Volume 12 Number 2
April 2015
Article Contents
Kayode Owa, Sanjay Sharma and Robert Sutton. A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System. International Journal of Automation and Computing, vol. 12, no. 2, pp. 156-170, 2015. doi: 10.1007/s11633-014-0825-2
Cite as: Kayode Owa, Sanjay Sharma and Robert Sutton. A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System. International Journal of Automation and Computing, vol. 12, no. 2, pp. 156-170, 2015. doi: 10.1007/s11633-014-0825-2

A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System

  • Received: 2013-11-17
Fund Project:

This work was supported by Petroleum Training Development Fund, Nigeria.

  • In this paper, a novel real time non-linear model predictive controller (NMPC) for a multi-variable coupled tank system (CTS) is designed. CTSs are highly non-linear and can be found in many industrial process applications. The involvement of multi-input multi-output (MIMO) system makes the design of an effective controller a challenging task. MIMO systems have inherent couplings, interactions in-between the process input-output variables and generally have an complex internal structure. The aim of this paper is to design, simulate, and implement a novel real time constrained NMPC for a multi-variable CTS with the aid of intelligent system techniques. There are two major formidable challenges hindering the success of the implementation of a NMPC strategy in the MIMO case. The first is the difficulty of obtaining a good non-linear model by training a non-convex complex network to avoid being trapped in a local minimum solution. The second is the online real time optimisation (RTO) of the manipulated variable at every sampling time. A novel wavelet neural network (WNN) with high predicting precision and time-frequency localisation characteristic was selected for an MIMO model and a fast stochastic wavelet gradient algorithm was used for initial training of the network. Furthermore, a genetic algorithm was used to obtain the optimised parameters of the WNN as well as the RTO during the NMPC strategy. The proposed strategy performed well in both simulation and real time on an MIMO CTS. The results indicated that WNN provided better trajectory regulation with less mean-squared-error and average control energy compared to an artificial neural network. It is also shown that the WNN is more robust during abnormal operating conditions.
  • [1] R. Findeisen, F. Allgower. An introduction to non-linear model predictive control. Information and Control, vol. 11, no. 1-2, pp. 1-23, 2002.
    [2] D. E. Seborg, T. F. Edgar, D. A. Mellichamp, F. J. Doyle III. Process Dynamics and Control, 3rd ed., Inc United States: John Wiley Sons, 2011.
    [3] E. Laubwald. Coupled tank system. Control Systems Prin-ciples, pp. 1-8, 2005.
    [4] K. Owa, S. K. Sharma, R. Sutton. Non-linear model pre-dictive control strategy based on soft computing approaches and real time implementation on a coupled-tank system. In-ternational Journal of Advanced Research in Computer Sci-ence and Software Engineering, vol. 3, no. 5, pp. 1350-1359, 2013.
    [5] W. Grega, A. Maciejczyk. Digital control of a tank system. IEEE Transactions on Education, vol. 37, no. 3, pp. 271-276, 1994.
    [6] S. M. Nawi, A. N. Abdalla, M. S. Ramli. Improved coupled tank liquid levels system based on hybrid genetic-immune adaptive tuning of PI controller. In Proceedings of the Inter-national Conference on Electrical, Control and Computer Engineering, IEEE, Pahang, Malaysia, pp. 247-252, 2011.
    [7] M. U. Khalid, M. B. Kadri. Liquid level control of non-linear coupled tanks system using linear model predictive control. In Proceedings of International Conference on Emerging Technologies, no. 1, pp. 1-5, 2012.
    [8] I. Holič, V. Vesely. Robust PID controller design for coupled-tank process. In Proceedings of the 18th Interna-tional Conference on Process Control, Tatranska Lomnica, Slovakia, pp. 506-512, 2011.
    [9] V. Ramakrishnan, Y. Zhuang, S. Y. Hu, J. P. Chen, C. C. Ko, B. M. Chen, K. C. Tan. Development of a web-based control experiment for a coupled tank apparatus. In Pro-ceedings of American Control Conference, Chicago, Illinois, USA, pp. 4409-4413, 2000.
    [10] M. F. Rahmat, S. M. Rozali. Modeling and controller de-sign for a coupled-tank liquid level system: Analysis and comparison. Jurnal Teknology, vol. 48, no. D, pp. 113-141, 2008.
    [11] M. Kubalcik, V. Bobal. Adaptive control of three-tank-system: Comparison of two methods. In Proceedings of the 16th Mediterranean Conference on Control and Automa-tion, IEEE, Ajaccio, pp. 1041-1046, 2008.
    [12] M. Majstorovic, I. Nikolic, J. Radovic, G. Kvaščev. Neural network control approach for a two-tank system. In Pro-ceedings of the 9th Symposium on Neural Network Appli-cations in Electrical Engineering, IEEE, Belgrade, Serbia, pp. 215-218, 2008.
    [13] I. Alvarado, D. Limon, A. Ferramosca, E. F. Cama-cho. Robust tubed-based MPC for tracking applied to the quadruple-tank process. In Proceedings of the 17th IEEE International Conference on Control Applications, IEEE, San Antonio, Texas, USA, vol. 3, no. 3, pp. 305-310, 2008.
    [14] TecQuipment. CE105MV. Control Engineering, Sensors and Instrumentation, pp. 1-3, 2013.
    [15] K. Owa, S. K. Sharma, R. Sutton. Optimised multivariable non-linear predictive control for coupled tank applications. In Proceedings of the 1st IET Control and Automation Con-ference, Conference Aston Lakeside Centre, IET, Birming-ham, UK, pp. 1-6, 2013.
    [16] T. Tani, S. Murakoshi, M. Umano. Neuro-fuzzy hybrid con-trol system of tank level in petroleum plant. IEEE Trans-actions on Fuzzy Systems, vol. 4, no. 3, pp. 360-368, 1996.
    [17] B. Guo, A. Jiang, X. Hua, A. Jutan. Non-linear adaptive control for multivariable chemical processes. Chemical En-gineering Science, vol. 56, no. 23, pp. 6781-6791, 2001.
    [18] M. Senthilkumar, S. A. Lincon. Design of stabilizing PI controller for coupled tank MIMO process. International Journal of Engineering Research and Development, vol. 3, no. 10, pp. 47-55, 2012.
    [19] K. A. Kosanovich, M. J. Piovoso, V. Rokhlenko, A. Guez. Non-linear adaptive control with parameter estimation of a CSTR. Journal of Process Control, vol. 5, no. 3, pp. 137-148, 1995.
    [20] C. Tricaud, Y. Q. Chen. Linear and non-linear model pre-dictive control using a general purpose optimal control problem solver RIOTS 95. In Proceedings of the 2008 Chi-nese Control Decision Conference, IEEE, Yantai, China, pp. 1552-1557, 2008.
    [21] T. Y. Chai, Y. J. Zhang, H.Wang, C. Y. Su. Data-based vir-tual unmodeled dynamics driven multivariable non-linear adaptive switching control. IEEE Transactions on Neural Networks, vol. 22, no. 12, pp. 2154-2172, 2011.
    [22] R. Jain, T. Vinoprabha, N. Sivakumaran, T. K. Radhakr-ishnan. Design and implementation of controllers for MIMO process. In Proceedings of 2009 International Conference on Advances in Recent Technologies in Communication and Computing, IEEE, Kottayam, Kerala, India, vol. 1, pp. 750-752, 2009.
    [23] J. Richalet. Industrial applications of model based predic-tive control. Automatica, vol. 29, no. 5, pp. 1251-1274, 1993.
    [24] H. Zhao, J. Guiver, R. Neelakantan, L. T. Biegler. A non-linear industrial model predictive controller using in-tegrated PLS and neural net state-space model. Control Engineering Practice, vol. 9, no. 2, pp. 125-133, 2001.
    [25] M. A. S. Al-Qaisy. Linear and non-linear multi-input multi-output model predictive control of continuous stirred tank reactor. Tikrit Journal of Engineering Science, vol. 19, no. 3, pp. 41-57, 2012.
    [26] T. Heckenthaler, S. Engell. Approximately time-optimal fuzzy control of a two-tank system. IEEE Control Systems Magazine, vol. 14, no. 3, pp. 24-30, 1994.
    [27] A. A. R. Diniz, P. R. M. Pires, J. D. de Melo, A. D. D. Neto, A. J. J. L. Filho, S. M. Kanazava. Reinforcement learning for controlling a coupled tank system based on the scheduling of different controllers. In Proceedings of the 2010 Eleventh Brazilian Symposium on Neural Networks, IEEE, Sao Paulo, Brazil, pp. 212-216, 2010.
    [28] M. Senthilkumar, D. S. AbrahamLincon, P. Selvakumar. Design of PI controller using characteristic ratio assign-ment method for coupled tank SISO process. International Journal of Computer Applications, vol. 25, no. 9, pp. 49-53, 2011.
    [29] A. G. Ram, S. A. Lincoln. A model reference-based fuzzy adaptive PI controller for non-linear level process system. International Journal of Research and Reviews in Applied Sciences, vol. 14, no. 2, pp. 477-486, 2013.
    [30] A. Maalla, C. Wei, M. H. Hafiz. Model parameter iden-tification of a coupled industrial tank system based on a wavelet neural network. Dcabes 2008 Proceedings, Vols I II, pp. 1251-1254, 2008.
    [31] Y. Oussar, I. Rivals, L. Personnaz, G. Dreyfus. Training wavelet networks for non-linear dynamic input-output mod-elling. Neurocomputing, vol. 20, no. 1-3, pp. 173-188, 1998.
    [32] D. Huang, Y. Wang, Y. Jin. Non-linear MIMO Adaptive Predictive Control Based on Wavelet Network Model. In Proceedings of International Symposium on Advanced Con-trol of Chemical Processes, IFAC, Hongkong, China, 2004.
    [33] C. J. Lin, C. C. Chin, C. L. Lee. A wavelet-based neuro-fuzzy system and its applications. In Proceedings of the International Joint Conference on Neural Networks, IEEE, Portland, OR, USA, pp. 1921-1926, 2003.
    [34] F. Jajangiri, A. Doustmohammadi, M. B. Menhaj. Identi-fication of twin-tanks dynamics using adaptive wavelet dif-ferential neural networks. In Proceedings of International Joint Conference on Neural Networks, IEEE, Barcelona, Spain, pp. 1-5, 2010.
    [35] J. C. Lu, Z. H. Gu, H. Q. Wang. Research on the appli-cation of the wavelet neural network model in peak load forecasting considering the climate factors. In Proceedings of 2005 International Conference on Machine Learning and Cybernetics, IEEE, Guangzhou, China, pp. 538-543, 2005.
    [36] M. Meng, W. Sun. Short-term load forecasting based on rough set and wavelet neural network. International Con-ference on Computational Intelligence and Security, IEEE, Suzhou, China, pp. 446-450, 2008.
    [37] Y. R. Kuraz. Design of multi wavelet network identifier for multi input multi output nonlinear functions. In Proceed-ings of International Arab Conference on Information Tech-nology, vol. 2, pp. 7-9, 2006.
    [38] L. L. Wei, D. F. Xu, H. Sun, M. X. Zhou. Application of op-timized wavelet neural network based on genetic algorithm in stock market prediction. China Computer and Commu-nication, vol. 11, n5. 1, pp. 130-131, 2001. (in Chinese)
    [39] D. Coca, S. A. Billings. System identification using wavelets. Control Systems Robotics and Automation, vol. 6, pp. 1-10, 2012.
    [40] C. M. Leavey, M. N. James, J. Summerscales, R. Sutton. An introduction to wavelet transforms: A tutorial approach. Insight, vol. 45, no. 5, pp. 344-353, 2003.
    [41] F. Jahangiri, A. Doustmohammadi, M. B. Menhaj. An adaptive wavelet differential neural networks based iden-tifier and its stability analysis. Neurocomputing, vol. 77, no. 1, pp. 12-19, 2012.
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A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System

