Advertisement

A Composite Controller for Piezoelectric Actuators Based on Action Dependent Dual Heuristic Programming and Model Predictive Control

  • Shijie Qin
  • Long ChengEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11741)

Abstract

Piezoelectric actuators (PEAs) have been widely applied in nanopositioning applications due to the advantages of the rapid response, large mechanical force and high resolution. However, due to the inherent hysteresis nonlinear property, the high-precision control of PEAs is challenging. To achieve the goal of high-precision motion control, various control methods have been reported in the literature. Recently, adaptive dynamic programming (ADP) has gained much attention to solve optimal control problems. Action dependent dual heuristic programming (ADDHP) is one of the effective structures of ADP, which can estimate the gradient of the cost function by using both the control action and the state as the input of the critic networks. In addition, model predictive control (MPC) is a form of control that uses the current state and the model predicted states to obtain the control action. In this paper, a composite controller is designed for the tracking control of PEAs with ADDHP and MPC. A multilayer feedforward neural network (MFNN) is proposed to model PEAs and is then instantaneously linearized for real-time finding the solutions to the optimization problem in MPC. Experiments are designed to verify the effectiveness of the proposed control method and some comparative experiments with other control methods are also conducted to show that the proposed method can achieve a better tracking performance.

Keywords

Action Dependent Dual Heuristic Programming (ADDHP) Model Predictive Control (MPC) Instantaneous linearization Piezoelectric Actuators (PEAs) 

Notes

Acknowledgement

This work was supported in part by the National Nature Science Foundation under Grant 61873268, Grant 61421004, and Grant 61633016, in part by the Research Fund for Young Top-Notch Talent of National Ten Thousand Talent Program, in part by the Beijing Municipal Natural Science Foundation under Grant L182060, and in part by the Major Science and Technology Fund of Beijing under Grant Z181100003118006.

References

  1. 1.
    Gu, G.-Y., Zhu, L.-M., Su, C.-Y.: Modeling and control of piezo-actuated nanopositioning stages: a survey. IEEE Trans. Autom. Sci. Eng. 13(1), 313–332 (2016)CrossRefGoogle Scholar
  2. 2.
    Xu, Q.: Robust impedance control of a compliant microgripper for high-speed position/force regulation. IEEE Trans. Ind. Electron. 62(2), 1201–1209 (2015)CrossRefGoogle Scholar
  3. 3.
    Wang, G., Zhou, X., Ma, P., Wang, R., Meng, G., Yang, X.: A novel vibration assisted polishing device based on the flexural mechanism driven by the piezoelectric actuators. AIP Adv. 8(1), 015012 (2018)CrossRefGoogle Scholar
  4. 4.
    Wu, J., et al.: Effective tilting angles for a dual probes AFM system to achieve high-precision scanning. IEEE/ASME Trans. Mechatron. 21(5), 2512–2521 (2016)CrossRefGoogle Scholar
  5. 5.
    Clayton, G.M., Tien, S., Leang, K.M., Zou, Q., Devasia, S.: A review of feedforward control approaches in nanopositioning for high-speed SPM. J. Dyn. Syst. Meas. Contr. 131(6), 061101 (2009)CrossRefGoogle Scholar
  6. 6.
    Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cheng, L., Liu, W., Hou, Z.-G., Yu, J., Tan, M.: Neural network based nonlinear model predictive control for piezoelectric actuators. IEEE Trans. Ind. Electron. 62(12), 7717–7727 (2015)CrossRefGoogle Scholar
  8. 8.
    Liu, W., Cheng, L., Yu, J., Hou, Z.-G., Tan, M.: An inversion-free predictive controller for piezoelectric actuators based on a dynamic linearized neural network model. IEEE/ASME Trans. Mechatron. 21(1), 214–226 (2016)Google Scholar
  9. 9.
    Cheng, L., Liu, W., Yang, C., Hou, Z.-G., Huang, T., Tan, M.: A neural-network-based controller for piezoelectric-actuated stick-slip devices. IEEE Trans. Ind. Electron. 65(3), 2598–2607 (2018)CrossRefGoogle Scholar
  10. 10.
    Cheng, L., Liu, W., Hou, Z.-G., Huang, T., Yu, J., Tan, M.: An adaptive Takagi-Sugeno model based fuzzy predictive controller for piezoelectric actuators. IEEE Trans. Ind. Electron. 64(4), 3048–3058 (2017)CrossRefGoogle Scholar
  11. 11.
    Cao, Y., Cheng, L., Peng, J., Chen, X.: An inversion-based model predictive control with an integral-of-error state variable for piezoelectric actuators. IEEE/ASME Trans. Mechatron. 18(3), 895–904 (2013)CrossRefGoogle Scholar
  12. 12.
    Lewis, F.L., Vrabie, D.: Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circ. Syst. Mag. 9(3), 32–50 (2009)CrossRefGoogle Scholar
  13. 13.
    Werbos, P.: Advanced forecasting methods for global crisis warning and models of intelligence. Gen. Syst. Yearb. 22, 25–38 (1977)Google Scholar
  14. 14.
    Werbos, P.: Approximate dynamic programming for real-time control and neural modeling. In: White, D.A., Sofge, D.A. (eds.) Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches, Chap. 13, pp. 493–525. Van Nostrand, New York (1992)Google Scholar
  15. 15.
    Wang, F.-Y., Zhang, H., Liu, D.: Adaptive dynamic programming: an introduction. IEEE Comput. Intell. Mag. 4(2), 39–47 (2009)CrossRefGoogle Scholar
  16. 16.
    Lewis, F.L.: Applied Optimal Control and Estimation. PrenticeHall, Upper Saddle River (1992)zbMATHGoogle Scholar
  17. 17.
    Lewis, F.L., Syrmos, V.L.: Optimal Control. Wiley, New York (1995)Google Scholar
  18. 18.
    Prokhorov, D.V., Wunsch, D.C.: Adaptive critic designs. IEEE Trans. Neural Netw. 8(5), 997–1007 (1997)CrossRefGoogle Scholar
  19. 19.
    Lendaris, G.G., Shannon, T.T., Schultz, L.J., Hutsell, S., Rogers, A.: Dual heuristic programming for fuzzy control. In: Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver, pp. 551–556. IEEE (2001)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Management and Control for Complex SystemsInstitute of Automation, Chinese Academy of SciencesBeijingChina
  2. 2.School of Artificial IntelligenceUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations