Linear Matrix Inequality Based Synthesis of PI Controllers for PMSM with Uncertain Parameters

Authors

  • Gustavo G. Koch Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil
  • Thieli S. Gabbi Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil
  • Rodrigo P. Vieira Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil
  • Humberto Pinheiro Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil
  • Thiago A. Bernardes Federal Institute of Brasília – IFB, Brasília – DF, Brazil
  • Ricardo C. L. F. Oliveira University of Campinas – UNICAMP, Campinas – SP, Brazil
  • Vinícius F. Montagner Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil

DOI:

https://doi.org/10.18618/REP.2018.3.2786

Keywords:

Linear Matrix Inequalities, Permanent Magnet Synchronous Motor, Robust Control, Uncertain Parameter

Abstract

This paper addresses the design of robust PI controllers for permanent magnet synchronous motors in terms of a linear matrix inequality based problem. A polytopic model of the plant is obtained and validated for the motor uncertain parameters belonging to intervals. The design procedure proposed here encompasses: i. suitable plant uncertainties inclusion and the use of practical design control constraints; ii. robust PI computation based on linear matrix inequalities with a very fast solution; iii. simulation analyses; and iv. experimental evaluations. The robust PI controller can produce superior speed regulation than a PI controller designed only for the nominal parameters, including better disturbance rejection and H-infinity performance. Experimental results confirm the viability of the proposal, which can be seen as an efficient alternative to trade off performance and robustness for PI controllers in this application.

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Author Biographies

Gustavo G. Koch, Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil

was born in Ijuí, RS, Brazil, in 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering in 2013 and 2015, respectively, from the Federal University of Santa Maria, Santa Maria, Brazil, where he is currently working toward the Ph.D. degree. His research interests include robust control, and control theory applications.

Thieli S. Gabbi, Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil

was born in Santa Maria, RS, Brazil, in 1989. She received the B.Sc. and M.Sc. degrees in electrical engineering in 2013 and 2015, respectively, from the Federal University of Santa Maria, Santa Maria, Brazil, where she is currently working toward the Ph.D. degree. Her research interests include control systems and eletrical machine drives.

Rodrigo P. Vieira, Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil

was born in Cruz Alta, Brazil. He received the B.S. degree in electrical engineering from the Universidade Regional do Noroeste do Estado do Rio Grande do Sul (UNIJUI), Ijuí, Brazil, in 2007, and the M.S. and Dr. Eng. degrees in electrical engineering from the Federal University of Santa Maria (UFSM), Santa Maria, Brazil, in 2008 and 2012, respectively. From 2010 to 2014, he was with the Federal University of Pampa, Alegrete, Brazil. Since 2014, he has been with the UFSM, where he is currently an Adjunct Professor. His research interests include electrical machine drives, sliding mode control, and digital control techniques of static converters.

Humberto Pinheiro, Federal University of Santa Maria – UFSM, Santa Maria – RS, Brazil

was born in Santa Maria, Brazil, in 1960. He received the B.Sc. degree from the Federal University of Santa Maria, Santa Maria, Brazil, in 1983, the M.Eng. degree from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1987, and the Ph.D. degree from Concordia University, Montreal, QC, Canada, in 1999. From 1987 to 1990, he was a Research Engineer with a Brazilian UPS company and then joined the Pontifícia Universidade Católica do Rio Grande do Sul, Brazil, where he lectured on power electronics. Since 1991, he has been with the Federal University of Santa Maria. His current research interests include grid-connected three-phase converters, wind energy conversion systems, and control applied to power electronics.

Thiago A. Bernardes, Federal Institute of Brasília – IFB, Brasília – DF, Brazil

was born in Natal, RN, Brazil, in 1983. He received the B.Sc. degree in electrical engineering from the Federal University of Ceara in2007, and the M.Sc. and D.Sc. degrees in electrical engineering from Federal University of Santa Maria, Santa Maria, Brazil, in 2009 and 2013, respectively. He is effective professor at the Federal Institute of Ceará - Sobral. His research interests include: sliding mode control, control applied to power electronics systems, wind energy conversion systems, control systems connected to the grid and energy efficiency.

Ricardo C. L. F. Oliveira, University of Campinas – UNICAMP, Campinas – SP, Brazil

was born in Assis Chateaubriand, Parana, Brazil, in 1978. He 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, UNICAMP. His research interests include the development of numerical tools for stability analysis and the control design of uncertain linear and fuzzy systems.

Vinícius F. Montagner, Federal University of 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 (GEPOC). His research interests include robust stability and control applied to power electronics.

References

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

A. M. EL-Refaie, "Fractional-Slot Concentrated-Windings Synchronous Permanent Magnet Machines: Opportunities and Challenges", IEEE Transactions on Industrial Electronics, vol. 57, no. 1, pp. 107-121, Jan2010. https://doi.org/10.1109/TIE.2009.2030211 DOI: https://doi.org/10.1109/TIE.2009.2030211

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

B. Hafez, A. S. Abdel-Khalik, A. M. Massoud,S. Ahmed, R. D. Lorenz, "Single-Sensor-Based Three-Phase Permanent-Magnet Synchronous MotorDrive System With Luenberger Observers for Motor Line Current Reconstruction", IEEE Transactions on Industry Applications, vol. 50, no. 4, pp. 2602-2613,July 2014. https://doi.org/10.1109/TIA.2013.2296625 DOI: https://doi.org/10.1109/TIA.2013.2296625

R. Ni, D. Xu, G. Wang, L. Ding, G. Zhang,L. Qu, "Maximum Efficiency Per Ampere Control of Permanent-Magnet Synchronous Machines",IEEE Transactions on Industrial Electronics, vol. 62, no. 4,pp. 2135-2143, April 2015. https://doi.org/10.1109/TIE.2014.2354238 DOI: https://doi.org/10.1109/TIE.2014.2354238

C. Xia, B. Ji, Y. Yan, "Smooth Speed Control for Low-Speed High-Torque Permanent-Magnet Synchronous Motor Using Proportional-Integral-Resonant Controller", IEEE Transactions on Industrial Electronics, vol. 62, no. 4, pp. 2123-2134, April 2015. https://doi.org/10.1109/TIE.2014.2354593 DOI: https://doi.org/10.1109/TIE.2014.2354593

J. Jang, M. Humza, B. Kim, "Design of a Variable-Flux Permanent-Magnet Synchronous Motor for Adjustable-Speed Operation", IEEE Transactions on Industry Applications, vol. 52, no. 4, pp. 2996-3004,July 2016. https://doi.org/10.1109/TIA.2016.2547986 DOI: https://doi.org/10.1109/TIA.2016.2547986

S. Yamamoto, H. Hirahara, A. Tanaka, T. Ara,K. Matsuse, "Universal Sensor less Vector Control of Induction and Permanent-Magnet Synchronous Motors Considering Equivalent Iron Loss Resistance", IEEE Transactions on Industry Applications, vol. 51,no. 2, pp. 1259-1267, March 2015. https://doi.org/10.1109/TIA.2014.2360962 DOI: https://doi.org/10.1109/TIA.2014.2360962

T. Bernardes, V. F. Montagner, H. A. Grundling,H. Pinheiro, "Discrete-Time Sliding Mode Observer for Sensorless Vector Control of Permanent Magnet Synchronous Machine", IEEE Transactions on Industrial Electronics, vol. 61, no. 4, pp. 1679-1691,April 2014. https://doi.org/10.1109/TIE.2013.2267700 DOI: https://doi.org/10.1109/TIE.2013.2267700

G. H. Negri, F. G. Nazário, J. de Oliveira, A. Nied,"Back-emf based rotor position estimation for low cost PMSM drive using fully connected cascade artificial neural networks", Eletrônica de Potência,vol. 23, no. 1, pp. 69 - 77, March 2018. https://doi.org/10.18618/REP.2018.1.2728 DOI: https://doi.org/10.18618/REP.2018.1.2728

