access icon free Enhanced discrete-time sliding mode strategy with application to piezoelectric actuator control

This study presents a new discrete-time sliding mode control (DSMC) scheme with applications to precise motion control of piezoelectric actuators. Different from existing DSMC algorithms whose implementations rely on the construction of state observers for providing the state feedback, a simple yet effective DSMC strategy is developed based on a discrete-time model without using the state observer. Hence, one distinctive feature of the proposed DSMC lies in that it is very easy to implement. Only a second-order plant model is needed whereas the modelling of piezoelectric non-linearities is not required, which further simplifies the practical implementation process. The local stability of the closed-loop system is proved in theory and the effectiveness of the DSMC is demonstrated by several experimental studies. Results show that the DSMC strategy is superior to proportional-integral-derivative control in terms of transient response speed, positioning accuracy and robustness against external disturbances. The reported method can be extended for precise motion control of other second-order systems as well.

Inspec keywords: discrete time systems; variable structure systems; stability; closed loop systems; motion control; piezoelectric actuators

Other keywords: piezoelectric actuator control; DSMC scheme; discrete-time sliding mode control scheme; discrete-time sliding mode strategy; second-order plant model; transient response speed; local stability; closed-loop system; positioning accuracy; precise motion control; external disturbances robustness

Subjects: Electric actuators and final control equipment; Multivariable control systems; Discrete control systems; Spatial variables control; Stability in control theory

