SKT içeren çok değişkenli bir sürecin matematiksel modellenmesi ve dinamik etkileşim giderme

Öz

Bu makalede, bir sürekli karıştırılan tank (SKT) içeren sıcaklık ve debi sürecinin matematiksel modeli ve dinamik etkileşim giderici tasarımı sunulmuştur. İki doğrusal olmayan diferansiyel denklemden oluşan dinamik matematiksel model geliştirilmiştir. Çok değişkenli (ÇD) sistem modeli, döngü etkileşimlerini dinamik yöntemle gidermeyi kolaylaştırmak için doğrusallaştırılarak transfer fonksiyonlarıyla ifade edilmiştir. Dinamik etkileşim giderme tasarımı elde edilen doğrusallaştırılmış model yardımıyla gerçekleştirilmiş ve döngülerin etkileşimlerinin ortadan kaldırılarak sürecin ayrıştırılmış tek döngülü geri beslemeli denetim için uygun hale getirildiği gösterilmiştir.

Anahtar Kelimeler

• Matematiksel modelleme,SKT,Dinamik Etkileşim giderme

Mathematical modeling and dynamic decoupling of a multivariable process with a CST

Abstract

In this paper, mathematical modeling and dynamic decoupler design of a temperature and flow rate process with a continuously stirred tank (CST) is presented. A dynamic mathematical model of the process that consists of two nonlinear differential equations is developed. The multivariable (MV) system model is linearized to make the elimination of loop interaction easier through dynamic decoupling and expressed in terms of system transfer functions. Dynamic decoupling is designed using obtained linearized model and it is shown that loop interactions are eliminated making the process suitable for decomposed single loop feedback controllers.

Keywords

• Mathematical Modelling,CST,Dynamic Decoupling

Kaynakça

1. Salehi S, Shahrokhi M. “Adaptive fuzzy backstepping approach for temperature control of continuous stirred tank reactors”. Fuzzy Sets and Systems, 160(12), 1804-1818, 2009.
2. Cloutier JR, Stansbery DT. “Control of a continuously stirred tank reactor using an asymmetric solution of the state-dependent Riccati equation”. IEEE International Conference on Control Applications, Hawaii, USA, 22-27 August 1999.
3. Yu DL, Gomm JB. “Implementation of neural network predictive control to a multivariable chemical reactor”. Control Engineering Practice, 11(11), 1315-1323, 2003.
4. Hoang H, Couenne F, Jallut C, Le Gorrec Y. “Lyapunov based control for non-isothermal continuous stirred tank reactor”. IFAC Proceedings Volumes, 41(2), 3854-3858, 2008.
5. Alvarez-Ramirez J, Morales A. “PI control of continuously stirred tank reactors: stability and performance”. Chemical Engineering Science, 55(22), 5497-5507, 2000.
6. Alvarez-Ramirez J, Suarez R, Femat R. “Control of continuous-stirred tank reactors: stabilization with unknown reaction rates”. Chemical Engineering Science, 51(17), 4183-4188, 1996.
7. Zhang T, Guay M. “Adaptive nonlinear control of continuously stirred tank reactor systems”. IEEE American Control Conference, Arlington, USA, 25-27 June 2001.
8. Tokuda M, Yamamoto T, Monden Y. “A design of multiloop PID controllers with neural-net based decoupler”. IEEE International Symposium on Intelligent Control, Vancouver, Canada, 30 October 2002.

9. Numsomran A, Wongkhum T, Suksri T, Nilas P, Chaoraingern J. “Design of decoupled controller for TITO system using characteristic ratio assignment”. ICCAS'07 International Conference on Control, Automation and Systems, Seoul, Korea, 17-20 October 2007.
10. Qinling Z, Zhiqiang G. “On decoupling control of uncertain and multivariable systems with time delays”. SICE 2015 54th Annual Conference of the Society of Instrument and Control Engineers of Japan, Hangzhou, China, 28-30 July 2015.
11. Dym C. Principles of Mathematical Modeling. London, UK, Elsevier Academic Press, 2004.
12. Seborg DE, Mellichamp DA, Edgar TF, Doyle III, FJ. Process Dynamics and Control. New York, USA, John Wiley & Sons, 2010.
13. Janevska G. “Mathematical Modeling of Pump System”. EIIC the 2nd Electronic International Interdisciplinary Conference, Zilina, Czech Republic, 2-6 September 2013.
14. Charles MO, Oku DE, Faithpraise FO, Obot EP. “Simulation and control of PMDC motor current and torque”. International Journal of Advanced Scientific and Technical Research, 5(7), 367-375, 2015.
15. Bernard A. Speed Control of Separately Excited DC Motor Using Artificial Intelligent Approach. PhD Thesis, University Tun Hussein Onn Malaysia, 2013.
16. Smith CA, Corripio AB. Principles and Practice of Automatic Process Control. New York, USA, Wiley, 2005.
17. Cochin I, Cadwallender W. Analysis and Design of Dynamic Systems. Prentice Hall, Reading, MA, USA, 1997.
18. Nijmeijer H, Respondek W. “Dynamic input-output decoupling of nonlinear control systems”. IEEE Transactions on Automatic Control, 33(11), 1065-1070, 1988.