

Overview of Models and Methods for Control of Stepper Motors
https://doi.org/10.17587/mau.24.352-363
Abstract
A review of models and algorithms for control of a stepper motor (SM) is presented. Due to high accuracy, improved power density, economy and reliability compared to other synchronous motors, stepper motors are widely used in various practical applications and scientific equipment. In aviation and space technology, step motors are actively used in actuating systems, such as drives for the movement of elements of large-sized structures, guidance, and stabilization systems, etc. The article describes some existing stepper motor control algorithms, which are both based on the knowledge of the parameters of the stepper motor model, and on the absence of this or that information. Of the many described algorithms, four were selected (PID controller, exact feedback linearization algorithm, adaptive control with partially unknown parameters and adaptive control with completely unknown parameters), which showed the best results of transient processes in tracking the angle of the rotor of the SM behind the reference value. A comparative numerical analysis among these four algorithms is also given, which showed that the best results of transients are demonstrated by adaptive controllers (in the sense of the smallest error in steady state), while the worst results are demonstrated by the PID controller. It is noted that the studied PID controller contains much fewer feedback loops compared to other algorithms, which simplifies the choice of adjustable parameters and reduces the dynamic order of the closed system, however, the design is based on knowing the exact parameters of the drive and is also sensitive to external disturbances. On the contrary, adaptive approaches successfully solve the problem of estimating parametric and functional perturbations, but their implementation is associated with significant difficulties.
About the Authors
I. B. FurtatRussian Federation
Furtat Igor B., Dr. of Tech.Sc., Professor
St. Petersburg, 199178
Y. A. Zhukov
Russian Federation
St. Petersburg, 199178
N. S. Slobodzyan
Russian Federation
St. Petersburg, 199178
References
1. Masandilov L. B., Sergievsky Yu. N., Kozyrev S. K. et al. Mechanical engineering. Encyclopedia Electric drives. T. IV, Masandilova L. B. ed., Moscow, Mashinostroenie, 2012, 520 p.
2. Mihalache G., Zbant A., Livint G. Open-Loop Control of Hybrid Stepper Motor with Two Phases Using Voltage to Frequency Converter, Proc. of the 8th International Symposium on Advanced Topics in Electrical Engineering, May 23—25, 2013, Bucharest, Romania.
3. AL-Sabbagh Q. S., Mahdi A. S. Pulse Width Modulation High Performance Hybrid Stepper Motor, Journal of Engineering, December 2010, vol. 16, no. 4.
4. Kelemen A., Crivii M. Motoare electrice pas cu pas, Bucuresti, Editura Tehnica, 1975.
5. Morar A. Comanda inteligentă a acţionărilor electrice cu motoare pascu pas, Cluj Napoca, Editura Mediamira, 2007.
6. Acarnley P. Stepping Motors — A guide to theory and practice, London, The Institution of Electrical Engineers, 2002.
7. Zribi M., Chiasson J. Position Control of a PM Stepper Motor by Exact Linearization, IEEE Transaction on Automatic Control, May 1991, vol. 36, no. 5.
8. Kenjo T. Stepping Motors and Their Microprocessor Controls. Oxford, U. K., Clarendon, 1984.
9. Marino R., Tomei P. Adaptive Control of Stepper Motors Via Nonlinear Extended Matching, IFAC Proceedings Volumes, October 1992, vol. 25, no. 29, part 1, pp. 135—139.
10. Ilic’-Spong M., Marino R., Peresada S. M., Taylor D. G. Feedback linearizing control of switched reluctance motors, IEEE Trans. Automatic Control, 1987, vol. 32, pp. 371—379.
11. Taylor D. G. Adaptive control design for a class of doublysalient motors, Proc. of the IEEE 90th Conf. on Decision and Control, Brighton, 1991, pp. 2903—2908.
12. Bodson M., Chiasson J. Application of nonlinear control methods to the positioning of a permanent magnet stepper motor, Proc. of the IEEE 28th Conf. on Decision and Control, Tampa, 1989, pp. 531—532.
13. Chen D., Paden B. Nonlinear adaptive torque-ripple cancellation for step motors, Proc. of the IEEE 29th Con/. on Decision and Control, Honolulu, 1990, pp. 3319—3324.
14. Kanellakopoulos I., Kokotovic P. V., Marino R. Marino. An extended direct scheme for robust adaptive nonlinear control, Automatica, 1991, vol. 27, pp. 247—255.
15. Chunlei W., Cao В., Qu X., Fan C. An Improved Finite Control Set Model Predictive Current Control for a Two-Phase Hybrid Stepper Motor Fed by a Three-Phase VSI, Energies, 2022, no. 3, p. 1222, https://doi.org/10.3390/en15031222
16. Kim W., Lee Y., Shin D., Chung C. C. Nonlinear Gain Position Control Using Only Position Feedback for Permanent Magnet Stepper Motors, IEEE Transactions on Power Electronics, 2021, doi: 10.1109/tpel.2020.3046849
17. Shin D., Kim W., Lee Y., Chung C. C. Phase compensated microstepping for permanent magnet stepper motors, IEEE Trans. Ind. Electron., Dec. 2013, vol. 60, no. 12, pp. 5773—5780.
18. Chen J.-J., Chin K.-P. Automatic flux-weakening control of permanent magnet synchronous motors using a reduced-order controller, IEEE Trans. Power Electron., Sep. 2000, vol. 15, no. 5, pp. 881—890.
19. Lee J., Hong J., Nam K., Ortega R., Praly L., Astolfi A. Sensorless control of surface-mount permanent-magnet synchronous motors based on a nonlinear observer, IEEE Trans. Power Electron., Feb. 2010, vol. 25, no. 2, pp. 290—297.
20. Kim W., Shin D., Chung C. C. Microstepping with nonlinear torque modulation for permanent magnet stepper motors, IEEE Trans. Control Syst. Technol., Sep. 2013, vol. 21, no. 5, pp. 1971—1979.
21. Shin D., Kim W., Lee Y., Chung C. C. Nonlinear control with state-dependent reset integrator for a class of singularly perturbed interconnected nonlinear systems, IEEE Trans. Control Syst. Technol., Jul. 2017, vol. 25, no. 4, pp. 1193—1203.
22. Ivanov D., Maradzhiev I., Grigorova T. FPGA Implementation of Microstepping Control of Stepper Motor with Advanced Mixed Current Decay, Proc. of the. 12th National Conference with International Participation, Sofia, ELECTRONICA, 27—28 May 2021.
23. Shin D., Kim W., Lee Y., Chung C. C. Enhanced nonlinear damping for a class of singularly perturbed interconnected nonlinear systems, Automatica, 2016, vol. 65, no. 1, pp. 36—42.
24. Lee Y., Shin D., Kim W., Chung C. C. Nonlinear H2 control for a nonlinear system with bounded varying parameters: Application to PM stepper motors, IEEE/ASME Trans. Mechatronics, Jun. 2017, vol. 22, no. 3, pp. 1349—1359.
25. Le K. M., Hoang H. V., Jeon J. W. An advanced closedloop control to improve the performance of hybrid stepper motors, IEEE Trans. Power Electron., Sep. 2017, vol. 32, no. 9, pp. 7244—7255.
26. Bodson M., Chiasson J., Novotnak R., Rekowski R. Highperformance nonlinear feedback control of a permanent magnet stepper motor, IEEE Trans. Control Syst. Technol., Mar. 1993, vol. 1, no. 1, pp. 5—14.
27. Krishnamurthy P., Khorrami F. Voltage-fed permanentmagnet stepper motor control via position-only feedback, IEE Proc.-Control Theory Appl., Jul. 2004, vol. 151, no. 4, pp. 499—510.
28. Defoort M., Nollet F., Floquet T., Perruquetti W. A thirdorder sliding-mode controller for a stepper motor, IEEE Trans. Ind. Electron., Sep. 2009, vol. 56, no. 9, pp. 3337—3336.
29. Zhou Z., Xia C., Yan Y., Wang Z., Shi T. Disturbances attenuation of permanent magnet synchronous motor drives using cascaded predictiveintegral-resonant controllers, IEEE Trans. Power Electron., Feb. 2018, vol. 33, no. 2, pp. 1514—1527.
30. Lee Y., Gil J., Kim W. Velocity control for sideband harmonics compensation in permanent magnet synchronous motors with low switching frequency inverter, IEEE Trans. Ind. Electron, Apr. 2021, vol. 68, no. 4, pp. 3434—3444.
31. Guo X., Yin Z., Zhanga Y., Baia C. Position sensorless control of PMLSM based on adaptive complex coefficient sliding mode observer, Energy Reports, 2022, vol. 8, pp. 687—695, https://doi.org/10.1016/j.egyr.2022.02.271
32. Kommuri S. K., Defoort M., Karimi H. R., Veluvolu K. C. (2016). A Robust Observer-Based Sensor Fault-Tolerant Control for PMSM in Electric Vehicles, IEEE Transactions on Industrial Electronics, vol. 63, no. 12, pp. 7671—7681, doi:10.1109/ tie.2016.2590993
33. Qiao Z., Shi T., Wang Y., Yan Y., Xia C., He X. New sliding mode observer for position sensorless control of permanent magnet synchronous motor, IEEE Trans. Ind. Electron, Feb. 2013, vol. 60, no. 2, pp. 710—719.
34. Kommuri S. K., Lee S. B., Veluvolu K. C. Robust Sensors- Fault-Tolerance With Sliding Mode Estimation and Control for PMSM Drives, IEEE/ASME Transactions on Mechatronics, 2018, vol. 23, no. 1, pp. 17—28, doi: 10.1109/tmech.2017.2783888
35. Kommuri S. K., Lee S. B., Veluvolu K. C. Speed control for PMSM servo system using predictive functional control and extended state observer, IEEE Trans. Ind. Electron., Feb. 2012, vol. 59, no. 2, pp. 1171—1183.
36. Alecsa B., Cirstea M. N., Onea A. Simulink modeling and design of an efficient hardware-constrained FPGA-based PMSM speed controller, IEEE Trans. Ind. Informat., Aug. 2012, vol. 8, no. 3, pp. 554—562.
37. Jang J.-S., Park B.-G., Kim T.-S., Lee D. M., Hyun D.-S. Parallel reduced-order extended Kalman filter for PMSM sensorless drives, Proc. IEEE Ind. Electron. Soc. Annual Conf., Nov. 2008, pp. 1326—1331.
38. Gaeta A., Scelba G., Consoli A. Modeling and Control of Three-Phase PMSMs Under Open-Phase Fault, IEEE Transactions on Industry Applications, 2013, vol. 49, no. 1, pp. 74—83, doi: 10.1109/TIA.2012.2228614
39. Vas P. Sensorless vector and direct torque control, Oxford Univ., 1998.
40. Belda K., Vosmik D. (2016). Explicit Generalized Predictive Control of Speed and Position of PMSM Drives. IEEE Transactions on Industrial Electronics, 2016, vol. 63, no. 6, pp. 3889—3896, doi: 10.1109/tie.2016.2515061
41. Marino R., Peresada S., Tomei P. Nonlinear adaptive control of permanent magnet step motors, Automatica, 1995, vol. 31, iss. 11, pp. 1595—1604.
42. Furtat I. B. Robust Synchronization of the Structural Uncertainty Nonlinear Network with Delay and Disturbances, IFAC Proceedings Volumes (IFAC-PapersOnline). "11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP 2013 — Proceedings",2013, pp. 227—232.
43. Furtat I. B., Fradkov A. L. Robust Control of Multimachine Power Systems with Compensation of Disturbances, International Journal of Electrical Power & Energy Systems, 2015, vol. 73, pp. 584—590.
44. Furtat I. B., Tsykunov A. M. Adaptive control of objects with output delay, Izvestia of higher educational institutions. Instrumentation, 2005, vol. 48, no. 7, pp. 15—19.
45. Furtat I. B. Robust Control of Electric Generator with Compensation of Perturbations, Journal of Computer and Systems Sciences International, 2011, vol. 50, no. 5, pp. 785—792.
46. Margun A., Furtat I. Robust Control of Linear MIMO Systems in Conditions of Parametric Uncertainties, External Disturbances and Signal Quantization, Proc. of the 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR, 2015, pp. 341—346.
47. Furtat I., Orlov Y., Fradkov A. Finite-time sliding mode stabilization using dirty differentiation and disturbance compensation, International Journal of Robust and Nonlinear Control, 2019, vol. 29, no. 3, pp. 793—809.
Review
For citations:
Furtat I.B., Zhukov Y.A., Slobodzyan N.S. Overview of Models and Methods for Control of Stepper Motors. Mekhatronika, Avtomatizatsiya, Upravlenie. 2023;24(7):352-363. (In Russ.) https://doi.org/10.17587/mau.24.352-363