Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter

Authors

  • Edson Italo Mainardi Júnior Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil
  • Luciano de Souza Costa e Silva Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil
  • Diogo Ramalho de Oliveira Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil
  • Estelio da Silva Amorim Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil
  • Marcelo Carvalho Minhoto Teixeira Universidade Estatual Paulista, Ilha Solteira – SP, Brasil
  • Paulo Eduardo Menegheti Gonçalves Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

DOI:

https://doi.org/10.18618/REP.2023.2.0037

Keywords:

Bounded Sampling Time, Buck DC-DC converter, Linear Matrix Inequalities (LMIs), Lyapunov function, Switched Affine System

Abstract

The paper addresses the problem of designing a stabilizing control for switched affine and its experimental verification based on Linear Matrix Inequalities (LMIs). The main contribution is on the determination of a switching function that exploits the potential of LMI control approaches and which assures global stability and minimizes a guaranteed quadratic cost. Slack variables are introduced to reduce the design conservatism and new sufficient LMI conditions for the synthesis of the controllers are presented. Thus, it is showed that the performance of the control system is superior with a smaller guaranteed cost upper bound of that afforded by recent results. In addition, a theorem with sufficient conditions for the control of switched affine systems that allows a way to garantee a bounded sample time rate on the switching function is proposed. The implementation of the switching function taking into account a bounded sampling time is analysed and discussed with particular interest. Finally, the theoretical results are applied to Buck DC-DC converter. Several simulations show the usefulness of the methodology and experimental results obtained from a prototype validate this approach.

Downloads

Download data is not yet available.

Author Biographies

Edson Italo Mainardi Júnior, Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

was born in FernandópolisSP, Brazil, in 1984. He received the B.Sc. degree in electrical engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2009 and the D.Sc. degree in electrical engineering from Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2013. In 2012, he joined the Instituto Federal do Mato Grosso do Sul (IFMS), Três Lagoas – MS, Brazil, where he is currently a Professor. His research interests include control theory and applications, variable-structure systems, linearmatrix-inequality-based designs, nonlinear systems, adaptive systems, and switched systems.

Luciano de Souza Costa e Silva, Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

was born in MaríliaSP, Brazil, in 1985. He received the B.Sc. degree in electrical engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2009, the M.Sc. degree in electrical engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2011, and the D.Sc. degree in electrical engineering from Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2017. In 2013, he joined the Instituto Federal de Goias (IFG), Jatái, Brazil and in 2021 he joined the Instituto Federal do Mato Grosso do Sul (IFMS), TrêsLagoas – MS, Brazil, where he is currently a Professor. His research interests include control theory and applications, Power Systems, Power converters, Power quality and Power electronics and control in Renewable Energy Systems.

Diogo Ramalho de Oliveira, Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

was born in AndradinaSP, Brazil, in 1990. He received the B.Sc. degree in electrical engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2012 and the D.Sc. degree in electrical engineering from Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2017. In 2020, he held a postdoctoral position (UNESP). In 2017, he joined the Instituto Federal do Mato Grosso do Sul (IFMS), Três Lagoas – MS, Brazil, where he is currently a Professor. His research interests include control theory and applications, linear-matrix-inequality-based designs, switched systems, fuzzy systems and H∞ control.

Estelio da Silva Amorim, Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

was born in Cruzeiro do Sul-AC, Brazil, in 1977. He received the B.Sc. degree in electrical engineering from the Universidade Federaldo Mato Grosso do Sul (UFMS), Campo Grande, Brazil, in 2004 and the M.Sc. degree in electrical engineering from Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, in 2011. In 2017, he joined the Instituto Federal do Mato Grosso do Sul (IFMS), Três Lagoas – MS, Brazil, where he is currently a Professor. His research interests include Power Systems, Power converters, Power quality and Power electronics and control in Renewable Energy Systems.

Marcelo Carvalho Minhoto Teixeira, Universidade Estatual Paulista, Ilha Solteira – SP, Brasil

was born in Campo Grande-MS, Brazil, in 1957. He received the B.Sc. degree in electrical engineering from the Escola de Engenharia de Lins, Lins, Brazil, in 1979, the M.Sc. degree in electrical engineering from the Instituto Alberto Luiz Coimbra de Pósgraduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil, in 1982, and the D.Sc. degree in electrical engineering from Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, in 1989. In 1982, he joined the Department of Electrical Engineering, Universidade Estadual Paulista (UNESP), Ilha Solteira (FEIS), Brazil, where he is currently a Professor. His research interests include control theory and applications, neural networks, variable-structure systems, linear-matrixinequality-based designs, fuzzy systems, nonlinear systems, adaptive systems, and switched systems. From 2016 to 2020, he was an Associate Editor of the IEEE TRANSACTIONS ON FUZZY SYSTEMS.

