Global Hybrid Modeling and Control of a DC-DC Buck-Boost Converter via Mixed Logical Dynamical Systems
Subject Areas : electrical and computer engineering
Mohammad
Hejri
1
(Sahand University of Technology)
Keywords: Hybrid systemsextended mixed logical dynamical (EMLD) systems predictive controlbuck-boost converter,
Abstract :
This paper presents a new model for a DC-DC buck-boost converter considering its all controlled and uncontrolled switching phenomena in both continuous and discontinuous conduction modes. The proposed model is developed based on hybrid systems theory using mixed-logical dynamical (MLD) systems, and an improved version of these systems called as extended mixed-logical dynamical (EMLD) Systems. Compared to the existing MLD and EMLD models of the DC-DC converters, the proposed model contains fewer numbers of integer variables and inequalities, and, as a result, leads to the less complexity and solution time of the mixed integer optimization problems arising from the corresponding hybrid model predictive controllers. The advantage of the proposed modeling and control method is evaluated via the comparison of the existing MLD models and hybrid predictive controllers as well as classic proportional-integral (PI) controllers. Moreover, the theoretical challenges for the closed-loop stability proof are discussed and in this regard some future research outlines and ideas are introduced. The steady state and transient performance of the closed-loop control system over a wide range of the operation points show the satisfactory operation of the proposed modeling and control scheme for the DC-DC buck-boost converter.
[1] A. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, London: Springer-Verlag, 1999.
[2] J. Lunze and F. Lamnabhi-Lagarrigue, Handbook of Hybrid Systems Control, Cambridge: Cambridge University Press, 2009.
[3] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic, 2001.
[4] S. Bacha, I. Munteanu, and A. I. Bratcu, Power Electronic Converters Modeling and Control with Case Studies, London: Springer Verlag, 2014.
[5] J. Han, B. Zhang, and D. Qiu, "Unified model of boost converter in continuous and discontinuous conduction modes," IET Power Electronics, vol. 9, no. 10, pp. 2036-2043, Aug. 2016.
[6] J. Han, B. Zhang, and D. Qiu, "Bi-switching status modeling method for DC-DC converters in CCM and DCM operations," IEEE Trans. on Power Electronics, vol. 32, no. 3, pp. 2464-2472, Mar. 2017.
[7] H. Molla-Ahmadian, A. Karimpour, N. Pariz, and F. Tahami, "Hybrid modeling of a DC-DC series resonant converter: direct piecewise affine approach," IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 59, no. 12, pp. 3112-3120, Dec. 2012.
[8] H. Molla-Ahmadian, F. Tahami, A. Karimpour, and N. Pariz, "Hybrid control of DC-DC series resonant converters: the direct piecewise affine approach," IEEE Trans. on Power Electronics, vol. 30, no. 3, pp. 1714-1723, Mar. 2015.
[9] P. Karamanakos, T. Geyer, and S. Manias, "Direct model predictive current control strategy of DC-DC boost converters," IEEE J. of Emerging and Selected Topics in Power Electronics, vol. 4, no. 1, pp. 337-346, Dec. 2013.
[10] P. Karamanakos, T. Geyer, and S. Manias, "Direct voltage control of DC-DC boost converters using enumeration-based model predictive control," IEEE Trans. on Power Electronics, vol. 29, no. 2, pp. 968-978, Dec. 2014.
[11] G. Beccuti, G. Papafotiou, and M. Morari, "Optimal control of the buck DC-DC converter operating in both the continuous and discontinuous conduction regimes," in Proc. of the 45th IEEE Conf. on Decision & Control, pp. 6205-6210, San Diego, CA, USA, 13-15 Dec. 2006.
[12] T. A. F. Theunisse, J. Chai, R. G. Sanfelice, and W. P. M. H. Heemels, "Robust global stabilization of the DC-DC boost converter via hybrid control," IEEE Trans. on Circuits and Systems-I: Regular Papers, vol. 62, no. 4, pp. 1052-1061, Apr. 2015.
[13] M. Hejri and H. Mokhtari, "Global hybrid modeling and control of a buck converter: a novel concept," International J. of Circuit Theory and Applications, John Wiley and Sons, Inc., vol. 37, no. 9, pp. 968-986, Nov. 2009.
[14] M. Hejri and H. Mokhtari, "Hybrid predictive control of a DC-DC boost converter in both continuous and discontinous current modes of operations," Optimal Control, Applications and Methods, vol. 32, no. 3, pp. 270-284, May/Jun. 2011.
[15] M. Hejri and A. Giua, "Hybrid modeling and control of switching DC-DC converters via MLD systems," in Proc. of the IEEE Int. Conf. on Automation Science and Engineering, pp. 714-719, Trieste, Italy, 24-27 Aug. 2011.
[16] M. Hejri and H. Mokhtari, "Hybrid modeling and control of a DC-DC boost converter via extended mixed logical dynamical systems (EMLDs)," in Proc. of the 5th Annual Int. Power Electronics, Drive Systems and Technologies Conf., PEDSTC’14, pp. 373-378, Tehran, Iran, 5-6 Feb. 2014.
[17] A. Bemporad and M. Morari, "Control of systems integrating logic, dynamic and constraints," Automatica, vol. 35, no. 3, pp. 407-427, Mar. 1999.
[18] F. D. Torrisi and A. Bemporad, "HYSDEL-a tool for generating computational hybrid models for analysis and synthesis problems," IEEE Trans. on Control Systems Technology, vol. 12, no. 2, pp. 235-249, Mar. 2004.
[19] M. Hejri, A. Giua, and H. Mokhtari, "On the complexity and dynamical properties of mixed logical dynamical systems via an automaton based discrete-time hybrid automaton," International J. of Robust and Nonlinear Control, vol. 28, no. 16, pp. 4713-4746, 10 Nov. 2018.
[20] C. Bohn and D. P. Atherton, "An analysis package comparing PID antiwindup strategies," IEEE Control Systems Magazine, vol. 15, no. 2, pp. 34-40, Apr. 1995.
[21] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: stability and optimality," Automatica, vol. 36, no. 6, pp. 789-814, Jun. 2000.
[22] B. Picasso, S. Pancanti, A. Bemporad, and A. Bicchi, "Receding-horizon control of LTI systems with quantized inputs," IFAC Analysis and Design of Hybrid Systems, vol. 36, no. 6, pp. 259-264, Jun. 2003.
[23] A. Bemporad, "Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form," IEEE Trans. on Automatic Control, vol. 49, no. 5, pp. 832-838, May 2004.
[24] M. Lazar, W. P. M. H. Heemels, S. Weiland, and A. Bemporad, "Stabilizing model predictive control of hybrid systems," IEEE Trans. on Automatic Control, vol. 51, no. 11, pp. 1813-1818, Nov. 2006.
[25] P. Sindareh Esfahani and J. K. Pieper, "H∞ model predictive control for constrained discrete-time piecewise affine systems," International J. of Robust and Nonlinear Control, vol. 28, no. 6, pp. 1973-1995, 1 Apr. 2018.
[26] D. Q. Mayne and S. Rakovic, "Model predictive control of constrained piecewise affine discrete-time systems," International J. of Robust and Nonlinear Control, vol. 13, no. 3-4, pp. 261-279, Mar./Apr. 2003.
[27] R. P. Aguilera and D. E. Quevedo, "Stability analysis of quadratic MPC with a discrete input alphabet," IEEE Trans. on Automatic Control, vol. 58, no. 12, pp. 3190-3196, Dec. 2013.
[28] R. P. Aguilera and D. E. Quevedo, "Predictive control of power converters: designs with guaranteed performance," IEEE Trans. on Industrial Informatics, vol. 11, no. 1, pp. 53-63, Feb. 2015.
[29] J. Rodriguez and P. Cortes, Predictive Control of Power Converters and Electrical Drives, John Wiley & Sons, 2012.
[30] T. Geyer, Model Predictive Control of High Power Converters and Industrial Drives, John Wiley & Sons, Inc., 2016.