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Short Convergence Time Super-Twisting Sliding Mode Speed Control of Permanent Magnet Synchronous Motor

Year 2025, Volume: 8 Issue: 1, 12 - 23, 31.05.2025
https://doi.org/10.34088/kojose.1543011

Abstract

One of the most popular motors for precise control applications, such as electric vehicles, is the permanent magnet synchronous motor (PMSM). Under harsh conditions, PMSM and its drives are expected to provide robust control response against internal and external disturbances. Conventional controllers used in the vector control method have difficulty providing superior control responses due to the nonlinear structure of the PMSM. Although sliding mode control is a good control method to fulfill these control requirements, it has a chattering effect due to high-speed switching phenomenon. To reduce this effect and to obtain a better dynamic response, super-twisting sliding mode control (ST-SMC) is one of the control method candidates. In the classical ST-SMC control method, since the sliding surface consists of error or error-integral of the error, the finite time convergence to the equilibrium point is not fast enough. In this study, a new nonlinear sliding surface is designed in the ST-SMC controller for speed control of PMSM. In addition, equivalent control terms and an error-dependent exponential term are added to the control input to speed up the output response. In this way, the ST-SMC algorithm is experimentally applied to control the speed of the PMSM under harsh operating conditions with reduced chattering, shortened convergence time, and increased robustness against internal and external disturbances. The experimental implementation of the designed controller is carried out on a 400 W PMSM motor test setup. The superiority of the proposed control algorithm is comparatively demonstrated under operating conditions such as step speed reference and load torque.

References

  • [1] Bartolini, G., Punta, E., & Zolezzi, T. 2007. Approximability properties for second-order sliding mode control systems. IEEE Transactions on Automatic Control, 52(10),pp. 1813–1825.
  • [2] Bartoszewicz, A., & Lesniewski, P. 2016. New Switching and Nonswitching Type Reaching Laws for SMC of Discrete Time Systems. IEEE Transactions on Control Systems Technology, 24(2), pp. 670–677.
  • [3] Bramerdorfer, G., Winkler, S. M., Kommenda, M., Weidenholzer, G., Silber, S., Kronberger, G., Affenzeller, M., & Amrhein, W. 2014. Using FE calculations and data-based system identification techniques to model the nonlinear behavior of PMSMs. IEEE Transactions on Industrial Electronics, 61(11),pp. 6454–6462.
  • [4] Chatri, C., Ouassaid, M., Labbadi, M., & Errami, Y. 2022. Integral-type terminal sliding mode control approach for wind energy conversion system with uncertainties. Computers and Electrical Engineering, 99(January),pp 107775.
  • [5] Gonzalez, T., Moreno, J. A., & Fridman, L. 2012. Variable gain super-twisting sliding mode control. IEEE Transactions on Automatic Control, 57(8),pp. 2100–2105.
  • [6] Jiang, Y., Xu, W., Mu, C., & Liu, Y. 2018. Improved deadbeat predictive current control combined sliding mode strategy for PMSM drive system. IEEE Transactions on Vehicular Technology, 67(1),pp. 251–263.
  • [7] Junejo, A. K., Xu, W., Mu, C., Ismail, M. M., & Liu, Y. 2020. Adaptive Speed Control of PMSM Drive System Based a New Sliding-Mode Reaching Law. IEEE Transactions on Power Electronics, 35(11), pp.12110–12121.
  • [8] Kumari, K., Chalanga, A., & Bandyopadhyay, B. 2016. Implementation of Super-Twisting Control on Higher Order Perturbed Integrator System using Higher Order Sliding Mode Observer. IFAC-PapersOnLine, 49(18), pp. 873–878.
  • [9] Lascu, C., Boldea, I., & Blaabjerg, F. 2013. Super-twisting sliding mode control of torque and flux in permanent magnet synchronous machine drives. IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria, pp. 3171-3176.
  • [10] Lee, S. B. 2006. Closed-loop estimation of permanent magnet synchronous motor parameters by PI controller gain tuning. IEEE Transactions on Energy Conversion, 21(4), pp. 863–870.
  • [11] Levant, A. 1993. Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), pp.1247–1263.
  • [12] Li, K., Bouscayrol, A., Cui, S., & Cheng, Y. ,2021. A Hybrid Modular Cascade Machines System for Electric Vehicles Using Induction Machine and Permanent Magnet Synchronous Machine. IEEE Transactions on Vehicular Technology, 70(1), pp. 273–281.
  • [13] Li, Y., & Xu, Q. ,2010. Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Transactions on Control Systems Technology, 18(4), pp. 798–810.
  • [14] Linares-Flores, J., García-Rodríguez, C., Sira-Ramírez, H., & Ramírez-Cárdenas, O. D. , 2015. Robust Backstepping Tracking Controller for Low-Speed PMSM Positioning System: Design, Analysis, and Implementation. IEEE Transactions on Industrial Informatics, 11(5),pp. 1130–1141.
  • [15] Liu, M., Chan, K. W., Hu, J., Xu, W., & Rodriguez, J., 2019. Model Predictive Direct Speed Control With Torque Oscillation Reduction for PMSM Drives. IEEE Transactions on Industrial Informatics, 15(9), pp. 4944–4956.
  • [16] Liu, X., & Yu, H. ,2021. Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives. Nonlinear Dynamics, 104(2), pp.1429–1441.
  • [17] Mao, D., Wang, J., Tan, J., Liu, G., Xu, Y., & Li, J. ,2019. Location Planning of Fast Charging Station Considering its Impact on the Power Grid Assets. 2019 IEEE Transportation Electrification Conference and Expo (ITEC), Detroit, MI, USA,pp. 1-5.
  • [18] Moreno, J. A., & Osorio, M. ,2008. A Lyapunov approach to second-order sliding mode controllers and observers. 2008 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008, pp. 2856-2861
  • [19] Muñoz, F., Bonilla, M., González-Hernández, I., Salazar, S., & Lozano, R. ,2015. Super Twisting vs Modified Super Twisting algorithm for altitude control of an Unmanned Aircraft System. 2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, pp. 1-6
  • [20] Nguyen, N. P., Oh, H., & Moon, J., 2022. Continuous Nonsingular Terminal Sliding-Mode Control with Integral-Type Sliding Surface for Disturbed Systems: Application to Attitude Control for Quadrotor UAVs under External Disturbances. IEEE Transactions on Aerospace and Electronic Systems, 58(6),pp. 5635–5660.
  • [21] Ouledali, O., Meroufel, A., Wira, P., & Bentouba, S., 2015. Direct Torque Fuzzy Control of PMSM based on SVM. Energy Procedia, 74, pp.1314–1322.
  • [22] Pisu, P., & Rizzoni, G. ,2007. Strategies for Hybrid Electric Vehicles. IEEE Transsaction on Control System Technology, 15(3), pp. 506–518.
  • [23] Samaranayake, L., & Longo, S. ,2018. Degradation Control for Electric Vehicle Machines Using Nonlinear Model Predictive Control. IEEE Transactions on Control Systems Technology, 26(1), pp. 89–101.
  • [24] Savitski, D., Ivanov, V., Augsburg, K., Emmei, T., Fuse, H., Fujimoto, H., & Fridman, L. M. ,2020. Wheel Slip Control for the Electric Vehicle with In-Wheel Motors: Variable Structure and Sliding Mode Methods. IEEE Transactions on Industrial Electronics, 67(10), pp. 8535–8544.
  • [25] Shtessel, Y. B., Moreno, J. A., Plestan, F., Fridman, L. M., & Poznyak, A. S.,2010. Super-twisting adaptive sliding mode control: A Lyapunov design. 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, pp. 5109-5113.
  • [26] Stojic, D. M., Milinkovic, M., Veinovic, S., & Klasnic, I.,2015. Stationary Frame Induction Motor Feed Forward Current Controller with Back EMF Compensation. IEEE Transactions on Energy Conversion, 30(4),pp. 1356–1366.
  • [27] Teja, A. V. R., Chakraborty, C., & Pal, B. C. ,2018. Disturbance Rejection Analysis and FPGA-Based Implementation of a Second-Order Sliding Mode Controller Fed Induction Motor Drive. IEEE Transactions on Energy Conversion, 33(3),pp. 1453–1462.
  • [28] Wang, B., Dong, Z., Yu, Y., Wang, G., & Xu, D. ,2018. Static-Errorless Deadbeat Predictive Current Control Using Second-Order Sliding-Mode Disturbance Observer for Induction Machine Drives. IEEE Transactions on Power Electronics, 33(3), pp. 2395–2403.
  • [29] Wang, G., Liu, R., Zhao, N., Ding, D., & Xu, D. ,2019. Enhanced Linear ADRC Strategy for HF Pulse Voltage Signal Injection-Based Sensorless IPMSM Drives. IEEE Transactions on Power Electronics, 34(1),pp. 514–525.
  • [30] Wang, Y., Feng, Y., Zhang, X., & Liang, J. ,2020. A New Reaching Law for Antidisturbance Sliding-Mode Control of PMSM Speed Regulation System. IEEE Transactions on Power Electronics, 35(4), pp. 4117–4126.
  • [31] Wang, Y., Zhu, Y., Zhang, X., Tian, B., Wang, K., & Liang, J. ,2021. Antidisturbance Sliding Mode-Based Deadbeat Direct Torque Control for PMSM Speed Regulation System. IEEE Transactions on Transportation Electrification, 7(4), pp. 2705–2714.
  • [32] Xu, B., Zhang, L., & Ji, W. ,2021. Improved Non-Singular Fast Terminal Sliding Mode Control with Disturbance Observer for PMSM Drives. IEEE Transactions on Transportation Electrification, 7(4), pp . 2753–2762.
  • [33] Young, K. D., Utkin, V. I., & Özgüner, Ü. ,1999. A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology, 7(3), pp. 328–342.
  • [34] Zhang, Y., McLoone, S., Cao, W., Qiu, F., & Gerada, C. ,2017. Power Loss and Thermal Analysis of a MW High-Speed Permanent Magnet Synchronous Machine. IEEE Transactions on Energy Conversion, 32(4), pp. 1468–1478.
  • [35] Zhang, Z., Ma, R., Wang, L., & Zhang, J. ,2018. Novel PMSM Control for Anti-Lock Braking Considering Transmission Properties of the Electric Vehicle. IEEE Transactions on Vehicular Technology, 67(11), pp. 10378–10386.

