Robust Control Design Procedure Based on Particle Swarm Optimization and Kharitonov’s Theorem with an Application for PMSMs

Authors

  • Lucas Cielo Borin Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil
  • Caio Ruviaro Dantas Osório Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil
  • Gustavo Guilherme Koch Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil
  • Thieli Smidt Gabbi Universidade Federal do Rio Grande do Sul (UFRS) – Porto Alegre, RS, Brazil
  • Ricardo Coração de Leão Fontoura de Oliveira Universidade de Campinas (UNICAMP) – Campinas, SP, Brazil
  • Vinícius Foletto Montagner Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil

DOI:

https://doi.org/10.18618/REP.2020.2.0008

Keywords:

Kharitonov’s theorem, Particle swarm optimization, Permanent magnet synchronous motors, Power converters, Robust control

Abstract

This paper proposes an automatic procedure for robust control design applicable to power converters based on particle swarm optimization and Kharitonov's Theorem. The main benefit is to provide control gains that have a theoretical certificate of robust stability and also accomplish multiple performance criteria in a design less dependent of human-machine interaction. Regarding the particle swarm optimization, each particle represents a controller candidate whose performance is evaluated by means of an objective function, using the vertices of a polytopic model of the plant and the four polynomials of Kharitonov's Theorem. The effectiveness of the proposed procedure is illustrated by means of a case study that considers the speed control of a permanent magnet synchronous motor subject to uncertain mechanical and electrical parameters. The designed controllers, obtained in an off-line way, yield good trade-offs between performance and robustness, as confirmed by simulation and experimental evaluations. Analyses show superior results with the proposed strategy compared to a genetic algorithm and to a design tool specialized for PID tuning, indicating its viability as an alternative for robust control design in power electronics.

 

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Author Biographies

Lucas Cielo Borin, Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil

received the B.Sc. degree in computer engineering, in 2017, and the M.Sc. degree in electrical engineering, in 2020, from the Federal University of Santa Maria, Brazil, where he is currently working toward the D.Sc. degree in electrical engineering with the Power Electronics and Control Research Group. His research interests include: intelligent algorithms and control theory applications.

Caio Ruviaro Dantas Osório, Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil

received the B.Sc. and M.Sc. degrees in electrical engineering in 2015 and 2017, respectively, from thehttps://www.overleaf.com/project/5ef66290717bba0001d63ff9 Federal University of Santa Maria, Brazil, where he is currently working toward the D.Sc. degree in electrical engineering, with the Power Electronics and Control Research Group. His research interests include control theory applications on power electronics, robust control and robust stability analysis.

Gustavo Guilherme Koch, Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil

received the B.Sc., M.Sc. and D.Sc. degrees in electrical engineering in 2013, 2015 and 2019, respectively, from the Federal University of Santa Maria, Brazil, where he is currently working toward the posdoctorate with the Power Electronics and Control Research Group. His research interests include robust control, and control theory applications.

Thieli Smidt Gabbi, Universidade Federal do Rio Grande do Sul (UFRS) – Porto Alegre, RS, Brazil

received the B.Sc., M.Sc. and D.Sc. degrees in electrical engineering in 2013, 2015 and 2019, respectively, from the Federal University of Santa Maria, Brazil. She is currently a Professor in the Federal University of Rio Grande do Sul (UFRGS). Her research interests include control systems and electrical machine drives.

Ricardo Coração de Leão Fontoura de Oliveira, Universidade de Campinas (UNICAMP) – Campinas, SP, Brazil

received the B.Sc. degree in computer engineering from the Pontifical Catholic University of Parana in 2001 and the M.Sc. and Ph.D. degrees in electrical engineering from the University of Campinas (UNICAMP), Campinas, SP, Brazil, in 2003 and 2006, respectively. He is currently a Professor with the School of Electrical and Computer Engineering (FEEC/UNICAMP). His research interests include the development of numerical tools for stability analysis and the control design of uncertain linear and fuzzy systems.

Vinícius Foletto Montagner, Universidade Federal de Santa Maria (UFSM) – Santa Maria, RS, Brazil

received the Master’s degree in electrical engineering from the Federal University of Santa Maria, Santa Maria, Brazil, in 2000, and the Ph.D. degree in electrical engineering from the University of Campinas, Campinas, Brazil, in 2005. He is currently a Professor in the Federal University of Santa Maria, where he works with the Power Electronics and Control Research Group. His research interests include robust stability and control applied to power electronics.

References

K. Deb, Multi-objective optimization using evolutionary algorithms, vol. 16, John Wiley &Sons, July 2001.

S. S. Rao, Engineering optimization: theory and practice, John Wiley & Sons, June 2009. DOI: https://doi.org/10.1002/9780470549124

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

S. P. Bhattacharyya, L. H. Keel, "Robust control: the parametric approach”, in Advances in Control Education 1994, pp. 49-52, Elsevier, August 1994. https://doi.org/10.1016/B978-0-08-042230-5.50016-5 DOI: https://doi.org/10.1016/B978-0-08-042230-5.50016-5

R. Haupt, S. Haupt, Practical Genetic Algorithms, Wiley-Intercedence publication, John Wiley, May2004. https://doi.org/10.1002/0471671746 DOI: https://doi.org/10.1002/0471671746

R. Eberhart, J. Kennedy, "A new optimizer using particle swarm theory”, in In Proceedings of the Sixth International Symposium on Micro Machine and Human Science., pp. 39-43, IEEE, Oct 1995.

S. S. Sebtahmadi, H. B. Azad, S. H. A. Kaboli,M. D. Islam, S. Mekhilef, "A PSO-DQ current control scheme for performance enhancement of Z-source matrix converter to drive IM fed by abnormal voltage", IEEE Transactions on Power Electronics, vol. 33,no. 2, pp. 1666-1681, March 2017. https://doi.org/10.1109/TPEL.2017.2679118 DOI: https://doi.org/10.1109/TPEL.2017.2679118

R. Poli, J. Kennedy, T. Blackwell, "Particle swarm optimization: An Overview”, Swarm intelligence, Vol. 1, no. 1, pp. 33-57, August 2007. https://doi.org/10.1007/s11721-007-0002-0 DOI: https://doi.org/10.1007/s11721-007-0002-0

S. E. De León-Aldaco, H. Calleja, J. A. Alquicira,"Meta heuristic optimization methods applied to power converters: A review", IEEE Transactions on Power Electronics, vol. 30, no. 12, pp. 6791-6803, January2015. https://doi.org/10.1109/TPEL.2015.2397311 DOI: https://doi.org/10.1109/TPEL.2015.2397311

M. Thirumeni, D. Thangavelusamy, "Design and analysis of hybrid PSO-GSA tuned PI and SMC controller for DC-DC Cuk converter",IET Circuits, Devices & Systems, vol. 13, no. 3, pp. 374-384,January 2019.https://doi.org/10.1049/iet-cds.2018.5164 DOI: https://doi.org/10.1049/iet-cds.2018.5164

.[11]Z.-L. Gaing, "A particle swarm optimization approach for optimum design of PID controller in AVR system", IEEE transactions on energy conversion, vol. 19, no. 2,pp. 384-391, May 2004. https://doi.org/10.1109/TEC.2003.821821 DOI: https://doi.org/10.1109/TEC.2003.821821

R. A. Hanifah, S. F. Toha, S. Ahmad, M. K. Hassan," Swarm-Intelligence Tuned Current Reduction for Power-Assisted Steering Control in Electric Vehicles", IEEE Transactions on Industrial Electronics, vol. 65,no. 9, pp. 7202-7210, December 2017. https://doi.org/10.1109/TIE.2017.2784344 DOI: https://doi.org/10.1109/TIE.2017.2784344

I.-Y. Chung, W. Liu, D. A. Cartes, E. G. Collins, S.-I. Moon, "Control methods of inverter-interfaced distributed generators in a microgrid system", IEEE Trans Ind Appl, vol. 46, no. 3, pp. 1078-1088, March2010. https://doi.org/10.1109/TIA.2010.2044970 DOI: https://doi.org/10.1109/TIA.2010.2044970

J. Ackermann, Robust control: the parameter space approach, Springer Science & Business Media, July2012.

V. L. Kharitonov, J. A. Torres-Muñoz, M. B. Ortiz-Moctezuma, "Polytopic families of quasi-polynomials :vertex-type stability conditions", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 11, pp. 1413-1420,November 2003. https://doi.org/10.1109/TCSI.2003.817768 DOI: https://doi.org/10.1109/TCSI.2003.817768

K. E. L. Marcillo, D. A. P. Guingla, W. Barra, R. L. P. De Medeiros, E. M. Rocha, D. A. V. Benavides, F. G. Nogueira, "Interval robust controller to minimize oscillations effects caused by constant power load in a DC multi-converter buck-buck system", IEEE Access, vol. 7, pp. 26324-26342, February 2019. https://doi.org/10.1109/ACCESS.2019.2901441 DOI: https://doi.org/10.1109/ACCESS.2019.2901441

N. M. Dehkordi, N. Sadati, M. Hamzeh, "Robusttuning of transient droop gains based on Kharitonov’s stability theorem in droop-controlled microgrids", IET Generation, Transmission & Distribution, vol. 12,no. 14, pp. 3495-3501, August 2018. https://doi.org/10.1049/iet-gtd.2017.1767 DOI: https://doi.org/10.1049/iet-gtd.2017.1767

K. E. Lucas-Marcillo, D. A. P. Guingla, W. Barra,R. L. P. De Medeiros, E. M. Rocha, D. A. Vaca-Benavides, S. J. R. Orellana, E. V. H. Muentes, "Novelrobust methodology for controller design aiming to ensure DC microgrid stability under CPL power variation", IEEE Access, vol. 7, pp. 64206-64222,May 2019. https://doi.org/10.1109/ACCESS.2019.2915027 DOI: https://doi.org/10.1109/ACCESS.2019.2915027

A. J. S. J. Veronica, N. S. Kumar, F. Gonzalez-Longatt,"Robust PI controller design for frequency stabilisation in a hybrid microgrid system considering parameter uncertainties and communication time delay",IET Generation, Transmission & Distribution, vol. 13,no. 14, pp. 3048-3056, July 2019. https://doi.org/10.1049/iet-gtd.2018.5240 DOI: https://doi.org/10.1049/iet-gtd.2018.5240

R. He, Q. Han, "Dynamics and stability of permanent-magnet synchronous motor", Mathematical Problems in Engineering, vol. 2017, June 2017. https://doi.org/10.1155/2017/4923987 DOI: https://doi.org/10.1155/2017/4923987

A. K. Yadav, P. Gaur, P. Saxena, "Robust stability analysis of PMSM with parametric uncertainty using Kharitonov Theorem", Journal of Electrical Systems, vol. 12, no. 2, pp. 258-277, June 2016.

J. Jung, Y. Choi, V. Q. Leu, H. H. Choi, "Fuzzy PI-type current controllers for permanent magnet synchronous motors", IET Electric Power Applications, vol. 5, no. 1,pp. 143-152, February 2011. https://doi.org/10.1049/iet-epa.2010.0036 DOI: https://doi.org/10.1049/iet-epa.2010.0036

M. Sreejeth, M. Singh, P. Kumar, "Particle swarm optimisation in efficiency improvement of vector controlled surface mounted permanent magnet synchronous motor drive", IET Power Electronics, vol. 8, no. 5, pp. 760-769, April 2015.https://doi.org/10.1049/iet-pel.2014.0399 DOI: https://doi.org/10.1049/iet-pel.2014.0399