References

    1. 1)
      • 18. Xu, Q., Li, Y.: ‘Model predictive discrete-time sliding mode control of a nanopositioning piezostage without modeling hysteresis’, IEEE Trans. Control Syst. Technol., 2012, 20, (4), pp. 983994 (doi: 10.1109/TCST.2011.2157345).
    2. 2)
      • 10. Chen, X., Hisayama, T.: ‘Adaptive sliding-mode position control for piezo-actuated stage’, IEEE Trans. Ind. Electron., 2008, 55, (11), pp. 39273934 (doi: 10.1109/TIE.2008.926768).
    3. 3)
      • 21. Sha, D., Bajic, V.B.: ‘Robust discrete adaptive input-output-based sliding mode controller’, Int. J. Syst. Sci., 2000, 31, (12), pp. 16011614 (doi: 10.1080/00207720050217377).
    4. 4)
      • 19. Xu, J.X., Abidi, K.: ‘Discrete-time output integral sliding-mode control for a piezomotor-driven linear motion stage’, IEEE Trans. Ind. Electron., 2008, 55, (11), pp. 39173926 (doi: 10.1109/TIE.2008.2003194).
    5. 5)
      • 30. Furuta, K.: ‘Sliding mode control of a discrete system’, Syst. Control Lett., 1990, 14, (2), pp. 145152 (doi: 10.1016/0167-6911(90)90030-X).
    6. 6)
      • 11. Huang, S., Tan, K.K., Lee, T.H.: ‘Adaptive sliding-mode control of piezoelectric actuators’, IEEE Trans. Ind. Electron., 2009, 56, (9), pp. 35143522 (doi: 10.1109/TIE.2009.2012450).
    7. 7)
      • 13. Yan, M., Shi, Y.: ‘Robust discrete-time sliding mode control for uncertain systems with time-varying state delay’, IET Control Theory Appl., 2008, 2, (8), pp. 662674 (doi: 10.1049/iet-cta:20070460).
    8. 8)
      • 20. Xu, Q., Li, Y.: ‘Micro-/nanopositioning using model predictive output integral discrete sliding mode control’, IEEE Trans. Ind. Electron., 2012, 59, (2), pp. 11611170 (doi: 10.1109/TIE.2011.2157287).
    9. 9)
      • 25. Veselic, B., Perunicic-Drazenovic, B., Milosavljevic, C.: ‘Improved discrete-time sliding-mode position control using Euler velocity estimation’, IEEE Trans. Ind. Electron., 2010, 57, (11), pp. 38403847 (doi: 10.1109/TIE.2010.2042416).
    10. 10)
      • 9. Huang, P.K., Shieh, P.H., Lin, F.J., Shieh, H.J.: ‘Sliding-mode control for a two-dimensional piezo-positioning stage’, IET Control Theory Appl., 2007, 1, (4), pp. 11041113 (doi: 10.1049/iet-cta:20060371).
    11. 11)
      • 3. Xu, Q.: ‘Adaptive discrete-time sliding mode impedance control of a piezoelectric microgripper’, IEEE Trans. Robot., 2013, 29, (3), pp. 663673 (doi: 10.1109/TRO.2013.2239554).
    12. 12)
      • 32. Zhu, Y.: ‘Multivariable system identification for process control’ (Elsevier Science Inc., New York, 2001).
    13. 13)
      • 22. Lin, C.J., Chen, S.Y.: ‘Evolutionary algorithm based feedforward control for contouring of a biaxial piezo-actuated stage’, Mechatronics, 2009, 19, (6), pp. 829839 (doi: 10.1016/j.mechatronics.2009.04.007).
    14. 14)
      • 1. Yong, Y.K., Liu, K., Moheimani, S.O.R.: ‘Reducing cross-coupling in a compliant XY nanopositioner for fast and accurate raster scanning’, IEEE Trans. Control Syst. Technol., 2010, 18, (5), pp. 11721179 (doi: 10.1109/TCST.2009.2033201).
    15. 15)
      • 7. Wu, Y., Zou, Q.: ‘Robust-inversion-based 2-DOF control design for output tracking: Piezoelectric actuator example’, IEEE Trans. Control Syst. Technol., 2009, 17, (5), pp. 10691082 (doi: 10.1109/TCST.2008.2005111).
    16. 16)
      • 15. Niu, Y., Ho, D.W.C., Wang, Z.: ‘Improved sliding mode control for discrete-time systems via reaching law’, IET Control Theory Appl., 2010, 4, (11), pp. 22452251 (doi: 10.1049/iet-cta.2009.0296).
    17. 17)
      • 26. Bibian, S., Jin, H.: ‘Time delay compensation of digital control for DC switchmode power supplies using prediction techniques’, IEEE Trans. Power Electron., 2000, 15, (5), pp. 835842 (doi: 10.1109/63.867672).
    18. 18)
      • 16. Abidi, K., Xu, J.X., Yu, X.: ‘On the discrete-time integral sliding mode control’, IEEE Trans. Autom. Control, 2007, 52, (4), pp. 709715 (doi: 10.1109/TAC.2007.894537).
    19. 19)
      • 24. Galias, Z., Yu, X.: ‘Euler's discretization of single input sliding-mode control systems’, IEEE Trans. Autom. Control, 2007, 52, (9), pp. 17261730 (doi: 10.1109/TAC.2007.904289).
    20. 20)
      • 27. Elmali, H., Olgac, N.: ‘Implementation of sliding mode control with perturbation estimation (SMCPE)’, IEEE Trans. Control Syst. Technol., 1996, 4, (1), pp. 7985 (doi: 10.1109/87.481770).
    21. 21)
      • 5. Xu, Q.: ‘Identification and compensation of piezoelectric hysteresis without modeling hysteresis inverse’, IEEE Trans. Ind. Electron., 2013, 60, (9), pp. 39273937 (doi: 10.1109/TIE.2012.2206339).
    22. 22)
      • 8. Helfrich, B.E., Lee, C., Bristow, D.A., et al: ‘Combined H-feedback control and iterative learning control design with application to nanopositioning systems’, IEEE Trans. Control Syst. Technol., 2010, 18, (2), pp. 336351 (doi: 10.1109/TCST.2009.2018835).
    23. 23)
      • 31. Sarpturk, S., Istefanopulos, Y., Kaynak, O.: ‘On the stability of discrete-time sliding mode control systems’, IEEE Trans. Autom. Control, 1987, 32, (10), pp. 930932 (doi: 10.1109/TAC.1987.1104468).
    24. 24)
      • 29. Young, K.D., Utkin, V.I., Ozguner, U.: ‘A control engineer's guide to sliding mode control’, IEEE Trans. Control Syst. Technol., 1999, 7, (3), pp. 328342 (doi: 10.1109/87.761053).
    25. 25)
      • 12. Salah, M.H., McIntyre, M.L., Dawson, D.M., Wagner, J.R., Tatlicioglu, E.: ‘Charge feedback-based robust position tracking control for piezoelectric actuators’, IET Control Theory Appl., 2012, 6, (5), pp. 615628 (doi: 10.1049/iet-cta.2010.0568).
    26. 26)
      • 17. Xi, Z., Hesketh, T.: ‘Discrete time integral sliding mode control for overhead crane with uncertainties’, IET Control Theory Appl., 2010, 4, (10), pp. 20712081 (doi: 10.1049/iet-cta.2009.0558).
    27. 27)
      • 6. Liaw, H.C., Shirinzadeh, B., Smith, J.: ‘Robust motion tracking control of piezo-driven flexure-based four-bar mechanism for micro/nano manipulation’, Mechatronics, 2008, 18, (2), pp. 111120 (doi: 10.1016/j.mechatronics.2007.09.002).
    28. 28)
      • 2. Rakotondrabe, M., Ivan, I.A.: ‘Development and force/position control of a new hybrid thermo-piezoelectric microgripper dedicated to micromanipulation tasks’, IEEE Trans. Autom. Sci. Eng., 2011, 8, (4), pp. 824834 (doi: 10.1109/TASE.2011.2157683).
    29. 29)
      • 28. Monsees, G.: ‘Discrete-time sliding mode control’. PhD thesis, Delft University of Technology, 2002.
    30. 30)
      • 23. Tarokh, M.: ‘A discrete-time adaptive control scheme for robot manipulators’, J. Robot. Syst., 1990, 7, (2), pp. 145166 (doi: 10.1002/rob.4620070203).
    31. 31)
      • 4. Janaideh, M.A., Rakheja, S., Su, C.Y.: ‘Experimental characterization and modeling of rate-dependent hysteresis of a piezoceramic actuator’, Mechatronics, 2009, 19, (5), pp. 656670 (doi: 10.1016/j.mechatronics.2009.02.008).
    32. 32)
      • 14. Lin, C.F., Su, W.C., Liu, K.H.: ‘Post-filtering approach to output feedback variable structure control for single-input-single-output sampled-data systems’, IET Control Theory Appl., 2009, 3, (8), pp. 11451154 (doi: 10.1049/iet-cta.2008.0116).
    33. 33)
      • 33. Xu, Q., Jia, M.: ‘Model reference adaptive control with perturbation estimation for a micropositioning system’, IEEE Trans. Control Syst. Technol., 2013, doi: 10.1109/TCST.2013.2248061, in press.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0361
Loading

Related content

content/journals/10.1049/iet-cta.2013.0361
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading