A LQR Design With Rejection of Disturbances and Robustness to Load Variations Applied to a Buck Converter

Authors

  • Luiz A. Maccari Junior Universidade Federal de Santa Maria, Santa Maria - RS, Brasil
  • Rodolfo L. Valle Centro Federal de Educação Tecnológica de Minas Gerais, Leopoldina - MG, Brasil
  • André A. Ferreira Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brasil
  • Pedro G. Barbosa Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brasil
  • Vinícius F. Montagner Universidade Federal de Santa Maria, Santa Maria - RS, Brasil

DOI:

https://doi.org/10.18618/REP.2016.1.2551

Keywords:

Buck converter, LMI, LQR, Robust Hinf control

Abstract

This work presents a state feedback controller suitable to regulate the output voltage of DC-DC buck converters operating under input voltage disturbances and load variations. First, a state space model of the plant is given and the performance requirements are presented, in terms of bounds on rejection of disturbances, bounds on settling time of transient responses and robustness against load variations. Then, a control design procedure based on a linear quadratic regulator is proposed, having the following features: (a) an Hinf analysis condition to certify the bound on the rejection of disturbances, (b) an eigenvalue evaluation, to ensure the bound on the settling times of the slowest mode in the transient responses, and (c) a Lyapunov condition to ensure the robustness of the closed-loop system under load variations. The proposed design procedure produces control gains suitable for experimental implementation. For sake of comparison, a robust state feedback Hinf controller with pole location constraints is given, and show very large gains, not suitable for experimental implementation. Practical results with the proposed controller are shown, illustrating the very good performance of the system operating under input disturbance and load variations.

Downloads

Download data is not yet available.

Author Biographies

Luiz A. Maccari Junior, Universidade Federal de Santa Maria, Santa Maria - RS, Brasil

received the bachelor, master and doctor degrees in Electrical Engineering from Federal University of Santa Maria in 2009, 2011 and 2015 respectively. Since 2014 he is Assistant Professor at the Universidade Federal do Pampa (UNIPAMPA), RS, Brasil.

Rodolfo L. Valle, Centro Federal de Educação Tecnológica de Minas Gerais, Leopoldina - MG, Brasil

received the bachelor degree in Control and Automation Engineering from CEFET-MG, in 2010 and the master degree in Electrical Engineering from Federal University of Juiz de Fora in 2013, where he is pursing his doctorate. Since 2014 he is EBTT professor at Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Leopoldina, MG, Brasil.

André A. Ferreira, Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brasil

received the bachelor degree in Electrical Engineering from Federal University of Juiz de Fora in 2000 and the master and doctor degrees, both in Electrical Engineering, from State University of Campinas, SP, in 2002 and 2007, respectively. Currently, he is professor at the Federal University of Juiz de Fora, Juiz de Fora, Brazil. His research interest includes dc-dc power converters control, digital control and power quality.

Pedro G. Barbosa, Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brasil

received the bachelor degree in Electrical Engineering from Federal University of Juiz de Fora in 1986 and the master and doctor degrees, both in Electrical Engineering, from Federal University of Rio de Janeiro, in 1994 e 2000, respectively. Currently, he is professor at the Federal University of Juiz de Fora, Juiz de Fora, Brazil. His main research interests are modeling and control of power electronics converters, integration of renewable energy sources and active power filters.

Vinícius F. Montagner, Universidade Federal de Santa Maria, Santa Maria - RS, Brasil

received the bachelor and the master degrees in Electrical Engineering, in 1996 and 2000, from Federal University of Santa Maria and the doctor degree in Electrical Engineering from State University of Campinas in 2005. Currently, he is professor at Electric Power Processing Department in Federal University of Santa Maria. His research interests include control theory and applications.

References

S. Buso, 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

R. W. Erickson, D. Maksimovic, Fundamentals of power electronics, Springer Science & Business Media, 2007.

C.-T. Chen, Linear system theory and design, Oxford University Press, Inc., 1995.

P. Dorato, V. Cerone, C. Abdallah, Linear-quadratic control: an introduction, Simon & Schuster, 1994.

F. H. Leung, P. K. Tam, C. Li, "An improved LQR-based controller for switching DC-DC converters", IEEE Transactions on Industrial Electronics, vol. 40,no. 5, pp. 521-528, Oct. 1993. https://doi.org/10.1109/41.238013 DOI: https://doi.org/10.1109/41.238013

C. O. Moreira, F. Silva, S. F. Pinto, M. B. Santos,et al., "Digital LQR control with Kalman Estimator for DC-DC Buck converter", in 2011 IEEE EUROCON-International Conference on Computer as a Tool(EUROCON), pp. 1-4, 2011. https://doi.org/10.1109/EUROCON.2011.5929326 DOI: https://doi.org/10.1109/EUROCON.2011.5929326

V. F. Montagner, E. G. Carati, H. Grundling,et al.,"Design and analysis of a linear quadratic regulator with repetitive controller for ac power supplies",in2003 IEEE International Symposium on Industrial Electronics(ISIE'03), vol. 1, pp. 544-549, 2003. https://doi.org/10.1109/ISIE.2003.1267309 DOI: https://doi.org/10.1109/ISIE.2003.1267309

R. Priewasser, M. Agostinelli, C. Unterrieder,S. Marsili, M. Huemer, "Modeling, control, and implementation of DC-DC converters for variable frequency operation", IEEE Transactions on Power Electronics, vol. 29, no. 1, pp. 287-301, Jan. 2014. https://doi.org/10.1109/TPEL.2013.2248751 DOI: https://doi.org/10.1109/TPEL.2013.2248751

F. Dupont, V. Montagner, J. Pinheiro, H. Pinheiro,S. Oliveira, A. Péres, "Comparison of Linear Quadratic Controllers with Stability Analysis for DC-DC Boost Converters Under Large Load Range", Asian Journal of Control, vol. 15, no. 3, pp. 861-871, May 2013. https://doi.org/10.1002/asjc.561 DOI: https://doi.org/10.1002/asjc.561

M. Mahdavian, M. B. Poudeh, S. Eshtehardiha,"DC-DC converter with closed loop control through several optimizing methods", in 11th International Conference on Optimization of Electrical and Electronic Equipment, pp. 233-238, 2008.https://doi.org/10.1109/OPTIM.2008.4602414 DOI: https://doi.org/10.1109/OPTIM.2008.4602414

H. Sira-Ramirez, M. A. Oliver-Salazar, "On the robust control of Buck-converter DC-motor combinations", IEEE Transactions on Power Electronics, vol. 28,no. 8, pp. 3912-3922, Aug. 2013. https://doi.org/10.1109/TPEL.2012.2227806 DOI: https://doi.org/10.1109/TPEL.2012.2227806

E. W. Zurita-Bustamante, J. Linares-Flores,E. Guzmán-Ramírez, H. Sira-Ramírez, "A comparison between the GPI and PID controllers for the stabilization of a DC-DC Buck converter: a field programmable gate array implementation",IEEE Transactions on Industrial Electronics, vol. 58, no. 11,pp. 5251-5262, Nov. 2011. https://doi.org/10.1109/TIE.2011.2123857 DOI: https://doi.org/10.1109/TIE.2011.2123857

R. de Castro, R. E. Araujo, J. P. F. Trovão, P. G.Pereirinha, P. Melo, D. Freitas, "Robust DC-link control in EVs with multiple energy storage systems", IEEE Transactions on Vehicular Technology, vol. 61,no. 8, pp. 3553-3565, Oct. 2012. https://doi.org/10.1109/TVT.2012.2208772 DOI: https://doi.org/10.1109/TVT.2012.2208772

C. Olalla, R. Leyva, A. El Aroudi, I. Queinnec,"Robust LQR control for PWM converters: anLMI approach",IEEE Transactions on Industrial Electronics, vol. 56, no. 7, pp. 2548-2558, July 2009. https://doi.org/10.1109/TIE.2009.2017556 DOI: https://doi.org/10.1109/TIE.2009.2017556

L. A. Maccari, V. F. Montagner, H. Pinheiro,R. C. Oliveira, "RobustH2control applied to boost converters: design, experimental validation and performance analysis",IET Control Theory &Applications, vol. 6, no. 12, pp. 1881-1888, Aug.2012. https://doi.org/10.1049/iet-cta.2011.0755 DOI: https://doi.org/10.1049/iet-cta.2011.0755

C. Olalla, R. Leyva, A. El Aroudi, P. Garces,I. Queinnec, "LMI robust control design for boost PWM converters",IET Power Electronics, vol. 3, no. 1,pp. 75-85, Jan. 2010. https://doi.org/10.1049/iet-pel.2008.0271 DOI: https://doi.org/10.1049/iet-pel.2008.0271

C. Olalla, I. Queinnec, R. Leyva, A. El Aroudi,"Robust optimal control of bilinear DC-DC converters",Control Engineering Practice, vol. 19,no. 7, pp. 688-699, July 2011. https://doi.org/10.1016/j.conengprac.2011.03.004 DOI: https://doi.org/10.1016/j.conengprac.2011.03.004

G. S. Deaecto, J. C. Geromel, F. Garcia, J. Pomilio,"Switched affine systems control design with application to DC-DC converters",IET control theory & applications, vol. 4, no. 7, pp. 1201-1210,July 2010. https://doi.org/10.1049/iet-cta.2009.0246 DOI: https://doi.org/10.1049/iet-cta.2009.0246

T. Hu, "A nonlinear-system approach to analysis and design of power-electronic converters with saturation and bilinear terms", IEEE Transactions on Power Electronics, vol. 26, no. 2, pp. 399-410, Feb. 2011. https://doi.org/10.1109/TPEL.2010.2054115 DOI: https://doi.org/10.1109/TPEL.2010.2054115

L. Martínez-Salamero, G. García, M. Orellana,C. Lahore, B. Estibals, C. Alonso, C. E. Carrejo,"Analysis and design of a sliding-mode strategy for start-up control and voltage regulation in a buck converter", IET Power Electronics, vol. 6, no. 1, pp.52-59, Jan. 2013. https://doi.org/10.1049/iet-pel.2011.0494 DOI: https://doi.org/10.1049/iet-pel.2011.0494