E. de M. Fernandes, A. C. Oliveira, A. M. N. Lima,C. B. Jacobina, "Estimação de posição rotórica de motor PMSM com minimização da distorção da tensão de alta frequência", Eletrônica de Potência, vol. 17, no. 1, pp. 447 -455, February 2012. https://doi.org/10.18618/REP.2012.1.447455 DOI: https://doi.org/10.18618/REP.2012.1.447455

S. Li, Z. Liu, "Adaptive Speed Control for Permanent-Magnet Synchronous Motor System With Variations of Load Inertia", IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 3050-3059, Aug 2009. https://doi.org/10.1109/TIE.2009.2024655 DOI: https://doi.org/10.1109/TIE.2009.2024655

J. W. Jung, V. Q. Leu, T. D. Do, E. K. Kim,H. H. Choi, "Adaptive PID Speed Control Design forPermanent Magnet Synchronous Motor Drives",IEEE Transactions on Power Electronics, vol. 30, no. 2, pp.900-908, Feb 2015. https://doi.org/10.1109/TPEL.2014.2311462 DOI: https://doi.org/10.1109/TPEL.2014.2311462

X. Zhang, L. Sun, K. Zhao, L. Sun, "Nonlinear Speed Control for PMSM System Using Sliding-Mode Control and Disturbance Compensation Techniques", IEEE Transactions on Power Electronics, vol. 28,no. 3, pp. 1358-1365, March 2013. https://doi.org/10.1109/TPEL.2012.2206610 DOI: https://doi.org/10.1109/TPEL.2012.2206610

A. G. Bartsch, G. H. Negri, C. R. Scalabrin, M. S. M.Cavalca, A. Nied, J. de Oliveira, "Predictive control approach for permanent magnet synchronous motor drive ", Eletrônica de Potência, vol. 20, no. 4,pp. 395 - 403, November 2015. https://doi.org/10.18618/REP.2015.4.2567 DOI: https://doi.org/10.18618/REP.2015.4.2567

V. Q. Leu, H. H. Choi, J. W. Jung, "Fuzzy Sliding Mode Speed Controller for PM Synchronous Motors With a Load Torque Observer", IEEE Transactions on Power Electronics, vol. 27, no. 3, pp. 1530-1539,March 2012.

https://doi.org/10.1109/TPEL.2011.2161488 DOI: https://doi.org/10.1109/TPEL.2011.2161488

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

H. H. Choi, N. T. T. Vu, J. W. Jung, "Design and Implementation of a Takagi-Sugeno Fuzzy Speed Regulator for a Permanent Magnet Synchronous Motor", IEEE Transactions on Industrial Electronics, vol. 59, no. 8, pp. 3069-3077, Aug 2012. https://doi.org/10.1109/TIE.2011.2141091 DOI: https://doi.org/10.1109/TIE.2011.2141091

R. C. García, J. O. P. Pinto, E. A. Batista, L. Galotto,"Design of a MIMO IMC-TS fuzzy speed controller for PMSM",in Proc. of Brazilian Power Electronics Conference (COBEP), pp. 1-6, 2017. https://doi.org/10.1109/COBEP.2017.8257434 DOI: https://doi.org/10.1109/COBEP.2017.8257434

K. Astrom, T. Hagglund, PID Controllers, International Society for Measurement and Control,1995.

J. Dannehl, F. W. Fuchs, S. Hansen, P. B. Thogersen,"Investigation of Active Damping Approaches for PI-Based Current Control of Grid-Connected Pulse Width Modulation Converters With LCL Filters", IEEE Transactions on Industry Applications, vol. 46,no. 4, pp. 1509-1517, July 2010. https://doi.org/10.1109/TIA.2010.2049974 DOI: https://doi.org/10.1109/TIA.2010.2049974

R. Kadri, J. P. Gaubert, G. Champenois, "An Improved Maximum Power Point Tracking for Photovoltaic Grid-Connected Inverter Based on Voltage-Oriented Control", IEEE Transactions on Industrial Electronics, vol. 58, no. 1, pp. 66-75, Jan 2011. https://doi.org/10.1109/TIE.2010.2044733 DOI: https://doi.org/10.1109/TIE.2010.2044733

D. R. Espinoza-Trejo, E. Barcenas-Barcenas, D. U.Campos-Delgado, C. H. D. Angelo, "Voltage-Oriented Input-Output Linearization Controllers Maximum Power Point Tracking Technique for Photovoltaic Systems", IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3499-3507,June 2015.

