Autors: Mishkov, R. L., Petrov, V. S.
Title: Multiple reference frames state space models of brushless dc motor for feedback linearization
Keywords: Nonlinear systems, Nonlinear transformations, Feedback linearization, Brushless DC motor, Power invariance

Abstract: Multiple reference frames orientated state space nonlinear mathematical models for brushless DC motors are derived in the paper using the power invariant dqo transformation in rotating and stationary form. The nonlinear state space models obtained are strictly orientated, decoupled, and linear with respect to the model parameters. This allows convenient application of advanced control theory differential geometric design approaches including multi-input multi-output feedback linearization and nonlinear adaptive systems design. Moreover the decoupling of the currents permits closed-loop nonlinear systems synthesis accomplishing simultaneous elimination of the torque pulsations and copper losses minimization. The nonlinear state space models derived are simulated to investigate their properties.


  1. Al-Mashakbeh, A. S. O., 2009, Proportional Integral and Derivative Control of Brushless DC Motor, European Journal of Scientific Research, Volume 35(2), pp. 198-203
  2. Chapman, P.L., Sudhoff, S. D., Whitcomb, C. A., 1999, Multiple Reference Frame Analysis of Non-sinusoidal Brushless DC Drives, IEEE Transactions on Energy Conversion, Volume 14(3), pp. 440-446
  3. Chiasson, J., 2005, Modeling and High Performance Control of Electric Machines, New York, A JOHN WILEY & SONS, INC
  4. Grenier, D., Dessaint, L.-A., Akhrif, O., Louis, J.-P., 1995, IEEE IECON 21st International Conference on Industrial Electronics, Control, and Instrumentation, Orlando, FL, USA, 6-10 November 1995, <Proceedings of IECON '95 - 21st Annual Conference on IEEE Industrial Electronics>, IEEE
  5. Kanellakopoulos, I.,Kokotovic, P., Morse, A., 1991, Systematic design of adaptive controllers for feedback linearizable systems, IEEE Transactions on Automatic control, Volume 36(11), pp. 1241-1253
  6. Krishnan, R., 2010, Permanent Magnet Synchronous and Brushless DC Motor Drives, Boca Raton, FL, USA, Taylor and Francis Group, LLC
  7. Krishnan, R., 2001, Electric Motor Drives: Modeling, Analysis and Control, Upper Saddle River, New Jersey, USA, Prentice Hall
  8. Krstic, M., 1995, Asymptotic properties of adaptive nonlinear stabilizers, Seattle, WA, USA, 21-23 June 1995, <Proceedings of 1995 American Control Conference - ACC'95>, IEEE
  9. Krstic, M., Kanellakopoulos, I., Kokotovic, P., 1995, Nonlinear and adaptive control design, New York, NY, USA, John Wiley and Sons, Inc.
  10. Kumar, P., Bauer, P., 2008, Improved Analytical Model of a Permanent-Magnet Brushless DC Motor, IEEE Transactions on Magnetics, Volume 44(10), pp. 2299-2309
  11. Mahesh, B.,Ravi, G.,Chakrabarti, R., 2009, Sensorless Speed Control of Brushless DC Motor with Fuzzy Based Estimation, Iranian Journal of Electrical and Computer Engineering, Volume 8(2), pp. 119-125
  12. Mishkov, R., 2007, Feedback Linearization and Nonlinear Observers for a DC Motor Controlled Inverted Pendulum, Maribor, Slovenia, 14 - 28 Septembe, 2007, <Proceedings of the International Web Conference Information Systems in Automation – CEEPUS Summer School 2007>, University of Maribor
  13. Mishkov, R., 2005, Nonlinear Observer Design by Reduced Generalized Observer Canonical Form, International Journal of Control, Volume 78(3), pp. 172-185
  14. Mishkov, R., 2010, Inverted pendulum control by feedback linearization and nonlinear observer, Sofia, Bulgaria, 3–7 October 2010, <Sofia, Bulgaria>, The John Atanasoff society of automatics and informatics
  15. Muruganantham, N., Palani, S., 2010, State space modeling and simulation of sensorless permanent magnet BLDC motor, International Journal of Engineering Science and Technology, Volume 2(10), pp. 5099-5106
  16. Pillay, P., Krishnan, R., 1988, Modeling of Permanent-magnet Motor Drives, IEEE Transactions on Industrial Electronics, Volume 35(4), pp. 537 - 541
  17. Pillay, P., Krishnan, R., 1989, Modeling, Simulation, and Analysis of Permanent-Magnet Motor Drives, Part II: The Brushless DC Motor Drive, IEEE Transactions on Industry Applications, Volume 25(2), pp. 274-279


International Conference Automatics and Informatics'11, pp. B-71 - B-74, 2011, Bulgaria,

Full text of the publication

Вид: публикация в международен форум