Robust dynamic decoupling control for permanent magnet spherical actuators based on extended state observer

Robust dynamic decoupling control for permanent magnet spherical actuators based on extended state observer

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This study presents a robust dynamic decoupling control strategy to solve the trajectory tracking problem for the permanent magnet spherical actuator (PMSA). The dynamic model of PMSA obtained by the Lagrange–Euler formalism is obviously a multi-variable non-linear system with strong cross-couplings. Furthermore, uncertainties such as model errors and external disturbances will also affect the precision of the control system. In the active disturbance rejection control (ADRC) framework, the decoupling problem can be reformulated as disturbance rejection by merging the cross channel interference into the lumped disturbance, which consists of internal dynamics and external disturbances. The lumped disturbance is then estimated using extended state observer (ESO) and canceled out in the control law. Herein, the linear active disturbance rejection control is selected for PMSAs, as the tuning process can be greatly simplified by making all the parameters of ESO or controller a function of bandwidth. Simulations and experiments are presented to corroborate the effectiveness and robustness of the proposed strategy, showing that the proposed control algorithm can decouple and linearise the system in the presence of model errors as well as the load and random disturbances. Meanwhile, the modified system has better static and dynamic performances with strong robustness to uncertainties.


    1. 1)
      • 1. Toyama, S., Sugitani, S., Guoqiang, Z., et al: ‘Multi degree of freedom spherical ultrasonic motor’. Proc. 1995 IEEE Int. Conf. on Robot. Autom.1995, Vol. 3, pp. 29352940.
    2. 2)
      • 2. Shigeki, T., Guoqiang, Z., Osamu, M.: ‘Development of new generation spherical ultrasonic motor’. Proc. 1996 IEEE Int. Conf. on Robot. Autom., 1996, Vol. 3, pp. 28712876.
    3. 3)
      • 3. Lee, K.-M., Kwan, C.-K.: ‘Design concept development of a spherical stepper for robotic applications’, IEEE Trans. Robot. Autom., 1991, 7, (1), pp. 175181.
    4. 4)
      • 4. Son, H., Lee, K.-M.: ‘Open-loop controller design and dynamic characteristics of a spherical wheel motor’, IEEE Trans. Ind. Electron., 2010, 57, (10), pp. 34753482.
    5. 5)
      • 5. Wang, J., Wang, W., Jewell, G.W., et al: ‘A novel spherical permanent magnet actuator with three degrees-of-freedom’, IEEE Trans. Magn., 1998, 34, (4), pp. 20782080.
    6. 6)
      • 6. Xia, C., Li, H., Shi, T.: ‘3-d magnetic field and torque analysis of a novel Halbach array permanent-magnet spherical motor’, IEEE Trans. Magn., 2008, 44, (8), pp. 20162020.
    7. 7)
      • 7. Xia, C., Song, P., Li, H., et al: ‘Research on torque calculation method of permanent-magnet spherical motor based on the finite-element method’, IEEE Trans. Magn., 2009, 45, (4), pp. 20152022.
    8. 8)
      • 8. Chen, W., Zhang, L., Yan, L., et al: ‘Design and control of a three degree-of-freedom permanent magnet spherical actuator’, Sens. Actuators A Phys., 2012, 180, pp. 7586.
    9. 9)
      • 9. Bai, K., Lee, K.-M.: ‘Direct field-feedback control of a ball-joint-like permanent-magnet spherical motor’, IEEE/ASME Trans. Mechatron., 2014, 19, (3), pp. 975986.
    10. 10)
      • 10. Son, H., Lee, K.-M.: ‘Control system design and input shape for orientation of spherical wheel motor’, Control Eng. Pract., 2014, 24, pp. 120128.
    11. 11)
      • 11. Guo, W., Yang, J., Yang, W., et al: ‘Regulation quality for frequency response of turbine regulating system of isolated hydroelectric power plant with surge tank’, Int. J. Electr. Power Energy Syst., 2015, 73, pp. 528538.
    12. 12)
      • 12. Guo, W., Yang, J., Wang, M., et al: ‘Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance’, Energy Convers. Manag., 2015, 106, pp. 127138.
    13. 13)
      • 13. Guo, W., Yang, J., Chen, J., et al: ‘Nonlinear modeling and dynamic control of hydro-turbine governing system with upstream surge tank and sloping ceiling tailrace tunnel’, Nonlinear Dyn., 2016, 84, (3), pp. 13831397.
    14. 14)
      • 14. Lee, K.-M., Roth, R.B., Zhou, Z.: ‘Dynamic modeling and control of a ball-joint-like variable-reluctance spherical motor’, J. Dyn. Syst. Meas. Control, 1996, 118, (1), pp. 2940.
    15. 15)
      • 15. Wang, W., Wang, J., Jewell, G., et al: ‘Design and control of a novel spherical permanent magnet actuator with three degrees of freedom’, IEEE/ASME Trans. Mechatron., 2003, 8, (4), pp. 457468.
    16. 16)
      • 16. Xia, C., Guo, C., Shi, T.: ‘A neural-network-identifier and fuzzy-controller-based algorithm for dynamic decoupling control of permanent-magnet spherical motor’, IEEE Trans. Ind. Electron., 2010, 57, (8), pp. 28682878.
    17. 17)
      • 17. Chu, J., Niguchi, N., Hirata, K.: ‘Feedback control of outer rotor spherical actuator using adaptive neuro-fuzzy inference system’. 2013 Seventh Int. Conf. IEEE Sens. Technol. (ICST), 2013, pp. 401405.
    18. 18)
      • 18. Zhang, L., Chen, W., Liu, J., et al: ‘A robust adaptive iterative learning control for trajectory tracking of permanent-magnet spherical actuator’, IEEE Trans. Ind. Electron., 2016, 63, (1), pp. 291301.
    19. 19)
      • 19. Su, J., Qiu, W., Ma, H., et al: ‘Calibration-free robotic eye-hand coordination based on an auto disturbance-rejection controller’, IEEE Trans. Robot., 2004, 20, (5), pp. 899907.
    20. 20)
      • 20. Su, J., Ma, H., Qiu, W., et al: ‘Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer’, IEEE Trans. Syst. Man Cybern. B Cybern., 2004, 34, (4), pp. 19171922.
    21. 21)
      • 21. Su, Y.X., Zheng, C.H., Duan, B.Y.: ‘Automatic disturbances rejection controller for precise motion control of permanent-magnet synchronous motors’, IEEE Trans. Ind. Electron., 2005, 52, (3), pp. 814823.
    22. 22)
      • 22. Li, S., Liu, Z.: ‘Adaptive speed control for permanent-magnet synchronous motor system with variations of load inertia’, IEEE Trans. Ind. Electron., 2009, 56, (8), pp. 30503059.
    23. 23)
      • 23. Li, S., Yang, X., Yang, D.: ‘Active disturbance rejection control for high pointing accuracy and rotation speed’, Automatica, 2009, 45, (8), pp. 18541860.
    24. 24)
      • 24. Xia, Y., Zhu, Z., Fu, M., et al: ‘Attitude tracking of rigid spacecraft with bounded disturbances’, IEEE Trans. Ind. Electron., 2011, 58, (2), pp. 647659.
    25. 25)
      • 25. Wang, J., Ma, H., Cai, W., et al: ‘Research on micro quadrotor control based on adrc’, J. Projectiles Rockets, Missiles Guid., 2008, 3, p. 008.
    26. 26)
      • 26. Gong, X., Tian, Y., Bai, Y., et al: ‘Trajectory tacking control of a quad-rotor based on active disturbance rejection control’, 2012 IEEE Int. Conf. IEEE Autom. Logist. (ICAL), 2012, pp. 254259.
    27. 27)
      • 27. Huang, Y., Xu, K., Han, J., et al: ‘Flight control design using extended state observer and non-smooth feedback’. Proc. IEEE Conf. on Decision and Control, 2001, Vol. 1, pp. 223228, available at:
    28. 28)
      • 28. Zheng, Q., Chen, Z., Gao, Z.: ‘A practical approach to disturbance decoupling control’, Control Eng. Pract., 2009, 17, (9), pp. 10161025.
    29. 29)
      • 29. Hall, C.E., Shtessel, Y.B.: ‘Sliding mode disturbance observer-based control for a reusable launch vehicle’, J. Guid. Control Dyn., 2006, 29, (6), pp. 13151328.
    30. 30)
      • 30. Miklosovic, R., Gao, Z.: ‘A dynamic decoupling method for controlling high performance turbofan engines’. Proc. of the 16th IFAC World Congress, 2005, pp. 48.
    31. 31)
      • 31. Gao, Z.: ‘Scaling and bandwidth-parameterization based controller tuning’. Proc. American Control Conf., 2006, vol. 6, pp. 49894996.
    32. 32)
      • 32. Gao, Z.: ‘Active disturbance rejection control: a paradigm shift in feedback control system design’. 2006 IEEE American Control Conf., 2006, 7pp.
    33. 33)
      • 33. Zheng, Q., Gao, L.Q., Gao, Z.: ‘On validation of extended state observer through analysis and experimentation’, J. Dyn. Syst. Meas. Control, 2012, 134, (2), p. 024505.

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