Piezoelectric actuators (PEAs) are essential elements in many systems that require high precision and accuracy. However, the difficulty with the use of PEAs is their actuator uncertainties including the highly non-linear behaviour which is a consequence of the hysteresis property inherently within PEAs. Therefore, a robust control system is essential for such actuators. This study proposes a systematic control method that utilises a fast non-singular terminal sliding mode (FNTSM) for PEAs. Unlike the conventional sliding mode (CSM), the FNTSM control method is characterised by chatter free. Besides, a zero error convergence can be guaranteed in finite time in the presence of disturbance and system uncertainties. The design of the FNTSM control is based on the bounded information of parametric uncertainties. The feedback velocity is provided for the FNTSM controller by using the a model-free velocity estimator. Theoretical analysis and experimental results reveal that the FNTSM controller can achieve faster and higher precision performance in comparison with either a CSM or a linear controller.

References

1. 1)
  - 21. Hu, Q., Du, C., Xie, L., et al : ‘Discrete-time sliding mode control with time-varying surface for hard disk drives’, IEEE Trans. Control Syst. Technol., 2009, 17, (1), pp. 175–183 (doi: 10.1109/TCST.2008.922505).
2. 2)
  - 35. Mercorelli, P.: ‘A two-stage augmented extended Kalman filter as an observer for sensorless valve control in camless internal combustion engines’, IEEE Trans. Ind. Electron., 2012, 59, (11), pp. 4236–4247 (doi: 10.1109/TIE.2012.2192892).
3. 3)
  - 20. Shen, J.-C., Jywe, W.-Y., Liu, C.-H., et al : ‘Sliding-mode control of a three-degrees-of-freedom nanopositioner’, Asian J. Control, 2008, 10, (3), pp. 267–276 (doi: 10.1002/asjc.33).
4. 4)
  - 10. Devasia, S., Eleftheriou, E., Moheimani, S.R.: ‘A survey of control issues in nanopositioning’, IEEE Trans. Control Syst. Technol., 2007, 15, (5), pp. 802–823 (doi: 10.1109/TCST.2007.903345).
5. 5)
  - 3. Aphale, S., Fleming, A., Moheimani, S.: ‘High speed nano-scale positioning using a piezoelectric tube actuator with active shunt control’, Micro Nano Lett., 2007, 2, (1), pp. 9–12 (doi: 10.1049/mnl:20065075).
6. 6)
  - 44. Shotorbani, A.M., Ajami, A., Zadeh, S.G., Aghababa, M.P., Mahboubi, B.: ‘Robust terminal sliding mode power flow controller using unified power flow controller with adaptive observer and local measurement’, IET Gener. Transm. Distrib., 2014, 8, pp. 1712–1723 (doi: 10.1049/iet-gtd.2013.0637).
7. 7)
  - 23. Mercorelli, P.: ‘An antisaturating adaptive preaction and a slide surface to achieve soft landing control for electromagnetic actuators’, IEEE/ASME Trans. Mechatron., 2012, 17, (1), pp. 76–85 (doi: 10.1109/TMECH.2010.2089467).
8. 8)
  - 15. Stepanenko, Y., Su, C.-Y. ‘Intelligent control of piezoelectric actuators’, Proc. IEEE Conf. Decision Control, 1998, 4, pp. 4234–4239.
9. 9)
  - 33. Simon, D.: ‘Optimal state estimation: Kalman, H infinity, and nonlinear approaches’ (John Wiley & Sons, 2006).
10. 10)
  - 9. Sitti, M.: ‘Survey of nanomanipulation systems’, Proc. IEEE Conf. Nanotechnology2001, pp. 75–80.
11. 11)
  - 31. Haimo, V.T.: ‘Finite time controllers’, SIAM J. Control Optim., 1986, 24, (4), pp. 760–770 (doi: 10.1137/0324047).
12. 12)
  - 7. Chan, K.W., Liao, W.-H.: ‘Precision positioning of hard disk drives using piezoelectric actuators with passive damping’, Proc. IEEE Int. Conf. on Mechatronics and Automation2006, pp. 1269–1274.
13. 13)
  - 1. Binnig, G., Rohrer, H.: ‘Scanning tunneling microscopy’, IBM J. Res. Dev., 2000, 44, (1–2), pp. 279–293.
14. 14)
  - 18. 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 (doi: 10.1109/TCST.2009.2028878).
15. 15)
  - 14. Wu, Y., Zou, Q. ‘Iterative control approach to compensate for both the hysteresis and the dynamics effects of piezo actuators’, IEEE Trans. Control Syst. Technol., 2007, 15, (5), pp. 936–944 (doi: 10.1109/TCST.2007.899722).
16. 16)
  - 17. Chen, C.-Q., Shen, Y.-P.: ‘Optimal control of active structures with piezoelectric modal sensors and actuators’, Smart Mater. Struct., 1997, 6, (4), pp. 403–409 (doi: 10.1088/0964-1726/6/4/003).
17. 17)
  - 26. Yu, S.H., Yu, X.H., Shirinzadeh, B., Man, Z.H.: ‘Continuous finite-time control for robotic manipulators with terminal sliding mode’, Automatica, 2005, 41, (11), pp. 1957–1964 (doi: 10.1016/j.automatica.2005.07.001).
18. 18)