Short Convergence Time Super-Twisting Sliding Mode Speed Control of Permanent Magnet Synchronous Motor

Year 2025, Volume: 8 Issue: 1, 12 - 23, 31.05.2025
https://doi.org/10.34088/kojose.1543011

Abstract

One of the most popular motors for precise control applications, such as electric vehicles, is the permanent magnet synchronous motor (PMSM). Under harsh conditions, PMSM and its drives are expected to provide robust control response against internal and external disturbances. Conventional controllers used in the vector control method have difficulty providing superior control responses due to the nonlinear structure of the PMSM. Although sliding mode control is a good control method to fulfill these control requirements, it has a chattering effect due to high-speed switching phenomenon. To reduce this effect and to obtain a better dynamic response, super-twisting sliding mode control (ST-SMC) is one of the control method candidates. In the classical ST-SMC control method, since the sliding surface consists of error or error-integral of the error, the finite time convergence to the equilibrium point is not fast enough. In this study, a new nonlinear sliding surface is designed in the ST-SMC controller for speed control of PMSM. In addition, equivalent control terms and an error-dependent exponential term are added to the control input to speed up the output response. In this way, the ST-SMC algorithm is experimentally applied to control the speed of the PMSM under harsh operating conditions with reduced chattering, shortened convergence time, and increased robustness against internal and external disturbances. The experimental implementation of the designed controller is carried out on a 400 W PMSM motor test setup. The superiority of the proposed control algorithm is comparatively demonstrated under operating conditions such as step speed reference and load torque.

