Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon openaccess Second-order terminal sliding mode control based on perturbation estimation for nanopositioning stage

This is an open access article published by the IET and Zhejiang University Press under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)
Received 30/04/2020, Accepted 17/08/2020, Revised 30/07/2020, Published 18/08/2020

This study proposes a robust second-order terminal sliding mode control with perturbation estimation (2OTSMCPE) strategy with application to trajectory tracking control of the flexure-based nanopositioning system. The proposed controller advantages not only lie on its finite-time convergence but also can provide a high tracking precision with a chattering alleviation which is attend by employing a second-order sliding surface with the switching function. The model of the piezo-driven nanopositioning system is presented first. Second, the sliding variable is designed such as proportional–integral–derivative form to enhance the dynamic response of the control system. Then, a non-singular terminal sliding function (NTSM) is used to achieve the finite-time convergence of the linear sliding variable. Next, a perturbation estimation technique is integrated with the control structure for online estimation of the system uncertainties, thus the prior knowledge of the bounds of system uncertainties are not needed in the proposed control design. Afterwards, the theoretical analysis of the 2OTSMCPE with stability proof is investigated herein. Finally, the system performance with the proposed controller is experimentally verified. The results reveal that the 2OTSMCPE has stronger robustness and also has smoother control signals in comparison with both conventional sliding mode control and the NTSM controller.

Inspec keywords: robust control; convergence; perturbation techniques; switching systems (control); variable structure systems; nanopositioning; control system synthesis

Other keywords: control system; stability proof; NTSM controller; tracking precision; chattering alleviation; nanopositioning stage; system performance; proportional-integral-derivative form; switching function; control signals; nonsingular terminal sliding function; robust second-order terminal sliding mode control; flexure-based nanopositioning system; 2OTSMCPE; system uncertainties; trajectory tracking control; perturbation estimation technique; perturbation estimation strategy; piezo-driven nanopositioning system; robustness; online estimation; linear sliding variable; control structure; control design; finite-time convergence

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Stability in control theory; Time-varying control systems; Spatial variables control; Multivariable control systems