Fund Project:

This work was supported by Petroleum Training Development Fund, Nigeria.

Abstract: In this paper, a novel real time non-linear model predictive controller (NMPC) for a multi-variable coupled tank system (CTS) is designed. CTSs are highly non-linear and can be found in many industrial process applications. The involvement of multi-input multi-output (MIMO) system makes the design of an effective controller a challenging task. MIMO systems have inherent couplings, interactions in-between the process input-output variables and generally have an complex internal structure. The aim of this paper is to design, simulate, and implement a novel real time constrained NMPC for a multi-variable CTS with the aid of intelligent system techniques. There are two major formidable challenges hindering the success of the implementation of a NMPC strategy in the MIMO case. The first is the difficulty of obtaining a good non-linear model by training a non-convex complex network to avoid being trapped in a local minimum solution. The second is the online real time optimisation (RTO) of the manipulated variable at every sampling time. A novel wavelet neural network (WNN) with high predicting precision and time-frequency localisation characteristic was selected for an MIMO model and a fast stochastic wavelet gradient algorithm was used for initial training of the network. Furthermore, a genetic algorithm was used to obtain the optimised parameters of the WNN as well as the RTO during the NMPC strategy. The proposed strategy performed well in both simulation and real time on an MIMO CTS. The results indicated that WNN provided better trajectory regulation with less mean-squared-error and average control energy compared to an artificial neural network. It is also shown that the WNN is more robust during abnormal operating conditions.

Kayode Owa, Sanjay Sharma and Robert Sutton. A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System. International Journal of Automation and Computing, vol. 12, no. 2, pp. 156-170, 2015. doi: 10.1007/s11633-014-0825-2
Citation: Kayode Owa, Sanjay Sharma and Robert Sutton. A Wavelet Neural Network Based Non-linear Model Predictive Controller for a Multi-variable Coupled Tank System. International Journal of Automation and Computing, vol. 12, no. 2, pp. 156-170, 2015. doi: 10.1007/s11633-014-0825-2
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