Paulo Eduardo Menegheti Gonçalves, Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso do Sul, Três Lagoas – MS, Brasil

was born in Andradina-SP, Brazil, in 1998. In 2018, he joined the Instituto Federal do Mato Grosso do Sul (IFMS), Três Lagoas – MS, Brazil, where he is currently a student in the course of Control Engineering and Automation. His research interests include Power Systems, Power converters, Power quality and Power electronics and control in Renewable Energy Systems.

References

R. A. Decarlo, M. S. Branicky, S. Pettersson, B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems",Proceedings of the IEEE, vol. 88, no. 7, pp. 1069-1082, Jul. 2000. DOI: https://doi.org/10.1109/5.871309

Z. Sun, S. S. Ge, Switched Linear Systems: Control and Design, Communications and Control Engineering, 1 ed., Springer, London, 2005. https://doi.org/10.1007/1-84628-131-8 DOI: https://doi.org/10.1007/1-84628-131-8

W. A. de Souza, M. C. M. Teixeira, M. P. A. Santim, R. Cardim, E. Assunção, "On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties", Mathematical Problems in Engineering, vol. 2013, pp. 1-10, May 2013. DOI: https://doi.org/10.1155/2013/595029

U. N. L. T. Alves, M. C. M. Teixeira, D. R. de Oliveira, R. Cardim, E. Assunção, W. A. de Souza, "Smoothing switched control laws for uncertain nonlinear systems subject to actuator saturation", International Journal of Adaptive Control and Signal Processing, vol. 30, no. 8-10, pp. 1408-1433, Aug.-Oct. 2016. https://doi.org/10.1002/acs.2671 DOI: https://doi.org/10.1002/acs.2671

D. R. de Oliveira, M. C. M. Teixeira, U. N. L. T. Alves, W. A. de Souza, E. Assunção, R. Cardim, "On local H∞ switched controller design for uncertain T-S fuzzy systems subject to actuator saturation with unknown membership functions", Fuzzy Sets and Systems, vol. 344, pp. 1-26, Aug. 2018. https://doi.org/10.1016/j.fss.2017.12.004 DOI: https://doi.org/10.1016/j.fss.2017.12.004

R. G. Teodoro, W. R. B. M. Nunes, R. de Araujo, M. A. A. Sanches, M. C. M. Teixeira, A. A.

de Carvalho, "Robust switched control design for electrically stimulated lower limbs: A linear model analysis in healthy and spinal cord injured subjects", Control Engineering Practice, vol. 102, p. 104530, Sep.. 2020. DOI: https://doi.org/10.1016/j.conengprac.2020.104530

W. R. B. M. Nunes, U. N. L. T. Alves, M. A. A. Sanches, "Electrically Stimulated Lower Limb using a Takagi-Sugeno Fuzzy Model and Robust Switched Controller Subject to Actuator Saturation and Fault under Nonideal Conditions", Int J Fuzzy Syst, vol. 24, pp. 57-72, Feb. 2022. https://doi.org/10.1007/s40815-021-01115-9 DOI: https://doi.org/10.1007/s40815-021-01115-9

H. Lin, P. J. Antsaklis, "Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results", IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308-322, Feb. 2009. https://doi.org/10.1109/TAC.2008.2012009 DOI: https://doi.org/10.1109/TAC.2008.2012009

D. Liberzon, Switching in Systems and Control, Foundations & Applications, 14 ed., Systems & control, Birkhuser, 2003. DOI: https://doi.org/10.1007/978-1-4612-0017-8

Z. Ji, L. Wang, G. Xie, "Quadratic stabilization of switched systems", International Journal of Systems Science, vol. 36, no. 7, pp. 395-404, 2005. https://doi.org/10.1080/00207720500140003 DOI: https://doi.org/10.1080/00207720500140003

J. C. Geromel, G. S. Deaecto, "Switched state feedback control for continuous-time uncertain systems", Automatica, vol. 45, no. 2, pp. 593-597, Feb. 2009. https://doi.org/10.1016/j.automatica.2008.10.010 DOI: https://doi.org/10.1016/j.automatica.2008.10.010

M. Ali, M. Yaqoob, L. Cao, K. H. Loo, "Disturbance- Observer-Based DC-Bus Voltage Control for Ripple Mitigation and Improved Dynamic Response in Two-Stage Single-Phase Inverter System", IEEE Transactions on Industrial Electronics, vol. 66, no. 9, pp. 6836-6845, Sep.. 2019. https://doi.org/10.1109/TIE.2018.2879294 DOI: https://doi.org/10.1109/TIE.2018.2879294

F. D. Esteban, F. M. Serra, C. H. De Angelo, "Control of a DC-DC Dual Active Bridge Converter in DC Microgrids Applications", IEEE Latin America Transactions, vol. 19, no. 8, pp. 1261-1269, Mar. 2021. https://doi.org/10.1109/TLA.2021.9475856 DOI: https://doi.org/10.1109/TLA.2021.9475856

D. J. S. Oncoy, R. Cardim, M. C. M. Teixeira, "Switched Control Based on Takagi-Sugeno Fuzzy Model for Dual Active Bridge DC-DC Converter", in IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1-7, 2022. DOI: https://doi.org/10.1109/FUZZ-IEEE55066.2022.9882569

W. Ma, B. Zhang, "Periodic Time-Triggered Hybrid Control for DC-DC Converter Based on Switched Affine System Model", IEEE Transactions on Industrial Electronics, vol. 70, no. 1, pp. 311-321, Jan. 2023.

https://doi.org/10.1109/TIE.2022.3150085 DOI: https://doi.org/10.1109/TIE.2022.3150085

R. Cardim, M. C. M. Teixeira, E. Assunção, M. R. Covacic, "Variable-structure control design of switched systems with an application to a DC-DC power converter", IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3505-3513, Sep. 2009. https://doi.org/10.1109/TIE.2009.2026381 DOI: https://doi.org/10.1109/TIE.2009.2026381

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

V. L. Yoshimura, E. Assunção, M. C. M. Teixeira, E. I. Mainardi Júnior, "Stability of Switched Linear and Affine Systems via Geometrical Conditions: Applications to Non-Strict Hurwitz Combination Systems and DC-DC Converters", in Anais do X Simpósio Brasileiro de Automação Inteligente, pp. 344-349, 2011.

E. I. Mainardi Júnior, M. C. M. Teixeira, R. Cardim, M. R. Moreira, E. Assunção, V. L. Yoshimura, On Control Design of Switched Affine Systems with Application to DC-DC Converters, chap. 5, Frontiers in Advanced Control Systems, InTechOpen, Rijeka, Jul. 2012. DOI: https://doi.org/10.5772/39127

T. Hashemi, A. Farnam, R. M. Esfanjani, H. M. Kojabadi, "A new approach to design switching strategy for the Buck converters", in Proceedings on Power Electronics, Drive Systems and Technologies Conference (PEDSTC), pp. 301-305, 2013. DOI: https://doi.org/10.1109/PEDSTC.2013.6506722

V. L. Yoshimura, E. Assunção, E. R. P. da Silva, M. C. M. Teixeira, E. I. Mainardi Júnior, "Observer-Based Control Design for Switched Affine Systems and Applications to DC-DC Converters", Journal of Control, Automation and Electrical Systems, vol. 24, pp. 535-543, Aug. 2013. https://doi.org/10.1007/s40313-013-0044-z DOI: https://doi.org/10.1007/s40313-013-0044-z

R. Cacau, T. Lazzarin, M. Villanueva, I. Barbi, "Study of High Step-Up Gain DC-DC Converters based on Stacking of Non-Isolated Topologies", Eletrônica de Potência, vol. 23, pp. 1-11, Dec. 2018. https://doi.org/10.18618/REP.2018.4.0029 DOI: https://doi.org/10.18618/REP.2018.4.0029

G. H. A. Bastos, J. M. Souza, L. F. Costa, R. P. T. Bascope, "Generation of DC-DC Converters with Wide Conversion Range based on the Multistate Switching Cell", Eletrônica de Potência, vol. 21, pp. 63-70, Feb. 2016. DOI: https://doi.org/10.18618/REP.2016.1.2588

