A new method based on piecewise affine approximation is proposed to model a distillation column and a novel robust MPC is addressed for PWA systems considering multiple prediction trajectories. Distillation columns have highly nonlinear and complex behavior. However, even in a rigorous dynamical model a number of model simplifications are included. Piecewise affine maps have universal approximation properties which are useful for modeling of nonlinear systems in a wide range of operation. Model predictive control for PWA systems faces multiple prediction trajectories at each sample time due to different system dynamics over prediction horizon. Thus, the computational burden increases exponentially with the prediction horizon length. In order to decrease the computational burden, a suboptimal method is used to solve MIQP problems in MPC for PWA systems in presents of model uncertainty and disturbances. A real distillation column of a debutanizer unit in South Pars Gas refineries is modeled with PWA method and validated using the appropriate nonlinear model. A tube-based model predictive control proposed in such a way that the optimization problem can be solved considering multiple prediction trajectories at each sample time. In the proposed method, the computational burden is increased linearly by the prediction horizon length.

Type of Article: Research paper |
Subject:
Special

Received: 2021/09/13 | Accepted: 2022/01/7 | ePublished ahead of print: 2022/01/19

Received: 2021/09/13 | Accepted: 2022/01/7 | ePublished ahead of print: 2022/01/19

1. [1] P. Petsagkourakis, W. P. Heath, and C. Theodoropoulos, "Stability analysis of piecewise affine systems with multi-model predictive control," Automatica, vol. 111, p. 108539, 2020. [DOI:10.1016/j.automatica.2019.108539]

2. [2] A. Pavlov, I. Shames, and C. Manzie, "Minimax strategy in approximate model predictive control," Automatica, p. 108649, 2019. [DOI:10.1016/j.automatica.2019.108649]

3. [3] F. Ke, Z. Li, and C. Yang, "Robust Tube-Based Predictive Control for Visual Servoing of Constrained Differential-Drive Mobile Robots," IEEE Transactions on Industrial Electronics, vol. 65, pp. 3437-3446, 2018. [DOI:10.1109/TIE.2017.2756595]

4. [4] J. Xu and L. Xie, "2 - Piecewise affine systems," in Control and Estimation of Piecewise Affine Systems, J. Xu and L. Xie, Eds., ed: Woodhead Publishing, 2014, pp. 17-39. [DOI:10.1533/9781782421627.17]

5. [5] R. Iervolino, D. Tangredi, and F. Vasca, "Lyapunov stability for piecewise affine systems via cone-copositivity," Automatica, vol. 81, pp. 22-29, 2017. [DOI:10.1016/j.automatica.2017.03.011]

6. [6] M. Adelirad and A. A. Afzalian, "Multiple prediction trajectories in MPC for PWA systems," in 2020 28th Iranian Conference on Electrical Engineering (ICEE), 2020, pp. 1-6. [DOI:10.1109/ICEE50131.2020.9260767]

7. [7] M. Peña, E. F. Camacho, and S. Piñón, "Hybrid Systems for Solving Model Predictive Control of Piecewise Affine System," IFAC Proceedings Volumes, vol. 36, pp. 57-62, 2003. [DOI:10.1016/S1474-6670(17)36407-8]

8. [8] M. S. Ghasemi and A. A. Afzalian, "Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances," Nonlinear Analysis: Hybrid Systems, vol. 26, pp. 86-100, 2017. [DOI:10.1016/j.nahs.2017.04.007]

9. [9] K. Hariprasad and S. Bhartiya, "An Efficient and Stabilizing Model Predictive Control of Switched Systems," IEEE Transactions on Automatic Control, vol. 62, pp. 3401-3407, 2017. [DOI:10.1109/TAC.2016.2613909]

10. [10] A. P. Tharadevi, G. G. Devadhas, and M. M. Shinu, "Survey on Different Control Schemes for Distillation Columns," in 2018 International Conference on Control, Power, Communication and Computing Technologies (ICCPCCT), 2018, pp. 605-609. [DOI:10.1109/ICCPCCT.2018.8574247]

11. [11] Y. Shin, R. Smith, and S. Hwang, "Development of model predictive control system using an artificial neural network: A case study with a distillation column," Journal of Cleaner Production, vol. 277, p. 124124, 2020. [DOI:10.1016/j.jclepro.2020.124124]

12. [12] P. Rofouie and M. Shahrokhi, "Model Predictive Inferential Control of a Distillation Column," Journal of Chemical and Petroleum Engineering, vol. 44, pp. 31-42, 2011.

13. [13] S. Skogestad, "Dynamics and Control of Distillation Columns - A Critical Survey," IFAC Proceedings Volumes, vol. 25, pp. 11-35, 1992. [DOI:10.1016/S1474-6670(17)50966-0]

14. [14] B. Medi and H. Bakuei Katrimi, "Dynamic Simulation and Control of the Demethanizer Unit in Natural Gas Refining Plant," joc-isice, vol. 14, pp. 47-61, 2020. [DOI:10.29252/joc.14.2.47]

15. [15] م. رزازان و ا. رمضانی، "دفع اثر اغشاشات ورودی و خروجی و تضعیف نویزهای وارد بر فرآیند برج تقطیر نفت خام با استفاده از یک ساختار فیلتر شده الگوریتم کنترل پیشبین تعمیم یافته،" پژوهش نفت، vol. 26،

16. pp. 57-67، 2016.

17. [16] S. Skogestad and M. Morari, "Understanding the dynamic behavior of distillation columns," Industrial & Engineering Chemistry Research, vol. 27, pp. 1848-1862, 1988. [DOI:10.1021/ie00082a018]

18. [17] F. Borrelli, M. Baotić, A. Bemporad, and M. Morari, "Dynamic programming for constrained optimal control of discrete-time linear hybrid systems," Automatica, vol. 41, pp. 1709-1721, 2005. [DOI:10.1016/j.automatica.2005.04.017]

19. [18] A. K. Jana, "Differential Geometry-Based Adaptive Nonlinear Control Law: Application to an Industrial Refinery Process," IEEE Transactions on Industrial Informatics, vol. 9, pp. 2014-2022, 2013. [DOI:10.1109/TII.2012.2228661]

20. [19] R. Castro, J. Alvarez, and J. Alvarez, "Nonlinear disturbance decoupling control of a binary distillation column," Automatica, vol. 26, pp. 567-572, 1990. [DOI:10.1016/0005-1098(90)90027-F]

21. [20] P. O. G. Company, "PROCESS DATA SHEET FOR DEBUTANISER 107-C-102," in SPP-1516-107-C-102, ed: CONSORTIUM of GHORB, IOEC, ISOICO, and SAFF, 2008.

22. [21] P. O. G. Company, "NGL Fractionation Process Flow Diagram," in PFD-1516-107-0020-0001, ed: CONSORTIUM of GHORB, IOEC, ISOICO, and SAFF, 2008.

23. [22] K. Hariprasad and S. Bhartiya, "A computationally efficient robust tube based MPC for linear switched systems," Nonlinear Analysis: Hybrid Systems, vol. 19, pp. 60-76, 2016. [DOI:10.1016/j.nahs.2015.07.002]

24. [23] P. O. G. Company, "NGL Fractionation Process Flow Diagram," in PFD-1516-107-0020-0002, ed: CONSORTIUM of GHORB, IOEC, ISOICO, and SAFF, 2008.

Rights and permissions | |

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |