This paper proposes a novel structure of model predictive control algorithm for piecewise affine systems as a particular class of hybrid systems. Due to the time consuming and computational complexity of online optimization problem in MPC algorithm, the explicit form of MPC which is called Explicit MPC (EMPC) is applied in order to control of buck converter. Since the EMPC solves the optimization problem only once and in offline manner, this strategy is suitable for hybrid systems with fast dynamics. As opposed to typical EMPC that is uses only the first element of optimal input vector, the proposed strategy uses all entries of the control sequence with optimal weighting factors. In proposed EMPC, two separate optimization problems are solved at each algorithm step. The first one is related to EMPC optimization problem and the second optimization problem is concerned to finding optimal weighting factors so as to minimize the error signal at each step. The convergence property of the proposed EMPC towards to the desired value has been proved and the simulation results shows the better performance of the proposed EMPC strategy than the typical one, if the weighting factors and control horizons are adjusted properly.

Type of Article: Research paper |
Subject:
Special

Received: 2020/04/29 | Accepted: 2021/05/20 | ePublished ahead of print: 2021/08/14 | Published: 2022/05/31

Received: 2020/04/29 | Accepted: 2021/05/20 | ePublished ahead of print: 2021/08/14 | Published: 2022/05/31

1. [1] T.A. Johansen, J. Kalkkuhl, J. L¨udemann, and I. Petersen, "Hybrid control strategies in ABS," In American Control Conference, Arlington, Virginia, pp. 1704-1705, 2001. [DOI:10.1109/ACC.2001.945974]

2. [2] A. Bemporad, P. Borodani, and M. Mannelli. "Hybrid control of an automotive robotized gearbox for reduction of consumptions and emissions," in Lecture Notes in Computer Science, pp. 81-96. Springer-Verlag, 2003. [DOI:10.1007/3-540-36580-X_9]

3. [3] M. Sarailoo, Z. Rahmani and B. Rezaie, "Modeling of three-tank system with nonlinear valves based on hybrid system approach", Journal of control engineering and technology, vol. 3, no. 1, pp. 20-23, 2013.

4. [4] R. Alur, et al., "The algorithmic analysis of hybrid systems". Theoretical and Computer Science, vol. 138, pp. 3-34, 1995. [DOI:10.1016/0304-3975(94)00202-T]

5. [5] P. M. H. Heemels, B. De Schutter, and A. Bemporad, "Equivalence of hybrid dynamical models," Automatica, vol. 37, pp. 1085-1091, 2001. [DOI:10.1016/S0005-1098(01)00059-0]

6. [6] M .Sarailoo, B. Rezaie and Z. Rahmani, Fuzzy predictive control of three-tank system based on a modeling framework of hybrid systems, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 228, no. 6, pp. 369-384, 2014. [DOI:10.1177/0959651814524948]

7. [7] M. Zamani Behbahani, R. Mahboobi Esfanjani and M. Hejri, "Design of switching rule for Buck converters using explicit predictive control," The 6th Power Electronics, Drive Systems & Technologies Conference (PEDSTC2015), Tehran, pp. 486-491, 2015. [DOI:10.1109/PEDSTC.2015.7093323]

8. [8] M. R. Zamani, Z. Rahmani and B. Rezaie, "A Controller Design based on Iterative Learning method and Model Predictive Control for a nonlinear process system," 2019 6th International Conference on Control, Instrumentation and Automation (ICCIA), Sanandaj, Iran, pp. 1-7, 2019.

9. [9] J. A Rossiter. "Model-Based Predictive Control: A Practical Approach," CRC Press, 2003.

10. [10] EN. Pistikopoulos, V. Dua, "On-line optimization via off-line parametric optimization tools," Computers and Chemical Engineering, vol. 26, pp. 175-185, 2002. [DOI:10.1016/S0098-1354(01)00739-6]

11. [11] M. Herceg, "Real-Time Explicit Model Predictive Control of Processes," Dissertation Thesis, Slovak University of Technology in Bratislava, 2001.

12. [12] O. Stanojev, U. Markovic, P. Aristidou, et al., "MPC-Based Fast Frequency Control of Voltage Source Converters in Low-Inertia Power Systems," arXiv preprint arXiv:2004.02442, 2020. URL https://arxiv.org/abs/2004.02442.

13. [13] J. Chen, Y. Chen, L. Tong, et al., "A Back-Propagation Neutral Network based Explicit Model Predictive Control for DC-DC converters with High Switching Frequency," IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020. [DOI:10.1109/JESTPE.2020.2968475]

14. [14] K. Kiš and M. Klaučo , "Neural Network Based Explicit MPC for Chemical Reactor Control," arXiv preprint arXiv:1912.04684, 2019. URL https://arxiv.org/abs/1912.04684 [DOI:10.2478/acs-2019-0030]

15. [15] M. Sarailoo, Z. Rahmani and B. Rezaie, "Fuzzy predictive control of a boiler-turbine system based on a hybrid model system", Industrial & Engineering Chemistry Research, vol. 53, no. 6, pp. 2362-2381, 2014. [DOI:10.1021/ie402649u]

16. [16] Y. Chen and M. Lazar, "An Efficient MPC Algorithm for Switched Nonlinear Systems with Minimum Dwell Time Constraints," arXiv preprint arXiv:2002.09658, 2020. URL https://arxiv.org/abs/2002.09658.

17. [17] L. Wang, Q. H. Wu, YK. Tao, et al., "Switching Control of Buck Converter Based on Energy Conservation Principle," IEEE Transactions on Control Systems Technology, vol. 24, pp. 1779-1787, 2016. [DOI:10.1109/TCST.2015.2505625]

18. [18] EF. Camacho, DR. Ramirez, D. Limon, et al., "Model predictive control techniques for hybrid systems," Annual Reviews in Control, vol. 34, pp. 21-31,2010. [DOI:10.1016/j.arcontrol.2010.02.002]

19. [19] T. Marcucci and R. Tedrake, "Mixed-integer formulations for optimal control of piecewise-affine systems," Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control. Montreal, Quebec, Canada: Association for Computing Machinery, pp. 230-239, 2019. [DOI:10.1145/3302504.3311801]

20. [20] P. Petsagkourakis, WP. Heath and C. Theodoropoulos, "Stability analysis of piecewise affine systems with multi-model predictive control," Automatica 111: 108539, 2020. URL http://arxiv.org/abs/1808.00307. [DOI:10.1016/j.automatica.2019.108539]

21. [21] M. R. Zamani, Z. Rahmani and B. Rezaie, "A novel model predictive control strategy for constrained and unconstrained systems in presence of disturbance," IMA Journal of Mathematical Control and Information, vol. 37, pp. 208-225, 2020. [DOI:10.1093/imamci/dny046]

22. [22] M. Hejri and A. Giua. "Hybrid modeling and control of switching DC-DC converters via MLD systems," Automation Science and Engineering (CASE), Trieste, Italy, pp. 714-19, 2011. [DOI:10.1109/CASE.2011.6042522]

23. [23] R. Alur, C. Courcoubetis, N. Halbwachs, T. Henzinger, P.-H. Ho, X. Nicollin, A. Oliveiro, J. Sifakis, and S. Yovine. "The algorithmic analysis of hybrid systems". Theoretical and Computer Science, vol. 138, 3-34, 1995. [DOI:10.1016/0304-3975(94)00202-T]

24. [24] A. Bemporad and M. Morari. "Control of systems integrating logic, dynamics, and constraints". Automatica, vol. 35, 407-427, 1999. [DOI:10.1016/S0005-1098(98)00178-2]

25. [25] W. P. M. H. Heemels, J. M. Schumacher, and S. Weiland. "Linear complementarity systems". SIAM J. Appl. Math., vol. 60, 1234-1269, 2000. [DOI:10.1137/S0036139997325199]

26. [26] J. Hätönen. "Issues of algebra and optimality in iterative learning control," Ph.D. dissertation, Dept. Process Environ. Eng., Univ. Oulu, Oulu, Finland 2004.

27. [27] P. TøNdel, T. A. Johansen, A. Bemporad, "An algorithm for multi-parametric quadratic programming and explicit MPC solutions," Automatica, vol. 39, pp. 489-497, 2003. [DOI:10.1016/S0005-1098(02)00250-9]

28. [28] A. Bemporad and M. Morari. "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, pp. 407-427, 1999. [DOI:10.1016/S0005-1098(98)00178-2]

29. [29] M. R. Zamani, Z. Rahmani and B. Rezaie, "A novel model predictive control for a piecewise affine class of hybrid system with repetitive disturbance," ISA Transactions, vol. 108, pp. 18-34, 2021. [DOI:10.1016/j.isatra.2020.08.023]

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