Dynamic Neural Network Based Nonlinear Control of a Distillation Column

Author(s)
Feng Li

ABSTRACT

Taking advantage of the knowledge of top and bottom compositions of a distillation column, a dynamic neural network (DNN) is designed to identify the input-output relationship of the column. The weight-training algorithm is derived from a Lyapunov function. Based on this empirical model, a nonlinear H_{∞} controller is synthesized. The effectiveness of the control strategy is demonstrated using simulation results.

Taking advantage of the knowledge of top and bottom compositions of a distillation column, a dynamic neural network (DNN) is designed to identify the input-output relationship of the column. The weight-training algorithm is derived from a Lyapunov function. Based on this empirical model, a nonlinear H

Cite this paper

nullF. Li, "Dynamic Neural Network Based Nonlinear Control of a Distillation Column,"*Intelligent Control and Automation*, Vol. 2 No. 4, 2011, pp. 383-387. doi: 10.4236/ica.2011.24043.

nullF. Li, "Dynamic Neural Network Based Nonlinear Control of a Distillation Column,"

References

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[2] S. Skogestad and M. Morari, “Understanding the Dynamic Behavior of Distillation Columns,” Industrial & Engineering Chemistry Research, Vol. 27, No. 10, 1988, pp. 1848-1862. doi:10.1021/ie00082a018

[3] J. Lévine and P. Rouchon, “Quality Control of Binary Distillation Columns via Nonlinear Aggregated Models,” Automatica, Vol. 27, No. 3, 1991, pp. 463-480. doi:10.1016/0005-1098(91)90104-A

[4] F. Viel, E. Busvelle and J. P. Gauthier. “A Stable Control Structure for Binary Distillation Columns,” International Journal of Control, Vol. 67, No. 4, 1997, pp. 475-505. doi:10.1080/002071797224036

[5] N. F. Jerome and W. H. Ray, “High-Performance Multivariable Control Strategies for Systems Having Time Delays,” AIChE, Vol. 32, No. 6, 1986, pp. 914-931. doi:10.1002/aic.690320603

[6] S. Skogestad, M. Morari and J. C. Doyle, “Robust Control of Ill-Conditioned Plants: High Purity Distillation,” IEEE Transactions on Automatic Control, Vol. 33, No. 12, 1988, pp. 1092-1105. doi:10.1109/9.14431

[7] J. Savkovic, “Neural Net Controller by Inverse Modeling for a Distillation Plant,” Computers & Chemical Engineering, Vol. 20, No. S2, 1996, pp. S925-S930. doi:10.1016/0098-1354(96)00162-7

[8] W. Yu, S. Alexander and J. A. Poznykz, “Neuro Control for Multicomponent Distillation Column,” 1999 IFAC World Congress, Beijing, 5-9 July 1999, pp. 379-383.

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[10] K. Hunt, J. D. Sbarbaro, R. Zbikowshi and P. J. Gawthrop, “Neural Networks for Control Systems—A Survey,” Automatica, Vol. 28, No. 6, 1992, pp. 1083-1112. doi:10.1016/0005-1098(92)90053-I

[11] M. J. Wills, G. A. Montague, C. Di Massimo, M. T. Tham and A. J. Morris, “Artificial Neural Networks in Process Esitmation and Control,” Automatica, Vol. 28, No. 6, 1992, pp. 1181-1187. doi:10.1016/0005-1098(92)90059-O

[12] P. Turner, G. Montagueand J. Morris, “Dynamic Neural Networks in Nonlinear Predictive Control,” Computers & Chemical Engineering, Vol. 20, No. S2, 1996, pp. S937- S942. doi:10.1016/0098-1354(96)00164-0

[13] S. Li and F. Li, “Dynamic Neural Network Based Nonlinear Adaptive Control for a Distillation Column,” Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, June 28-July 2 2000, pp. 3087-3091.

[14] S. R. Li, H. T. Shi and F. Li. “RBFNN Based Direct Adaptive Control of MIMO Nonlinear System and Its Application to a Distillation Column,” Proceedings of World Conference of Intelligent Control and Automation, Shanghai, 10-14 June 2002, pp. 2896-2900.

[15] D. Muhammad, Z. Ahmad and N. Aziz, “Implementation of Internal Model Control (IMC) in Continuous Distillation Column,” Proceedings of the 5th International Symposium on Design, Operation and Control of Chemical Processes, Singapore, 16 February 2010, pp. 812-821.

[16] H. E. Tonnang and A. Olatunbosun, “Neural Network Controller for a Crude Oil Distillation Column,” Journal of Engineering and Applied Sciences, Vol. 5, No. 6, 2010, pp. 74-82.

[17] M. ?awryńczuk, “Explicit Nonlinear Predictive Control of a Distillation Column Based on Neural Models,” Chemical Engineering & Technology, Vol. 32, No. 10, 2011, pp. 1578-1587.

[18] S. R. Li, “Nonlinear H? Controller Design for a Class of Nonlinear Control Systems,” Proceedings of 23rd IEEE Industrial Electronics, Control and Instrumentation, New Orleans, 9-14 November 1997, pp. 291-294.

[19] A. Isidori, “Nonlinear Control Systems,” 2nd Edition, Springer-Verlag, New York, 1989.