  - 30. Zheng, J., Fu, M.: ‘A simple robust controller for hysteresis and resonance compensation of piezoelectric actuators’, Proc. IEEE Int. Control Auto. Robot Conf.2012, pp. 282–287.
19. 19)
  - 36. Mercorelli, P.: ‘A two-stage sliding mode high-gain observer to reduce uncertainties and disturbances effects for sensorless control in automotive applications’, IEEE Trans. Ind. Electron., 2015, 62, (9), pp. 5929–5940 (doi: 10.1109/TIE.2015.2450725).
20. 20)
  - 8. Crawley, E.F., De Luis, J.: ‘Use of piezoelectric actuators as elements of intelligent structures’, AIAA J., 1987, 25, (10), pp. 1373–1385 (doi: 10.2514/3.9792).
21. 21)
  - 39. Leang, K.K., Zou, Q., Devasia, S.: ‘Feedforward control of piezoactuators in atomic force microscope systems’, IEEE Control Syst. Mag., 2009, 29, (1), pp. 70–82 (doi: 10.1109/MCS.2008.930922).
22. 22)
  - 12. Ge, P., Jouaneh, M.: ‘Tracking control of a piezoceramic actuator’, IEEE Trans. Control Syst. Technol., 1996, 4, (3), pp. 209–216 (doi: 10.1109/87.491195).
23. 23)
  - 11. Croft, D., Shed, G., Devasia, S.: ‘Creep, hysteresis, and vibration compensation for piezoactuators: atomic force microscopy application’, ASME J. Dyn. Syst. Control, 2001, 123, (1), pp. 35–43 (doi: 10.1115/1.1341197).
24. 24)
  - 15. Levant, A.: ‘Sliding order and sliding accuracy in sliding mode control’, Int. J. Control, 1993, 58, (6), pp. 1247–1263 (doi: 10.1080/00207179308923053).
25. 25)
  - 19. Yi, J., Chang, S., Shen, Y.: ‘Disturbance-observer-based hysteresis compensation for piezoelectric actuators’, IEEE/ASME Trans. Mechatron., 2009, 14, (4), pp. 456–464 (doi: 10.1109/TMECH.2009.2023986).
26. 26)
  - 38. Shieh, N., Tung, P., Lin, C.-L.: ‘Robust output tracking control of a linear brushless dc motor with time-varying disturbances’, Inst. Electr. Eng. Power Appl., 2002, 149, (1), pp. 39–45 (doi: 10.1049/ip-epa:20020027).
27. 27)
  - 4. Vogl, W., Ma, B.K.-L., Sitti, M.: ‘Augmented reality user interface for an atomic force microscope-based nanorobotic system’, IEEE Trans. Nanotechnol., 2006, 5, (4), pp. 397–406 (doi: 10.1109/TNANO.2006.877421).
28. 28)
  - 26. Slotine, J.-J.E., Li, W.: ‘Applied nonlinear control’ (Prentice-Hall, Englewood Cliffs, NJ, 1991).
29. 29)
  - 22. 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. 111–120 (doi: 10.1016/j.mechatronics.2007.09.002).
30. 30)
  - 16. Tsai, M.-S., Chen, J.-S.: ‘Robust tracking control of a piezoactuator using a new approximate hysteresis model’, J. Dyn. Syst., Meas. Control, 2003, 125, (1), pp. 96–102 (doi: 10.1115/1.1540114).
31. 31)
  - 13. Parra-Vega, V., Arimoto, S., Liu, Y.-H., et al : ‘Dynamic sliding pid control for tracking of robot manipulators: theory and experiments’, IEEE Trans. Robot. Autom., 2003, 19, (6), pp. 967–976 (doi: 10.1109/TRA.2003.819600).
32. 32)
  - 24. Cunha, J., Costa, R., Lizarralde, F., et al : ‘Peaking free variable structure control of uncertain linear systems based on a high-gain observer’, Automatica, 2009, 45, (5), pp. 1156–1164 (doi: 10.1016/j.automatica.2008.12.018).
33. 33)
  - 5. Binnig, G., Smith, D.: ‘Single-tube three-dimensional scanner for scanning tunneling microscopy’, Rev. Sci. Instrum., 1986, 57, (8), pp. 1688–1689 (doi: 10.1063/1.1139196).
34. 34)
  - 2. Adriaens, H., De Koning, W., Banning, R.: ‘Modeling piezoelectric actuators’, IEEE/ASME Trans. Mechatron., 2000, 5, (4), pp. 331–341 (doi: 10.1109/3516.891044).
35. 35)
  - 6. Onal, C.D., Ozcan, O., Sitti, M.: ‘Automated 2-d nanoparticle manipulation using atomic force microscopy’, IEEE Trans. Nanotechnol., 2011, 10, (3), pp. 472–481 (doi: 10.1109/TNANO.2010.2047510).
36. 36)
  - 11. Feng, Y., Yu, X.H., Man, Z.H.: ‘Non-singular terminal sliding mode control of rigid manipulators’, Automatica, 2002, 38, (12), pp. 2159–2167 (doi: 10.1016/S0005-1098(02)00147-4).
37. 37)
  - 37. Levant, A.: ‘Robust exact differentiation via sliding mode technique’, Automatica, 1998, 34, (3), pp. 379–384 (doi: 10.1016/S0005-1098(97)00209-4).
38. 38)
  - 34. Hilairet, M., Auger, F., Darengosse, C.: ‘Two efficient Kalman filters for flux and velocity estimation of induction motors’, Proc. IEEE Power Electronics Specialists Conf., 2000, pp. 891–896.
39. 39)
  - 32. 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., 2014, 20, (4), pp. 1743–1752 (doi: 10.1109/TMECH.2014.2352647).

Robust and fast non-singular terminal sliding mode control for piezoelectric actuators

References

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