A Robust H2 State Feedback Controller Applied To Boost Converters

Vinícius F. Montagner; Luiz A. Maccari Jr.; Humberto Pinheiro; Ricardo C. L. F. Oliveira

doi:10.18618/REP.2011.1.068075

Authors

Vinícius F. Montagner Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil
Luiz A. Maccari Jr. Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil
Humberto Pinheiro Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil
Ricardo C. L. F. Oliveira School of Electrical and Computer Engineering University of Campinas - UNICAMP 13083-852, Campinas – SP, Brazil

DOI:

https://doi.org/10.18618/REP.2011.1.068075

Keywords:

Boost Converter, Linear Matrix Inequalities, Optimal Control, Polytopic Uncertainty, Robust Control

Abstract

This paper proposes the design and the experimental validation of a robust H2 control technique applied to boost converters. Differently from conventional techniques, the proposed controller has a certificate of stability and performance under arbitrary parameter variations. The design procedure adopts a linearized model with a polytopic structure for the converter affected by time-varying parameters. An optimal H2 state feedback controller (under quadratic stability) is synthesized using convex optimization based on linear matrix inequalities. This framework allows the determination of the control gains in a very fast way, using a finite set of inequalities to obtain a controller that ensures robust stability and performance for the entire set of uncertain parameters. An experimental setup of a boost converter is used to validate the controller designed here. The input voltage, the operating point duty cycle and the load are considered as arbitrarily time-varying uncertain parameters. The synthesized control gains produce good simulated and experimental results when compared to those obtained with a classical strategy based on PI controllers, without introducing additional implementation cost. The experimental validation proves the viability of practical application of this important robust control technique for boost converters.

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Author Biographies

Vinícius F. Montagner, Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil

received the B.S. and M.S. degrees in Electrical Engineering from Federal University of Santa Maria in 1996 and 2000, respectively. He received the PhD and post-doctoral degrees in Electrical Engineering from University of Campinas in 2005 and 2006, respectively. Currently, he is a professor at Electric Power Processing Department in Federal University of Santa Maria. His research interests include control theory and applications.

Luiz A. Maccari Jr., Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil

received the B.S. degree in Electrical Engineering from Federal University of Santa Maria in 2009. Currently, he is master’s student in PPGEE from Federal University of Santa Maria. His research interests include robust control and applications.

Humberto Pinheiro, Power Electronics and Control Research Group Federal University of Santa Maria 97105-900, Santa Maria – RS, Brazil

received the B.S. degree Electrical Engineering from Federal University of Santa Maria in 1983, the M.S. degree in Electrical Engineering from Federal University of Santa Catarina in 1987, and the PhD in Electrical Engineering from Concordia University, Canada, in 1999. Currently, he is associate professor at Electric Power Processing Department in Federal University of Santa Maria. His research interests include wind power systems and uninterruptible power supply systems.

Ricardo C. L. F. Oliveira, School of Electrical and Computer Engineering University of Campinas - UNICAMP 13083-852, Campinas – SP, Brazil

received the B.S. degree in Computer Engineering from Pontifical Catholic University of Paraná in 2001. He received M. Sc., the PhD and the post-doctoral degrees in Electrical Engineering from University of Campinas in 2003, and 2006 and 2009, respectively. Currently, he is a professor at Department of Telematics, School of Electrical and Computer Engineering, University of Campinas. His research interests include linear systems and control theory.

References

R. W. Erickson, Fundamentals of power electronics. New York: Chapman & Hall, 1997. https://doi.org/10.1007/978-1-4615-7646-4 DOI: https://doi.org/10.1007/978-1-4615-7646-4

R. C. Dorf and R. H. Bishop, Modern control systems, 11 ed. Upper Saddle River, USA: Prentice Hall, 2008.

P. Dorato, C. T. Abdallah, and V. Cerone, Linear quadratic control: an introduction. Malabar, USA: Krieger Pub. Co., 2000.

K. Zhou, J. C. Doyle, and K. Glover, Robust and optimal control. Upper Saddle River, USA: Prentice Hall, 1996.

C. Olalla, R. Leyva, A. El Aroudi, and I. Queinnec, "Robust LQR Control for PWM Converters: An LMI Approach," IEEE Transactions on Industrial Electronics, vol. 56, pp. 2548-2558, Jul 2009. https://doi.org/10.1109/TIE.2009.2017556 DOI: https://doi.org/10.1109/TIE.2009.2017556

F. H. F. Leung, P. K. S. Tam, and C. K. Li, "AnImproved Lqr-Based Controller for Switching Dc-Dc Converters," IEEE Transactions on Industrial Electronics, vol. 40, pp. 521-528, Oct 1993. https://doi.org/10.1109/41.238013 DOI: https://doi.org/10.1109/41.238013

F. H. Dupont, V. F. Montagner, J. R. Pinheiro, H. Pinheiro, S. V. G. Oliveira, and A. Péres, "Multiple controllers for boost converters under large load range: a GA and fuzzy logic based approach," Proceedings of the International Conference on Industrial Technologies, Viña del Mar, Chile, 2010. https://doi.org/10.1109/ICIT.2010.5472661 DOI: https://doi.org/10.1109/ICIT.2010.5472661

