.E. (2001). Stabilization of distributed systems using irreversible thermodynamics. Automatica. 37, 1739-1755.
[19] Dammers W.R. and Tels M. (1974). Thermodynamic stability and entropy production in adiabatic stirred flow reactors. Chem. Eng. Sci., 29(1):83-90.
[20] Tarbell J.M. (1977). A thermodynamic Lyapunov function for the near equilibrium CSTR. Chem. Eng. Sci., 32:1471-1476.
[21] Favache A. and Dochain D. (2009). Thermodynamics and chemical systems stability: The CSTR case study revisited. J. Proc. Control, 19(3):371-379.
[22] Eberard D., Maschke B. and Van Der Schaft A. (2007). An extension of pseudo-Hamiltonian systems to the thermodynamic space: Towards a geometry of non-equilibrium thermodynamics. Reports on Mathematical Physics,60(2):175-198.
[23] Ederer M., Gilles E.D. and Sawodny O. (2011). The Glansdorff-Prigogine stability criterion for biochemical reaction networks. Automatica, 47:1097-1104.
[24] Georgakis C. (1986). On the use of extensive variables in process dynamics and control. Chem. Eng. Sci., 41(6):1471-1484.
[25] Ramírez H., Maschke B. and Sbarbaro D. (2013). Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chem. Eng. Sci., 89:223-234.
[26] Dörfler F., Johnsen J.K. and Allgöwer F. (2009). An introduction to interconnection and damping assignment passivity-based control in process engineering. J. Proc. Control, 19, 1413-1426.
[27] Ramírez H., Sbarbaro D. and Ortega R. (2009). On the control of non-linear processes: An IDA-PBC approach. J. Proc. Control, 19, 405-414.
[28] Hangos K.M., Bokor J. and Szederkényi G. (2001). Hamiltonian view on process systems. AIChE journal, 47(8), 1819-1831.
[29] Du J., Laird C.M. and Ydstie B.E. (2010). The measurement selection of inventory control. Proc. American Control Conference, Marriott Waterfront, Baltimore, MD, USA June 30-July 02.
[30] Farschman C.A., Viswanath K.P. and Ydstie B.E. (1998). Process systems and inventory control. AIChE journal, 44(8), 1841-1857.
[31] Jillson K.R. and Ydstie B.E. (2007). Process networks with decentralized inventory and flow control. J. Proc. Control, 17:399-413.
[32] Khalil H.K. (2002). Nonlinear systems. 2nd edition, Prentice Hall.
[33] Couenne F., Jallut C., Maschke B., Breedveld P.C. and Tayakout M. (2006). Bond graph modelling for chemical reactors. Mathematical and Computer Modelling of Dynamical Systems, 12(2-3):159-174.
[34] Grmela Miroslav (2012). Fluctuations in extended mass-action-law dynamics. Physica D, 241:976-986.
[35] Hoang N. Ha, Dochain D. and Hudon N. (2014). A thermodynamic approach towards Lyapunov based control of reaction rate. Proc. 19th IFAC World Congress, Cape Town, South Africa. pp. 9117-9122.
[36] Hoang N. Ha, Dochain D. and Ydstie B.E. (2014). Partial inventory control of the CSTR via reaction- dependent generalized inventories. Proc. 19th IFAC World Congress, Cape Town, South Africa. pp. 9123- 9128.
[37] N. Ha Hoang and Denis Dochain (2013). On an evolution criterion of homogeneous multi-component mixtures with chemical transformation. Syst. & Contr Let., 62(2):170-177.
[38] Hoang N. Ha, Couenne F., Le Gorrec Y., Chen C.L. and Ydstie B.E. (2013). Passivity-based nonlinear control of CSTR via asymptotic observers. Annual Reviews in Control, 37(2):278-288.
[39] Nguyen Thanh Sang and Hoang Ngoc Ha (2014). Optimization and simulation in chemical engineering: Application to the production of Cyclopentenol from Cyclopentadiene. The VNU Journal of Science, 30(6S-A):32-43.
[40] Van Heerden C. (1953). Autothermic processes. Ind. Eng. Chem., 45(6):1242-1247.
[41] Isidori Alberto. Nonlinear control systems. 3rd edition, Springer, 1989.