B. R. Barmish, "A generalization of Kharitonov's four-polynomial concept for robust stability problems with linearly dependent coefficient perturbations", IEEE Transactions on Automatic Control, vol. 34, no. 2, pp.157-165, February 1989.https://doi.org/10.1109/9.21087 DOI: https://doi.org/10.1109/9.21087

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. Teodorescu, M. Liserre, P. Rodríguez,GridConverters for Photovoltaic and Wind Power Systems, Wiley - IEEE, John Wiley & Sons, February 2011.[27]A. Karimi, H. Khatibi, R. Longchamp, "Robust control of polytopic systems by convex optimization",Automatica, vol. 43, no. 8, pp. 1395-1402, August2007. https://doi.org/10.1016/j.automatica.2007.01.022 DOI: https://doi.org/10.1016/j.automatica.2007.01.022

R. C. Dorf, R. H. Bishop, Modern control systems, Pearson, 2011.[29]S. Banerjee, A. Ghosh, N. Rana, "An Improved Interleaved Boost Converter With PSO-Based Optimal Type-III Controller", IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 1, pp.323-337, March 2017. https://doi.org/10.1109/JESTPE.2016.2608504 DOI: https://doi.org/10.1109/JESTPE.2016.2608504

S. Sengupta, S. Basak, R. Peters, "Particle Swarm Optimization: A survey of historical and recent developments with hybridization perspectives”, Machine Learning and Knowledge Extraction, vol. 1,no. 1, pp. 157-191, October 2018. https://doi.org/10.3390/make1010010 DOI: https://doi.org/10.3390/make1010010

M. Veerachary, A. R. Saxena, "Optimized power stage design of low source current ripple fourth-order boost DC-DC converter: A PSO approach", IEEE Transactions on Industrial Electronics, vol. 62, no. 3,pp. 1491-1502, March 2015. https://doi.org/10.1109/TIE.2014.2361316 DOI: https://doi.org/10.1109/TIE.2014.2361316

R. C. Eberhart, Y. Shi, "Particle swarm optimization: developments, applications and resources”, in Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), vol. 1, pp.81-86, IEEE, May 2001.

Y. Shi, R. C. Eberhart, "Parameter selection in particles warm optimization”, in International conference on evolutionary programming, pp. 591-600, Springer, March 1998. https://doi.org/10.1007/BFb0040810 DOI: https://doi.org/10.1007/BFb0040810

P. Pillay, R. Krishnan, "Modeling, simulation, andanalysis of permanent-magnet motor drives. I. The permanent-magnet synchronous motor drive",IEEE Transactions on Industry Applications, vol. 25, no. 2,pp. 265-273, Mar/Apr 1989. https://doi.org/10.1109/28.25541 DOI: https://doi.org/10.1109/28.25541

P. Krause, O. Wasynczuk, S. Sudhoff, Analysis of Electric Machinery and Drive Systems, second ed.,Wiley-IEEE Press, United States of America, March2002. https://doi.org/10.1109/9780470544167 DOI: https://doi.org/10.1109/9780470544167

R. Krishnan, Electric motor drives: modeling, analysis, and control, Prentice Hall, February 2001.

M. J. Ryan, R. D. Lorenz, R. De Doncker,"Modeling of multileg sine-wave inverters: a geometric approach", IEEE Transactions on Industrial Electronics, vol. 46, no. 6, pp. 1183-1191, December 1999. https://doi.org/10.1109/41.808008 DOI: https://doi.org/10.1109/41.808008

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Published

2020-06-30

How to Cite

[1]
L. C. Borin, C. R. D. Osório, G. G. Koch, T. S. Gabbi, R. C. de L. F. de Oliveira, and V. F. Montagner, “Robust Control Design Procedure Based on Particle Swarm Optimization and Kharitonov’s Theorem with an Application for PMSMs”, Eletrônica de Potência, vol. 25, no. 2, pp. 219–229, Jun. 2020.

Issue

Vol. 25 No. 2 (2020)

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Original Papers

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