F. Botteron, H. Pinheiro, H. A. Grundling, J. R. Pinheiro, and H. L. Hey, "Digital voltage and current controllers for three-phase PWM inverter for UPS applications,"Proceedings of the Thirty-Sixth IAS Annual Meeting.IEEE Industry Applications Conference Chicago, USA, 2001. https://doi.org/10.1109/IAS.2001.955995 DOI: https://doi.org/10.1109/IAS.2001.955995

V. F. Montagner, E. G. Carati, and H. A. Grundling, "Design and analysis of a linear quadratic regulator with repetitive controller for AC power supplies " Proceedings of the IEEE International Symposium on Industrial Electronics, Rio de Janeiro, 2003. https://doi.org/10.1109/ISIE.2003.1267309 DOI: https://doi.org/10.1109/ISIE.2003.1267309

S. P. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994. https://doi.org/10.1137/1.9781611970777 DOI: https://doi.org/10.1137/1.9781611970777

S. Buso and P. Mattavelli, Digital control in power electronics: Morgan & Claypool Publishers, 2006. https://doi.org/10.1007/978-3-031-02495-5 DOI: https://doi.org/10.1007/978-3-031-02495-5

H. K. Khalil, Nonlinear systems, 3 ed. Upper Saddle River, USA: Prentice Hall, 2002.

A. Kugi and K. Schlacher, "Nonlinear H-infinity-controller design for a DC-to-DC power converter," IEEE Transactions on Control Systems Technology, vol. 7, pp. 230-237, Mar 1999. https://doi.org/10.1109/87.748149 DOI: https://doi.org/10.1109/87.748149

K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: a linear matrix inequality approach. New York, USA: John Wiley and Sons., 2001. https://doi.org/10.1002/0471224596 DOI: https://doi.org/10.1002/0471224596

J. Ackermann, Robust control : systems with uncertain parameters. London: Springer-Verlag, 1993.

J. Leyva-Ramos and J. A. Morales-Saldana, "Uncertainty models for switch-mode DC-DC converters," IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications, vol. 47, pp. 200-203, Feb 2000. https://doi.org/10.1109/81.828573 DOI: https://doi.org/10.1109/81.828573

I. J. Gabe, V. F. Montagner, and H. Pinheiro, "Design and Implementation of a Robust Current Controller for VSI Connected to the Grid Through an LCL Filter " IEEE Transactions on Power Electronics, vol. 24, pp. 1444 - 1452 2009. https://doi.org/10.1109/TPEL.2009.2016097 DOI: https://doi.org/10.1109/TPEL.2009.2016097

C. Olalla, R. Leyva, A. El Aroudi, P. Garces, and I. Queinnec, "LMI robust control design for boost PWM converters," IET Power Electronics, vol. 3, pp. 75-85, Jan 2010. https://doi.org/10.1049/iet-pel.2008.0271 DOI: https://doi.org/10.1049/iet-pel.2008.0271

V. F. Montagner and L. D. Peres, "H Infinity Control with Pole Location for a DC - DC Converter with a Switched Load," Proceedings of the IEEE International Symposium on Industrial Electronics 2003. https://doi.org/10.1109/ISIE.2003.1267310 DOI: https://doi.org/10.1109/ISIE.2003.1267310

K. Y. Lian, J. J. Liou, and C. Y. Huang, "LMI-based integral fuzzy control of DC-DC converters," IEEE Transactions on Fuzzy Systems, vol. 14, pp. 71-80, Feb 2006. https://doi.org/10.1109/TFUZZ.2005.861610 DOI: https://doi.org/10.1109/TFUZZ.2005.861610

P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox User's Guide. Natick, USA: The Mathworks Inc., 1995. https://doi.org/10.1109/CDC.1994.411440 DOI: https://doi.org/10.1109/CDC.1994.411440

J. C. Geromel, P. L. D. Peres, and S. R. Souza, "H2guaranteed cost control for uncertain continuous-time linear systems," Systems & Control Letters, vol. 19, pp. 23-27, July 1992. https://doi.org/10.1016/0167-6911(92)90035-Q DOI: https://doi.org/10.1016/0167-6911(92)90035-Q

J. Alvarez-Ramirez, G. Espinosa-Perez, and D. Noriega-Pineda, "Current-mode control of DC-DC power converters: a backstepping approach," Proceedings of the 2001 IEEE International Conference on Control Applications, 2001, pp. 190-195. https://doi.org/10.1109/CCA.2001.973862 DOI: https://doi.org/10.1109/CCA.2001.973862

R. D. Middlebrook, "Topics in Multiple-Loop Regulators and Current-Mode Programming," IEEE Transactions on Power Electronics, vol. PE-2, pp. 109-124, 1987. https://doi.org/10.1109/TPEL.1987.4766345 DOI: https://doi.org/10.1109/TPEL.1987.4766345