International Journal of Systems Science and Applied Mathematics

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Model Optimal Control of the Four Tank System

Received: 10 September 2016    Accepted: 26 September 2016    Published: 15 October 2016
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Abstract

The four tank system is a widely used mechatronic laboratory system in control theory. This work is aimed to choose the best controller for the four tank system (4TS) with two input force. The optimal control is one of the best techniques in a sense of performance, and is demonstrated for the level control of 4TS. There are several controller systems in optimal control for this purpose which are Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian Regulator (LQGR), H2, and H controller system. These controllers will be applied to this important mechatronic system (4TS) separately, and compared the performance for disturbance rejection with each other to study the effect of these controller systems on the 4TS controlled state. On the other hand the performances of the optimal control systems are compared with other controller performances available in literatures for the same case study. The results indicate that the Linear Quadratic Regulator (LQR) provides significant improvement over completely controllers. The simulations were carried out in MATLAB-Simulink.

DOI 10.11648/j.ijssam.20160104.11
Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4, November 2016)
Page(s) 30-41
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mechatronic System; Optimal Control; LQR; LQGR; H2 Method; H Method

References
[1] Chianeh, H. A. , Stigter, J. D. and Keesmana, K. J. (2011), “ Optimal input design for parameter estimation in a single and double tank system through direct control of parametric output sensitivities”, J. of Process Control, Vol. 21, No. 1, pp. 111–118.
[2] Skogestad, S. and Postlethwaite, I. (2001), “Multivariable Feedback Control”, Prentice Hall, New Jersey.
[3] Kovács, L., Borbély, E. and Benyó, Z. (2010), “Optimal Control of the Three Tank System in H2/H∞ space”, Proceedings of the 8th IEEE International Symposium on Applied Machine Intelligence and Informatics, Slovakia, 28-30 January.
[4] Iplikci, S. (2010), “A support vector machine based control application to the experimental three-tank system”, J. ISA Transactions, Vol. 49. No. 3, pp. 376–386.
[5] Altinisik, U. and Yildirim, M. (2012), “ A new fault tolerant control approach for the three-tank system using data mining”, J. Computers & Electrical Engineering, Vol. 38, No. 6, pp. 1627–1635.
[6] Sarailoo, M., Rahmani, Z. and Rezaie, Z. (2015), “A novel model predictive control scheme based on bees algorithm in a class of nonlinear systems: Application to a three tank system”, J. Neurocomputing, Vol. 152, No. 25, pp. 294–304.
[7] Gatzke, E. P., Meadows, E. S., Wang, C. and Doyle III, F. J. (2000), “Model Based Control of a Four-Tank System”, J. Computers and Chemical Engineering, Vol. 24, No. 2-7, pp. 1503-1509.
[8] Mercangoz, M., Francis, J. and Doyle III, F. J (2007), “Distributed model predictive control of an experimental four-tank system”, J. Process Control, Vol. 17, pp. 297-308.
[9] Drca, I. (2007), “Nonlinear Model Predictive Control of the Four Tank Process”, M.Sc. Dissertation, University of Seville, Stockholm, Sweden.
[10] Alvarado, I., Limon, D., la Peña, D. M., Maestre, J. M., Ridao, M. A., Scheu, H., Marquardt, W., Negenborn, R. R., De Schutter, B., Valencia, F. and Espinosa, J. (2011), “A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank benchmark”, J. of Process Control, Vol. 21, No. 5, pp.800–815.
[11] Ruscio, D. D. (2012), “ Discrete LQ optimal control with integral action: A simple controller on incremental form for MIMO systems”, J. Modeling, Identification and Control, Vol. 33, No. 2, pp. 35-44.
[12] Balsemin, A. and Picci, G. (2013), “Applications Oriented Optimal Input Design: An Analysis of a quadruple water tank process”, M.Sc. Dissertation, University of Padova, Italy.
[13] Khalid, U., Shah, Y. A., Qamar, S., Gohar, W., Raza, R. and Shah, W. A. (2014), “Flow and level control of coupled four tanks system using artificial neural network”, American Journal of Computation, Communication and Control, Vol. 1, No. 2, pp. 30-35.
[14] Gouta, H., Said, S. H. and M’sahli, F. (2015), “Model-based Predictive and Backstepping controllers for a state coupled four-tank system with bounded control inputs: A comparative study”, J. the Franklin Institute, Vol. 352, No. 11, pp. 4864-4889.
[15] Dai, L. and Åstrӧm, K. (1999), “Dynamic matrix control of a quadruple tank process”, Proceedings of The World Congress 14th IFAC, Beijing, China, July, pp. 295–300.
[16] Vadigepalli, R., Gatzke, E. P. and Doyle III, F. J. (2001), “Robust control of a multivariable experimental four-tank system”, Ind. Eng. Chem. Res. Vol. 40, No. 8, pp. 1916–1927.
[17] Abbas, H., Qamar, S. (2012), “Sliding Mode Control For Coupled-Tank Liquid Level Control System”, Proceedings of the 10th International Conference on Frontiers of Information Technology (FIT), Pakistan, 17-19 December, pp. 325-330.
[18] Wu, Dongrui, and Woei, W. T. (2004), “A type-2 fuzzy logic controller for the liquid-level process”, Proceedings of IEEE International Conference on Fuzzy System, Vol. 2, pp. 953-958.
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[20] Miaomiao ma, Chenz, H., Findeisen, R. and Ower, F. A. (2012), “Non-linear receding horizon control of quadruple tank system and real time implementation”, International Journal of Innovative Computing, Information and Control, Vol. 8, pp. 7083-7093.
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Author Information
  • Southeast University, International Institute for Urban Systems Engineering, Nanjing, China; Department of Mechanical Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt

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    Wael A. Altabey. (2016). Model Optimal Control of the Four Tank System. International Journal of Systems Science and Applied Mathematics, 1(4), 30-41. https://doi.org/10.11648/j.ijssam.20160104.11

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    Wael A. Altabey. Model Optimal Control of the Four Tank System. Int. J. Syst. Sci. Appl. Math. 2016, 1(4), 30-41. doi: 10.11648/j.ijssam.20160104.11

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    Wael A. Altabey. Model Optimal Control of the Four Tank System. Int J Syst Sci Appl Math. 2016;1(4):30-41. doi: 10.11648/j.ijssam.20160104.11

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  • @article{10.11648/j.ijssam.20160104.11,
      author = {Wael A. Altabey},
      title = {Model Optimal Control of the Four Tank System},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {1},
      number = {4},
      pages = {30-41},
      doi = {10.11648/j.ijssam.20160104.11},
      url = {https://doi.org/10.11648/j.ijssam.20160104.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijssam.20160104.11},
      abstract = {The four tank system is a widely used mechatronic laboratory system in control theory. This work is aimed to choose the best controller for the four tank system (4TS) with two input force. The optimal control is one of the best techniques in a sense of performance, and is demonstrated for the level control of 4TS. There are several controller systems in optimal control for this purpose which are Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian Regulator (LQGR), H2, and H∞ controller system. These controllers will be applied to this important mechatronic system (4TS) separately, and compared the performance for disturbance rejection with each other to study the effect of these controller systems on the 4TS controlled state. On the other hand the performances of the optimal control systems are compared with other controller performances available in literatures for the same case study. The results indicate that the Linear Quadratic Regulator (LQR) provides significant improvement over completely controllers. The simulations were carried out in MATLAB-Simulink.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Model Optimal Control of the Four Tank System
    AU  - Wael A. Altabey
    Y1  - 2016/10/15
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijssam.20160104.11
    DO  - 10.11648/j.ijssam.20160104.11
    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
    JO  - International Journal of Systems Science and Applied Mathematics
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    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ijssam.20160104.11
    AB  - The four tank system is a widely used mechatronic laboratory system in control theory. This work is aimed to choose the best controller for the four tank system (4TS) with two input force. The optimal control is one of the best techniques in a sense of performance, and is demonstrated for the level control of 4TS. There are several controller systems in optimal control for this purpose which are Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian Regulator (LQGR), H2, and H∞ controller system. These controllers will be applied to this important mechatronic system (4TS) separately, and compared the performance for disturbance rejection with each other to study the effect of these controller systems on the 4TS controlled state. On the other hand the performances of the optimal control systems are compared with other controller performances available in literatures for the same case study. The results indicate that the Linear Quadratic Regulator (LQR) provides significant improvement over completely controllers. The simulations were carried out in MATLAB-Simulink.
    VL  - 1
    IS  - 4
    ER  - 

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