H. de Battista, R. J. Mantz, "Variable structure control of a photovoltaic energy converter",IEE Proceedings-Control Theory and Applications, vol. 149, no. 4, pp.303-310, July 2002. https://doi.org/10.1049/ip-cta:20020556 DOI: https://doi.org/10.1049/ip-cta:20020556

Y. He, F. Luo, "Sliding-mode control for dc-dc converters with constant switching frequency",IEE Proceedings - Control Theory and Applications, vol.153, no. 1, pp. 37-45, Jan. 2006. https://doi.org/10.1049/ip-cta:20050030 DOI: https://doi.org/10.1049/ip-cta:20050030

A. Fradkov, J. Alvarez, D. Cortes, "Tracking control ofthe boost converter", IEE Proceedings - Control theoryand applications, vol. 151, no. 2, pp. 218-224, March2004. https://doi.org/10.1049/ip-cta:20040203 DOI: https://doi.org/10.1049/ip-cta:20040203

R. Leyva, A. Cid-Pastor, C. Alonso, I. Queinnec,S. Tarbouriech, L. Martinez-Salamero, "Passivity-based integral control of a boost converter for large-signal stability",IEE Proceedings - Control Theory and Applications, vol. 153, no. 2, pp. 139-146, March2006. https://doi.org/10.1049/ip-cta:20045223 DOI: https://doi.org/10.1049/ip-cta:20045223

H. Lam, S. Tan, "Stability analysis of fuzzy-model-based control systems: application on regulation of switching DC-DC converter",IET control theory &applications, vol. 3, no. 8, pp. 1093-1106, Aug. 2009. https://doi.org/10.1049/iet-cta.2008.0168 DOI: https://doi.org/10.1049/iet-cta.2008.0168

S.-K. Kim, J.-S. Kim, C. R. Park, Y. I. Lee, "Output-feedback model predictive controller for voltage regulation of a DC/DC converter", IET Control Theory& Applications, vol. 7, no. 16, pp. 1959-1968, Nov.2013. https://doi.org/10.1049/iet-cta.2013.0115 DOI: https://doi.org/10.1049/iet-cta.2013.0115

K. Zhou, J. C. Doyle, K. Glover,et al.,Robust and optimal control, vol. 40, Prentice Hall, 1996.

S. P. Boyd, V. Balakrishnan, Linear matrix inequalities in system and control theory, vol. 15, SIAM - Studies in Applied Mathematics, 1994. https://doi.org/10.1137/1.9781611970777 DOI: https://doi.org/10.1137/1.9781611970777

L. A. Maccari, V. Foletto Montagner, A. Ferreira,et al.,"A linear quadratic control applied to buck converter swith H-infinity constraints", in Power Electronics Conference (COBEP), 2013 Brazilian, pp. 339-344,2013. https://doi.org/10.1109/COBEP.2013.6785137 DOI: https://doi.org/10.1109/COBEP.2013.6785137

B. A. Francis, W. M. Wonham, "The internal model principle of control theory",Automatica, vol. 12, no. 5,pp. 457-465, Sep. 1976. https://doi.org/10.1016/0005-1098(76)90006-6 DOI: https://doi.org/10.1016/0005-1098(76)90006-6

K. Ogata, Modern control engineering, Prentice-Hall,1990.

D. Gosden, "Electric vehicle auxiliary power supply",in Proceedings of the Institution of Electrical Engineers, vol. 123, pp. 711-712, 1976. https://doi.org/10.1049/piee.1976.0156 DOI: https://doi.org/10.1049/piee.1976.0156

A. Emadi, Y. J. Lee, K. Rajashekara, "Power electronics and motor drives in electric, hybrid electric, and plug-in hybrid electric vehicles", IEEE Transactions on Industrial Electronics, vol. 55, no. 6,pp. 2237-2245, June 2008. https://doi.org/10.1109/TIE.2008.922768 DOI: https://doi.org/10.1109/TIE.2008.922768

A. Emadi, S. S. Williamson, A. Khaligh, "Power electronics intensive solutions for advanced electric, hybrid electric, and fuel cell vehicular power systems", 15IEEE Transactions on Power Electronics, vol. 21,no. 3, pp. 567-577, May 2006. https://doi.org/10.1109/TPEL.2006.872378 DOI: https://doi.org/10.1109/TPEL.2006.872378

Downloads

Published

2016-03-31

How to Cite

[1]
L. A. M. Junior, R. L. Valle, A. A. Ferreira, P. G. Barbosa, and V. F. Montagner, “A LQR Design With Rejection of Disturbances and Robustness to Load Variations Applied to a Buck Converter”, Eletrônica de Potência, vol. 21, no. 1, pp. 7–15, Mar. 2016.

Issue

Vol. 21 No. 1 (2016)

Section

Original Papers

License

Copyright (c) 2015 Revista Eletrônica de Potência

Creative Commons License

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

Crossref
Scopus
Google Scholar
Europe PMC