References

    1. 1)
      • 37. Zheng, J., Wang, H., Man, Z., et al: ‘Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode’, IEEE/ASME Trans. Mechatron., 2015, 20, (4), pp. 1743–1752.
    2. 2)
      • 11. Al-Ghanimi, A., Zheng, J., Man, Z.: ‘A fast non-singular terminal sliding mode control based on perturbation estimation for piezoelectric actuators systems’, Int. J. Control, 2016, 90, (3), pp. 480–491.
    3. 3)
      • 14. Xu, Q.: ‘Precision motion control of piezoelectric nanopositioning stage with chattering-free adaptive sliding mode control’, IEEE Trans. Autom. Sci. Eng., 2017, 14, (1), pp. 238–248.
    4. 4)
      • 35. Elmali, H., Olgac, N.: ‘Sliding mode control with perturbation estimation (smcpe): a new approach’, Int. J. Control, 1992, 56, (4), pp. 923–941.
    5. 5)
      • 27. Wang, G., Xu, Q.: ‘Adaptive terminal sliding mode control for motion tracking of a micropositioning system’, Asian. J. Control., 2018, 20, (3), pp. 1241–1252.
    6. 6)
      • 17. Qiao, L., Zhang, W.: ‘Adaptive second-order fast nonsingular terminal sliding mode tracking control for fully actuated autonomous underwater vehicles’, IEEE Oceanic Eng., 2019, 44, (2), pp. 363–385.
    7. 7)
      • 1. Wang, F., Shi, B., Tian, Y., et al: ‘Design of a novel dual-axis micromanipulator with an asymmetric compliant structure’, IEEE/ASME Trans. Mechatron., 2019, 24, (2), pp. 656–665.
    8. 8)
      • 24. Feng, Y., Han, X., Wang, Y., et al: ‘Second-order terminal sliding mode control of uncertain multivariable systems’, Int. J. Control, 2007, 80, (6), pp. 856–862.
    9. 9)
      • 33. Youcef-Toumi, K., Ito, O.: ‘A time delay controller for systems with unknown dynamics’, J. Dyn. Syst. Meas. Control, 1990, 112, (1), pp. 133–142.
    10. 10)
      • 21. Al-Ghanimi, A., Zheng, J., Man, Z.: ‘Robust and fast non-singular terminal sliding mode control for piezoelectric actuators’, IET Control Theory Appl., 2015, 9, (18), pp. 2678–2687.
    11. 11)
      • 6. Utkin, V., Guldner, J., Shi, J.: ‘Sliding mode control in electro-mechanical systems’ (CRC Press, Boca Raton, Florida, 2017).
    12. 12)
      • 36. Levant, A.: ‘Robust exact differentiation via sliding mode technique’, Automatica, 1998, 34, (3), pp. 379–384.
    13. 13)
      • 22. Xu, Q., Cao, Z.: ‘Piezoelectric positioning control with output-based discrete-time terminal sliding mode control’, IET Control Theory Appl., 2017, 11, (5), pp. 694–702.
    14. 14)
      • 28. Mobayen, S., Baleanu, D., Tchier, F.: ‘Second-order fast terminal sliding mode control design based on lmi for a class of non-linear uncertain systems and its application to chaotic systems’, J. Vib. Control, 2017, 23, (18), pp. 2912–2925.
    15. 15)
      • 26. Ruderman, M.: ‘Optimal terminal sliding-mode control for second-order motion systems’, arXiv preprint arXiv:200109043, 2020.
    16. 16)
      • 13. Li, Y.X., Yang, G.H.: ‘Adaptive integral sliding mode control fault tolerant control for a class of uncertain nonlinear systems’, IET Control Theory Appl., 2018, 12, (13), pp. 1864–1872.
    17. 17)
      • 9. Utkin, V., Poznyak, A., Orlov, Y.V., et al: ‘Road map for sliding mode control design’ (Springer International Publishing, 2020), https://link.springer.com/book/10.1007%2F978-3-030-41709-3.
    18. 18)
      • 29. Elmali, H., Olgac, N.: ‘Implementation of sliding mode control with perturbation estimation (smcpe)’, IEEE Trans. Control Syst. Technol., 1996, 4, (1), pp. 79–85.
    19. 19)
      • 30. Zheng, J., Fu, M.: ‘Saturation control of a piezoelectric actuator for fast settling-time performance’, IEEE Trans. Control Syst. Technol., 2013, 21, (1), pp. 220–228.
    20. 20)
      • 5. Xu, Q.: ‘Continuous integral terminal third-order sliding mode motion control for piezoelectric nanopositioning system’, IEEE/ASME Trans. Mechatron., 2017, 22, (4), pp. 1828–1838.
    21. 21)
      • 16. Xu, Q., Tan, K.K.: ‘Digital sliding-mode control of high-order systems’, in ‘Advances in industrial control’ (Springer International Publishing, 2015), pp. 147–165, https://link.springer.com/book/10.1007%2F978-3-319-21623-2#toc.
    22. 22)
      • 12. Hou, H., Yu, X., Xu, L., et al: ‘Discrete-time terminal sliding-mode tracking control with alleviated chattering’, IEEE/ASME Trans. Mechatron., 2019, 24, (4), pp. 1808–1817.
    23. 23)
      • 18. Zhihong, M., Paplinski, A.P., Wu, H.R.: ‘A robust mimo terminal sliding mode control scheme for rigid robotic manipulators’, IEEE Trans. Autom. Control, 1994, 39, (12), pp. 2464–2469.
    24. 24)
      • 4. Gu, G.Y., Zhu, L.M., Su, C.Y., et al: ‘Modeling and control of piezo-actuated nanopositioning stages: a survey’, IEEE Trans. Autom. Sci. Eng., 2016, 13, (1), pp. 313–332.
    25. 25)
    26. 26)
      • 2. Habibullah, H.: ‘30 years of atomic force microscopy: creep, hysteresis, cross-coupling, and vibration problems of piezoelectric tube scanners’, Measurement, 2020, 6, p. 107776.
    27. 27)
      • 19. Feng, Y., Yu, X., Man, Z.: ‘Non-singular terminal sliding mode control of rigid manipulators’, Automatica, 2002, 38, (12), pp. 2159–2167.
    28. 28)
      • 8. Xu, R., Zhang, X., Guo, H., et al: ‘Sliding mode tracking control with perturbation estimation for hysteresis nonlinearity of piezo-actuated stages’, IEEE Access, 2018, 6, pp. 30617–30629.
    29. 29)
      • 34. Ohnishi, K., Shibata, M., Murakami, T.: ‘Motion control for advanced mechatronics’, IEEE/ASME Trans. Mechatron., 1996, 1, (1), pp. 56–67.
    30. 30)
      • 20. Yu, S., Yu, X., Shirinzadeh, B., et al: ‘Continuous finite-time control for robotic manipulators with terminal sliding mode’, Automatica, 2005, 41, (11), pp. 1957–1964.
    31. 31)
      • 3. Liu, Y., Deng, J., Su, Q.: ‘Review on multi-degree-of-freedom piezoelectric motion stage’, IEEE Access, 2018, 6, pp. 59986–60004.
    32. 32)
      • 38. Xu, Q., Tan, K.K.: ‘Advanced control of piezoelectric micro-/nano-positioning systems’ (Springer International Publishing, 2016), https://link.springer.com/book/10.1007%2F978-3-319-21623-2.
    33. 33)
      • 25. Xu, Q.: ‘Piezoelectric nanopositioning control using second-order discrete-time terminal sliding-mode strategy’, IEEE Trans. Ind. Electron., 2015, 62, (12), pp. 7738–7748.
    34. 34)
      • 10. Edwards, C., Shtessel, Y.B.: ‘Adaptive continuous higher order sliding mode control’, Automatica, 2016, 65, pp. 183–190.
    35. 35)
      • 15. Levant, A.: ‘Sliding order and sliding accuracy in sliding mode control’, Int. J. Control, 1993, 58, (6), pp. 1247–1263.
    36. 36)
      • 23. Feng, Y., Zheng, X., Yu, X.: ‘Second-order nonsingular terminal sliding mode decomposed control of uncertain multivariable systems’, Asian. J. Control., 2003, 5, (4), pp. 505–512.
    37. 37)
      • 32. Li, Y., Xu, Q.: ‘Adaptive sliding mode control with perturbation estimation and pid sliding surface for motion tracking of a piezo-driven micromanipulator’, IEEE Trans. Control Syst. Technol., 2010, 18, (4), pp. 798–810.
    38. 38)
      • 7. Zhang, X., Zhang, Y., Xu, Q.: ‘Design and control of a novel piezo-driven XY parallel nanopositioning stage’, Microsyst. Technol., 2016, 23, (4), pp. 1067–1080.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-csr.2020.0024
Loading

Related content

content/journals/10.1049/iet-csr.2020.0024
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address