Cover
Vol. 15 No. 2 (2019)

Published: December 31, 2019

Pages: 10-20

Original Article

Liquid Mixing Enhancement by PLC-Based Chaotic Dynamics Implementation

Abstract

In this paper, we present a new programmable chaotic circuit based on the dynamical chaotic system introduced by E. Lorenz. The design and realization of the model are accomplished by using a programmable logic controller (PLC). The system can be modeled and realized with a structured texted. The nonlinear differential equations of Lorenz model are solved numerically. The generated chaotic signal by using PLC is applied to a single- phase induction motor via a variable frequency drive to create a chaotic perturbation in the experiments of liquid mixing. Colorization liquid experiments shows that the generated chaotic motion effectively makes an enhancement of the mixing process in the stirred-tank mixer model in our laboratory.

References

  1. G. A. Al-Suhail, F. R. Tahir, M. H. Abd, V.T. Pham, and L. Fortuna, “Modelling of long-wave chaotic radar system for anti-stealth applications,” Communications in Nonlinear Science and Numerical Simulation, vol. 57, pp. 80-96, 2018.
  2. M. H. Abd, F. R. Tahir, G. A. Al-Suhail, and V.-T. Pham, “An adaptive observer synchronization using chaotic time-delay system for secure communication,” Nonlinear Dynamics, vol. 90, no. 4, pp. 2583-2598, 2017.
  3. F. R. Tahir, K. M. Abdul-Hassan, M. A. Abdullah, V.-T. Pham, T. M. Hoang, and X. Wang, “Analysis and Stabilization of Chaos in Permanent Magnet DC Motor Driver,” Int. J. Bifurc. Chaos, vol. 27, no. 11, p. 1750173, 2017..
  4. G. Chen, and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and chaos, vol. 9, no. 07, pp. 1465-1466, 1999.
  5. S. Yu, J. Lu, G. Chen, and X. Yu, “Generating heteroclinic loops into switching systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 58, no. 5, pp. 314-318, 2011.
  6. J. Lü, G. Chen, D. Cheng, and S. Celikovsky, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos, vol. 12, no. 12, pp. 29172926, 2002
  7. J. Lü, and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and chaos, vol. 12, no. 03, pp. 659-661, 2002.
  8. A. Buscarino, L. Fortuna, and M. Frasca, “Experimental robust synchronization of hyperchaotic circuits,” Phys. D Nonlinear Phenom. , vol. 238, no. 18, pp. 1917–1922, 2009.
  9. J. Lü, and G. Chen, “Generating multiscroll chaotic attractors: theories, methods and applications,” International Journal of Bifurcation and Chaos, vol. 16, no. 04, pp. 775-858, 2006.
  10. R. Caponetto, G. Dongola, L. Fortuna, and A. controllers,” Commun. Nonlinear Sci. Numer. Simul., vol. 15, no. 4, pp. 997–1007, 2010.
  11. S. Abdallah, and S. Nijmeh, “Two axes sun tracking system with PLC control,” Energy Conversion and Management, vol. 45, no. 11-12, pp. 1931-1939, 2004.
  12. K. Yau and K.-P. Chow, “PLC forensics based on control program logic change detection,” J. Digit. Forensics, Secur. Law, vol. 10, no. 4, p. 5, 2015.
  13. S. Abdallah, and R. Abu-Mallouh, “Heating systems with PLC and frequency control,” Energy Conversion and Management, vol. 49, no. 11, pp. 3356-3361, 2008.
  14. R. Bayindir, and Y. Cetinceviz, “A water pumping control system with a programmable logic controller (PLC) and industrial wireless modules for industrial plants--an experimental setup,” ISA Trans, vol. 50, no. 2, pp. 321-8, Apr, 2011.
  15. Z. Zhang, Chen and S. Yu, "Hyperchaotic signal generation via DSP for efficient perturbations to liquid mixing", Applications, vol. 37, no. 1, pp. 31-41, 2009. Available: 10.1002/cta.470 [Accessed 11 June 2019].
  16. S. Ye, K. T. Chau, and S. Member, “Chaoization of DC Motors for Industrial Mixing,” vol. 54, no. 4, pp. 2024–2032, 2007.
  17. Z. Zhang and G. Chen, "Liquid mixing enhancement by chaotic perturbations in stirred tanks", Chaos, Solitons & Fractals, vol. 36, no. 1, pp. 144-149, 2008. Available: 10.1016/j.chaos.2006.06.024.
  18. G. Valencia-Palomo, and J. A. Rossiter, “Novel programmable logic controller Laguerre functions and multiparametric solutions,” IET Control Theory & Applications, vol. 6, no. 8, pp. 1003-1014, 2012.
  19. X. Yang, Q. Zhu, and H. Xu, “Design and practice of an elevator control system based on PLC,” Proc. - 2008 Work. Power Electron. Intell. Transp. Syst. PEITS 2008, pp. 94–99, 2008.
  20. N. He, V. Oke, and G. Allen, "Model-based verification of PLC programs using Simulink design." pp. 0211-0216.
  21. M. Jamro, “POU-oriented unit testing of iec 61131-3 control software,” IEEE Transactions on 1129, 2015
  22. S. S. Peng, and M. C. Zhou, “Ladder diagram and Petri-net-based discrete-event control design methods,” IEEE Transactions on Systems, Man, را ﻗﯾﺔ ﻟﻠﮭﻧ رو ﻧﯾﺔ and Cybernetics, Part C (Applications and Reviews), vol. 34, no. 4, pp. 523-531, 2004.
  23. T. Ovatman, A. Aral, D. Polat, and A. O. Ünver, “An overview of model checking practices on verification of PLC software,” Software & Systems Modeling, vol. 15, no. 4, pp. 937-960, 2014.
  24. M. A. Aseeri, M. I. Sobhy, and P. Lee, “Lorenz chaotic model using filed programmable Symposium on Circuits and Systems, 2002. MWSCAS-2002., 2002, vol. 1, p. I-527.
  25. R. Caponetto, A. Di Mauro, L. Fortuna, and M. Frasca, “Field programmable analog array to Bifurc. Chaos, vol. 15, no. 5, pp. 1829–1836, 2005.
  26. S. Yu, J. Lü, W. K. S. Tang, and G. Chen, “A realization via digital signal processors,” Chaos An Interdiscip. J. Nonlinear Sci., vol. 16, no. 3, p. 33126, 2006.
  27. E. Lorenz, ''Deterministic nonperiodic flow'', Journal of the atmospheric sciences, Vol. 20, pp. 130-141(1963).