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.

Downloads

Download data is not yet available.

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.

Downloads

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.

Issue

Section

Original Papers