J. C. Giacomini, P. F. S. Costa, A. M. S. S. Andrade, L. Schuch, M. L. S. Martins, "Desenvolvimento de um conversor CC-CC boost-forward integrado para aplicações com elevado ganho de tensão", Eletrônica de Potência, vol. 22, pp. 206-214, Jun. 2017. https://doi.org/10.18618/REP.2017.2.2675 DOI: https://doi.org/10.18618/REP.2017.2.2675

P. Bolzern, W. Spinelli, "Quadratic stabilization of a switched affine system about a nonequilibrium point", in American Control Conference, pp. 3890-3895, 2004. https://doi.org/10.23919/ACC.2004.1383918 DOI: https://doi.org/10.23919/ACC.2004.1383918

S. R. Sanders, G. C. Verguese, "Lyapunov-based control for switched power converters", IEEE Transactions on Industrial Electronics, vol. 7, no. 1, pp. 17-24, Jan 1992. DOI: https://doi.org/10.1109/63.124573

N. Kawasaki, H. Nomura, M. Masuhiro, "A new control law of bilinear DC-DC converters developed by direct application of Lyapunov", IEEE Transactionson Industrial Electronics, vol. 10, no. 3, pp. 318-325, May 1995. https://doi.org/10.1109/63.387997 DOI: https://doi.org/10.1109/63.387997

D. Cortes, J. Alvarez, A. Fradkov, "Tracking control of the boost converter", IEE Proceedings on Control Theory Applications, vol. 151, no. 2, pp. 218-24, Mar. 2004. https://doi.org/10.1049/ip-cta:20040203 DOI: https://doi.org/10.1049/ip-cta:20040203

Y. He, F. L. Luo, "Sliding-mode control for DC-DC converters with constant switching frequency", IEE Proceedings on Control Theory Applications, vol. 153, pp. 37-45, Jan. 2006. https://doi.org/10.1049/ip-cta:20050030 DOI: https://doi.org/10.1049/ip-cta:20050030

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 on Control Theory and Applications, vol. 153, no. 2, pp. 139-146, Mar. 2006. https://doi.org/10.1049/ip-cta:20045223 DOI: https://doi.org/10.1049/ip-cta:20045223

V. F. Montagner, L. A. Maccari, F. H. Dupont, H. Pinheiro, R. C. L. F. Oliveira, "A DLQR Applied to boost converters with switched loads: Design and analysis", in Power Electronics Conference (COBEP), pp. 68-73, 2011. https://doi.org/10.1109/COBEP.2011.6085201 DOI: https://doi.org/10.1109/COBEP.2011.6085201

S. Boyd, L. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, 2 ed., SIAM Studies in Applied Mathematics, 1994. https://doi.org/10.1137/1.9781611970777 DOI: https://doi.org/10.1137/1.9781611970777

P. Gahinet, A. Nemirovski, A. J. Laub, M. Chilali, LMI control toolbox - For use with Matlab, The Math Works Inc., 1995.

M. Corless, G. Leitmann, "Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems", Automatic Control, IEEE Transactions on, vol. 26, no. 5, pp. 1139-1144, Oct. 1981. DOI: https://doi.org/10.1109/TAC.1981.1102785

L. Hetel, E. Fridman, "Robust sampled-data control of switched affine systems", IEEE Transaction Automatic Control, vol. 58, pp. 2922-2928, Nov. 2013. https://doi.org/10.1109/TAC.2013.2258786 DOI: https://doi.org/10.1109/TAC.2013.2258786

V. L. Yoshimura, E. Assunção, M. C. M. Teixeira, E. I. Mainardi únior, "Performance Enhancement Of Switched Affine Systems By Switched Quadratic Lyapunov Functions: Applications In DC-DC Converters", in Proceedings of COBEP, 2013. https://doi.org/10.1109/COBEP.2013.6785133 DOI: https://doi.org/10.1109/COBEP.2013.6785133

E. I. Mainardi Júnior, Projeto de controladores para sistemas chaveados com aplicações em conversores CC-CC, Ph.D. thesis, Universidade Estadual Paulista Júlio de Mesquita Filho, 2013.

Downloads

Published

2023-05-12

How to Cite

[1]
E. I. Mainardi Júnior, L. de S. Costa e Silva, D. R. de Oliveira, E. da S. Amorim, M. C. M. Teixeira, and P. E. M. Gonçalves, “Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter”, Eletrônica de Potência, vol. 28, no. 2, pp. 141–150, May 2023.

Issue

Vol. 28 No. 2 (2023)

Section

Original Papers

License

Copyright (c) 2023 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