Compensative Microstepping Based Position Control with Passive Nonlinear Adaptive Observer for Permanent Magnet Stepper Motors

  • Kim, Wonhee (School of Energy Systems Engineering, Chung-Ang University) ;
  • Lee, Youngwoo (Department of Electrical and Computer Engineering, UNIST and Department of Mechanical Engineering, University of California) ;
  • Shin, Donghoon (Global R&D Center, MANDO Corporation) ;
  • Chung, Chung Choo (Division of Electrical and Biomedical Engineering, Hanyang University)
  • Received : 2017.05.22
  • Accepted : 2017.06.16
  • Published : 2017.09.01


This paper presents a compensative microstepping based position control with passive nonlinear adaptive observer for permanent magnet stepper motor. Due to the resistance uncertainties, a position error exists in the steady-state, and a ripple of position error appears during operation. The compensative microstepping is proposed to remedy this problem. The nonlinear controller guarantees the desired currents. The passive nonlinear adaptive observer is designed to estimate the phase resistances and the velocity. The closed-loop stability is proven using input to state stability. Simulation results show that the position error in the steady-state is removed by the proposed method if the persistent excitation conditions are satisfied. Furthermore, the position ripple is reduced, and the Lissajou curve of the phase currents is a circle.


Permanent magnet stepper motor;Microstepping;Adaptive control


Grant : Automatic lane change system for novice drivers

Supported by : Chung-Ang University, Ministry of Trade, Industry and Energy (MOTIE)


  1. T. Kenjo, Stepping Motors and Their Microprocessor Control. New York:Clarendon, 1984.
  2. M. Bodson, J. S. Sato, and S. R. Silver, "Spontaneous Speed Reversals in Stepper Motors," IEEE Trans. Control Syst. Technol., vol. 14, no. 2, pp. 369-273, Mar. 2006.
  3. D. W. Jones, "Control of stepping motors," Handbook of Small Electric Motors, W. H. Yeadon and A. W. Yeadon, Eds. McGraw-Hill, New York, 2001.
  4. Core techonologies. Motors and control systems for precise motion control. See also URL
  5. Manea, S., 2009. "Stepper motor control with dsPIC DSCs," Microchip Application Note, 1-26.
  6. A. Bellini, C. Concari, G. Franceschini, and A. Toscani, "Mixed-Mode PWM for High-Performance Stepping Motors," IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 3167-3177, Dec. 2007.
  7. Orientalmotor Basics of motion control. See also URL
  8. Sanyo-Denki, 2 Phase Stepping Systems. See also URL
  9. A. S. Ghafari and A. Alasty, "Design and real-time experimental im-plementation of gain scheduling PID fuzzy controller for hybrid stepper motor in micro-step operation," in Proc. IEEE Int. Conf. Mechatronics, 2004, pp. 421-426.
  10. A. S. Ghafari and M. Behzad, "Investigation of the micro-step control positioning system performance affected by random input signals," Mechatronics, vol. 15, no. 10, pp. 1175-1189, 2005.
  11. W. Kim, I. Choi, K. Bae, and C. C. Chung, "A Lyapunov Method in Microstepping Control for Permanent Magnet Stepper Motors," in Proc. IEEE Int. Conf. Mechatronics, 2009, pp. 1-5.
  12. W. Kim, D. Shin, and C. C. Chung, "The Lyapunovbased controller with a passive nonlinear observer to improve position tracking performance of microstepping in permanent magnet stepper motors," Automatica, vol. 48, no. 12, pp. 3064-3074, 2012.
  13. W. Kim, D. Shin, and C. C. Chung, "Microstepping Using a Disturbance Observer and a Variable Structure Controller for Permanent Magnet Stepper Motors," IEEE Trans. Ind. Electron., vol. 60, no. 7, pp. 2689-2699, 2013.
  14. W. Kim, D. Shin, Y. Lee, and C. C. Chung, "Microstepping with nonlinear torque modulation for permanent magnet stepper motors," IEEE Trans. Control Syst. Technol., vol. 21, no. 5, pp. 1971-1979, 2013.
  15. D. Shin, W. Kim, Y. Lee, and C. C. Chung, "Phase compensation microstepping for permanent magnet stepper motors," IEEE Trans. Ind. Electron., vol. 60, no. 12, pp. 5773-5780, 2013.
  16. M. Bendjedia, Y. A. Amirat, B. Walther, and A. Berthon, "Position control of a sensorless stepper motor," IEEE Trans. Power Electron., vol. 27, no. 2, pp. 578-587, 2012.
  17. R. Delpoux and T. Floquet, "High-order sliding mode control for sensorless trajectory tracking of a PMSM," Int. J. Control, vol. 87, no. 10, pp. 2140-2155, 2014.
  18. Autonics, Stepper Motor Datasheet. See also URL
  19. R. Marino, S. Peresada, and P. Tomei, "Nonlinear Adaptive Control of Permanent Magnet Step Motors," Automatica, vol. 31, no. 11, pp. 1595-1604, 1995.
  20. Y. M. Cho and R. Rajamani "A systematic approach to adaptive observer synthesis for nonlinear systems." IEEE Trans. Autom. Control, vol. 42, no. 4, pp. 534-537, 1997.
  21. F. Khorrami, P. Krishnamurthy, P, and H. Melkote, H., Modeling and Adaptive Nonlinear Control of Electric Motors, Heidelberg: Springer Verlag, 2003.
  22. J. Chiasson, Modeling and High-Performance Control of Electric Machines, Hoboken, NJ: Wiley-Interscience, 2005.
  23. M. Bodson, J. Chiasson, R. Novotnak, and R. Ftekowski, "High-Performance Nonlinear Feedback Control of a Permanent Magnet Stepper Motor," IEEE Trans. Control Syst. Technol., vol. 1, no. 1, pp. 5-14, Mar. 1993.
  24. Orientalmotor, "PK Series Stepping Motors," Hampshire, U.K. [Online]. Available:
  25. H. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
  26. R. Kosut, "Design of linear systems with saturating linear control and bounded states," IEEE Trans. Automat. Control, vol. 28, no. 1, pp. 121-124, 1983.
  27. P. A. Ioannou and J. Sun, Robust Adaptive Control, Englewood Cliffs, NJ: Prentice-Hall, 1996.