D. G. Holmes, B. P. McGrath, S. G. Parker, "Current Regulation Strategies for Vector-Controlled Induction Motor Drives", IEEE Transactions on Industrial Electronics, vol. 59, no. 10, pp. 3680-3689, Oct 2012. https://doi.org/10.1109/TIE.2011.2165455 DOI: https://doi.org/10.1109/TIE.2011.2165455

E. de M. Fernandes, D. R. Huller, A. C. Oliveira,M. B. de R. Corrêa, W. R. N. Santos, "Simulador em tempo real para motor síncrono como íma permanente baseado em dispositivos lógicos programáveis", Eletrônica de Potência, vol. 20, no. 3, pp. 244- 253, August 2015. https://doi.org/10.18618/REP.2015.3.2537 DOI: https://doi.org/10.18618/REP.2015.3.2537

M. Ge, M.-S. Chiu, Q.-G. Wang, "Robust PIDcontroller design via LMI approach", Journal ofProcess Control, vol. 12, no. 1, pp. 3 - 13, January2002. https://doi.org/10.1016/S0959-1524(00)00057-3 DOI: https://doi.org/10.1016/S0959-1524(00)00057-3

H. Zhang, Y. Shi, A. Mehr, "Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems", IEEE Transactions on Industrial Electronics, vol. 58, no. 12, pp. 5396 -5405,December 2011. https://doi.org/10.1109/TIE.2011.2107720 DOI: https://doi.org/10.1109/TIE.2011.2107720

A. Guagnano, G. Rizzello, F. Cupertino, D. Naso,"Robust Control of High-Speed Synchronous Reluctance Machines", IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 3990-4000,Sept 2016. https://doi.org/10.1109/TIA.2016.2574774 DOI: https://doi.org/10.1109/TIA.2016.2574774

X. Sun, Y. Yi, W. Zheng, T. Zhang, "Robust PI speed tracking control for PMSM system based on convex optimization algorithm”, in Proc. of the 33rd Chinese Control Conference, pp. 4294-4299, 2014.

https://doi.org/10.1109/ChiCC.2014.6895659 DOI: https://doi.org/10.1109/ChiCC.2014.6895659

P. Krause, O. Wasynczuk, S. Sudhoff, Analysis of Electric Machinery and Drive Systems, second ed., Wiley-IEEE Press, United States of America, 2002. https://doi.org/10.1109/9780470544167 DOI: https://doi.org/10.1109/9780470544167

K.-H. Kim, M.-J. Youn, "A nonlinear speed control for a PM synchronous motor using a simple disturbance estimation technique", IEEE Transactions on Industrial Electronics, vol. 49, no. 3, pp. 524-535,Jun 2002. https://doi.org/10.1109/TIE.2002.1005377 DOI: https://doi.org/10.1109/TIE.2002.1005377

R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives, Mechanical Engineering(Marcel Dekker), 1 ed., CRC Press, 2009.

M. Chilali, P. Gahinet, P. Apkarian, "Robust pole placement in LMI regions", IEEE Transactions on Automatic Control, vol. 44, no. 12, pp. 2257-2270,December 1999. https://doi.org/10.1109/9.811208 DOI: https://doi.org/10.1109/9.811208

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Published

2018-09-30

How to Cite

[1]
G. G. Koch, “Linear Matrix Inequality Based Synthesis of PI Controllers for PMSM with Uncertain Parameters”, Eletrônica de Potência, vol. 23, no. 3, pp. 310–319, Sep. 2018.

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Vol. 23 No. 3 (2018)

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Original Papers

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