[20] A. Isidori and A. Astolfi, “Disturbance Attenuation and H? Control via Measurement Feedback in Nonlinear Systems,” IEEE Transactions on Automatic Control, Vol. 37, No. 9, 1992, pp. 1283-1293. doi:10.1109/9.159566

[21] V. M. Popov, “Hyperstability of Control Systems,” 2nd Edition, Springer-Verlag, New York, 1973.

[1] T. J. McAvoy and Y. H. Wang, “Survey of Recent Distillation Control Results,” ISA Transactions, Vol. 25, No. 1, 1986, pp. 5-21.

[2] S. Skogestad and M. Morari, “Understanding the Dynamic Behavior of Distillation Columns,” Industrial & Engineering Chemistry Research, Vol. 27, No. 10, 1988, pp. 1848-1862. doi:10.1021/ie00082a018

[3] J. Lévine and P. Rouchon, “Quality Control of Binary Distillation Columns via Nonlinear Aggregated Models,” Automatica, Vol. 27, No. 3, 1991, pp. 463-480. doi:10.1016/0005-1098(91)90104-A

[4] F. Viel, E. Busvelle and J. P. Gauthier. “A Stable Control Structure for Binary Distillation Columns,” International Journal of Control, Vol. 67, No. 4, 1997, pp. 475-505. doi:10.1080/002071797224036

[5] N. F. Jerome and W. H. Ray, “High-Performance Multivariable Control Strategies for Systems Having Time Delays,” AIChE, Vol. 32, No. 6, 1986, pp. 914-931. doi:10.1002/aic.690320603

[6] S. Skogestad, M. Morari and J. C. Doyle, “Robust Control of Ill-Conditioned Plants: High Purity Distillation,” IEEE Transactions on Automatic Control, Vol. 33, No. 12, 1988, pp. 1092-1105. doi:10.1109/9.14431

[7] J. Savkovic, “Neural Net Controller by Inverse Modeling for a Distillation Plant,” Computers & Chemical Engineering, Vol. 20, No. S2, 1996, pp. S925-S930. doi:10.1016/0098-1354(96)00162-7

[8] W. Yu, S. Alexander and J. A. Poznykz, “Neuro Control for Multicomponent Distillation Column,” 1999 IFAC World Congress, Beijing, 5-9 July 1999, pp. 379-383.

[9] G. Cybenko, “Approximation by Superpositions of Sigmoidal Function,” Mathematics of Control, Signals, and Systems, Vol. 5, No. 4, 1989, pp. 303-314. doi:10.1007/BF02551274

[10] K. Hunt, J. D. Sbarbaro, R. Zbikowshi and P. J. Gawthrop, “Neural Networks for Control Systems—A Survey,” Automatica, Vol. 28, No. 6, 1992, pp. 1083-1112. doi:10.1016/0005-1098(92)90053-I

[11] M. J. Wills, G. A. Montague, C. Di Massimo, M. T. Tham and A. J. Morris, “Artificial Neural Networks in Process Esitmation and Control,” Automatica, Vol. 28, No. 6, 1992, pp. 1181-1187. doi:10.1016/0005-1098(92)90059-O

[12] P. Turner, G. Montagueand J. Morris, “Dynamic Neural Networks in Nonlinear Predictive Control,” Computers & Chemical Engineering, Vol. 20, No. S2, 1996, pp. S937- S942. doi:10.1016/0098-1354(96)00164-0

[13] S. Li and F. Li, “Dynamic Neural Network Based Nonlinear Adaptive Control for a Distillation Column,” Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, June 28-July 2 2000, pp. 3087-3091.

[14] S. R. Li, H. T. Shi and F. Li. “RBFNN Based Direct Adaptive Control of MIMO Nonlinear System and Its Application to a Distillation Column,” Proceedings of World Conference of Intelligent Control and Automation, Shanghai, 10-14 June 2002, pp. 2896-2900.

[15] D. Muhammad, Z. Ahmad and N. Aziz, “Implementation of Internal Model Control (IMC) in Continuous Distillation Column,” Proceedings of the 5th International Symposium on Design, Operation and Control of Chemical Processes, Singapore, 16 February 2010, pp. 812-821.

[16] H. E. Tonnang and A. Olatunbosun, “Neural Network Controller for a Crude Oil Distillation Column,” Journal of Engineering and Applied Sciences, Vol. 5, No. 6, 2010, pp. 74-82.

[17] M. ?awryńczuk, “Explicit Nonlinear Predictive Control of a Distillation Column Based on Neural Models,” Chemical Engineering & Technology, Vol. 32, No. 10, 2011, pp. 1578-1587.

[18] S. R. Li, “Nonlinear H? Controller Design for a Class of Nonlinear Control Systems,” Proceedings of 23rd IEEE Industrial Electronics, Control and Instrumentation, New Orleans, 9-14 November 1997, pp. 291-294.

[19] A. Isidori, “Nonlinear Control Systems,” 2nd Edition, Springer-Verlag, New York, 1989.

[20] A. Isidori and A. Astolfi, “Disturbance Attenuation and H? Control via Measurement Feedback in Nonlinear Systems,” IEEE Transactions on Automatic Control, Vol. 37, No. 9, 1992, pp. 1283-1293. doi:10.1109/9.159566

[21] V. M. Popov, “Hyperstability of Control Systems,” 2nd Edition, Springer-Verlag, New York, 1973.