References

  • [1] Bartolini, G., Punta, E., & Zolezzi, T. 2007. Approximability properties for second-order sliding mode control systems. IEEE Transactions on Automatic Control, 52(10),pp. 1813–1825.
  • [2] Bartoszewicz, A., & Lesniewski, P. 2016. New Switching and Nonswitching Type Reaching Laws for SMC of Discrete Time Systems. IEEE Transactions on Control Systems Technology, 24(2), pp. 670–677.
  • [3] Bramerdorfer, G., Winkler, S. M., Kommenda, M., Weidenholzer, G., Silber, S., Kronberger, G., Affenzeller, M., & Amrhein, W. 2014. Using FE calculations and data-based system identification techniques to model the nonlinear behavior of PMSMs. IEEE Transactions on Industrial Electronics, 61(11),pp. 6454–6462.
  • [4] Chatri, C., Ouassaid, M., Labbadi, M., & Errami, Y. 2022. Integral-type terminal sliding mode control approach for wind energy conversion system with uncertainties. Computers and Electrical Engineering, 99(January),pp 107775.
  • [5] Gonzalez, T., Moreno, J. A., & Fridman, L. 2012. Variable gain super-twisting sliding mode control. IEEE Transactions on Automatic Control, 57(8),pp. 2100–2105.
  • [6] Jiang, Y., Xu, W., Mu, C., & Liu, Y. 2018. Improved deadbeat predictive current control combined sliding mode strategy for PMSM drive system. IEEE Transactions on Vehicular Technology, 67(1),pp. 251–263.
  • [7] Junejo, A. K., Xu, W., Mu, C., Ismail, M. M., & Liu, Y. 2020. Adaptive Speed Control of PMSM Drive System Based a New Sliding-Mode Reaching Law. IEEE Transactions on Power Electronics, 35(11), pp.12110–12121.
  • [8] Kumari, K., Chalanga, A., & Bandyopadhyay, B. 2016. Implementation of Super-Twisting Control on Higher Order Perturbed Integrator System using Higher Order Sliding Mode Observer. IFAC-PapersOnLine, 49(18), pp. 873–878.
  • [9] Lascu, C., Boldea, I., & Blaabjerg, F. 2013. Super-twisting sliding mode control of torque and flux in permanent magnet synchronous machine drives. IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria, pp. 3171-3176.
  • [10] Lee, S. B. 2006. Closed-loop estimation of permanent magnet synchronous motor parameters by PI controller gain tuning. IEEE Transactions on Energy Conversion, 21(4), pp. 863–870.
  • [11] Levant, A. 1993. Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), pp.1247–1263.
  • [12] Li, K., Bouscayrol, A., Cui, S., & Cheng, Y. ,2021. A Hybrid Modular Cascade Machines System for Electric Vehicles Using Induction Machine and Permanent Magnet Synchronous Machine. IEEE Transactions on Vehicular Technology, 70(1), pp. 273–281.
  • [13] Li, Y., & Xu, Q. ,2010. Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Transactions on Control Systems Technology, 18(4), pp. 798–810.
  • [14] Linares-Flores, J., García-Rodríguez, C., Sira-Ramírez, H., & Ramírez-Cárdenas, O. D. , 2015. Robust Backstepping Tracking Controller for Low-Speed PMSM Positioning System: Design, Analysis, and Implementation. IEEE Transactions on Industrial Informatics, 11(5),pp. 1130–1141.
  • [15] Liu, M., Chan, K. W., Hu, J., Xu, W., & Rodriguez, J., 2019. Model Predictive Direct Speed Control With Torque Oscillation Reduction for PMSM Drives. IEEE Transactions on Industrial Informatics, 15(9), pp. 4944–4956.
  • [16] Liu, X., & Yu, H. ,2021. Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives. Nonlinear Dynamics, 104(2), pp.1429–1441.
  • [17] Mao, D., Wang, J., Tan, J., Liu, G., Xu, Y., & Li, J. ,2019. Location Planning of Fast Charging Station Considering its Impact on the Power Grid Assets. 2019 IEEE Transportation Electrification Conference and Expo (ITEC), Detroit, MI, USA,pp. 1-5.
  • [18] Moreno, J. A., & Osorio, M. ,2008. A Lyapunov approach to second-order sliding mode controllers and observers. 2008 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008, pp. 2856-2861
  • [19] Muñoz, F., Bonilla, M., González-Hernández, I., Salazar, S., & Lozano, R. ,2015. Super Twisting vs Modified Super Twisting algorithm for altitude control of an Unmanned Aircraft System. 2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, pp. 1-6
  • [20] Nguyen, N. P., Oh, H., & Moon, J., 2022. Continuous Nonsingular Terminal Sliding-Mode Control with Integral-Type Sliding Surface for Disturbed Systems: Application to Attitude Control for Quadrotor UAVs under External Disturbances. IEEE Transactions on Aerospace and Electronic Systems, 58(6),pp. 5635–5660.
  • [21] Ouledali, O., Meroufel, A., Wira, P., & Bentouba, S., 2015. Direct Torque Fuzzy Control of PMSM based on SVM. Energy Procedia, 74, pp.1314–1322.
  • [22] Pisu, P., & Rizzoni, G. ,2007. Strategies for Hybrid Electric Vehicles. IEEE Transsaction on Control System Technology, 15(3), pp. 506–518.
  • [23] Samaranayake, L., & Longo, S. ,2018. Degradation Control for Electric Vehicle Machines Using Nonlinear Model Predictive Control. IEEE Transactions on Control Systems Technology, 26(1), pp. 89–101.
  • [24] Savitski, D., Ivanov, V., Augsburg, K., Emmei, T., Fuse, H., Fujimoto, H., & Fridman, L. M. ,2020. Wheel Slip Control for the Electric Vehicle with In-Wheel Motors: Variable Structure and Sliding Mode Methods. IEEE Transactions on Industrial Electronics, 67(10), pp. 8535–8544.
  • [25] Shtessel, Y. B., Moreno, J. A., Plestan, F., Fridman, L. M., & Poznyak, A. S.,2010. Super-twisting adaptive sliding mode control: A Lyapunov design. 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, pp. 5109-5113.
  • [26] Stojic, D. M., Milinkovic, M., Veinovic, S., & Klasnic, I.,2015. Stationary Frame Induction Motor Feed Forward Current Controller with Back EMF Compensation. IEEE Transactions on Energy Conversion, 30(4),pp. 1356–1366.
  • [27] Teja, A. V. R., Chakraborty, C., & Pal, B. C. ,2018. Disturbance Rejection Analysis and FPGA-Based Implementation of a Second-Order Sliding Mode Controller Fed Induction Motor Drive. IEEE Transactions on Energy Conversion, 33(3),pp. 1453–1462.
  • [28] Wang, B., Dong, Z., Yu, Y., Wang, G., & Xu, D. ,2018. Static-Errorless Deadbeat Predictive Current Control Using Second-Order Sliding-Mode Disturbance Observer for Induction Machine Drives. IEEE Transactions on Power Electronics, 33(3), pp. 2395–2403.
  • [29] Wang, G., Liu, R., Zhao, N., Ding, D., & Xu, D. ,2019. Enhanced Linear ADRC Strategy for HF Pulse Voltage Signal Injection-Based Sensorless IPMSM Drives. IEEE Transactions on Power Electronics, 34(1),pp. 514–525.
  • [30] Wang, Y., Feng, Y., Zhang, X., & Liang, J. ,2020. A New Reaching Law for Antidisturbance Sliding-Mode Control of PMSM Speed Regulation System. IEEE Transactions on Power Electronics, 35(4), pp. 4117–4126.
  • [31] Wang, Y., Zhu, Y., Zhang, X., Tian, B., Wang, K., & Liang, J. ,2021. Antidisturbance Sliding Mode-Based Deadbeat Direct Torque Control for PMSM Speed Regulation System. IEEE Transactions on Transportation Electrification, 7(4), pp. 2705–2714.
  • [32] Xu, B., Zhang, L., & Ji, W. ,2021. Improved Non-Singular Fast Terminal Sliding Mode Control with Disturbance Observer for PMSM Drives. IEEE Transactions on Transportation Electrification, 7(4), pp . 2753–2762.
  • [33] Young, K. D., Utkin, V. I., & Özgüner, Ü. ,1999. A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology, 7(3), pp. 328–342.
  • [34] Zhang, Y., McLoone, S., Cao, W., Qiu, F., & Gerada, C. ,2017. Power Loss and Thermal Analysis of a MW High-Speed Permanent Magnet Synchronous Machine. IEEE Transactions on Energy Conversion, 32(4), pp. 1468–1478.
  • [35] Zhang, Z., Ma, R., Wang, L., & Zhang, J. ,2018. Novel PMSM Control for Anti-Lock Braking Considering Transmission Properties of the Electric Vehicle. IEEE Transactions on Vehicular Technology, 67(11), pp. 10378–10386.
There are 35 citations in total.

Details

Primary Language English
Subjects Control Engineering, Mechatronics and Robotics (Other)
Journal Section Articles
Authors

Fuat Kılıç 0000-0003-2502-3789

Publication Date May 31, 2025
Submission Date September 3, 2024
Acceptance Date October 13, 2024
Published in Issue Year 2025 Volume: 8 Issue: 1

Cite

APA Kılıç, F. (2025). Short Convergence Time Super-Twisting Sliding Mode Speed Control of Permanent Magnet Synchronous Motor. Kocaeli Journal of Science and Engineering, 8(1), 12-23. https://doi.org/10.34088/kojose.1543011