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Adaptive RBF-PIDSMC control method with estimated model parameters for a piezo-actuated stage

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Abstract

The aim of this work is to find an adaptive control scheme to realize precise position tracking for a piezo-actuated stage, which is usually very difficult to control due to the essential nonlinearity and unknown uncertainty. Firstly, a proportional-integral-derivative (PID) sliding mode controller is designed based on the established model and the estimated parameters. Then, in order to reduce the influence of model error, a radial basis function (RBF) neural network is integrated to the controller to improve the control performance. Eventually, an adaptive RBF based PID-type sliding mode controller (RBF-PIDSMC) is proposed and its stability is derived mathematically based on Lyapunov theory. Simulation results of the proposed controller are compared with the PID sliding mode controller to verify its tracking performance. Positioning tracking experiments with two different trajectories are also conducted to verify the correctness and effectiveness of the proposed controller. We can conclude that the proposed controller can be used to track commanded position trajectory for the piezoelectric stage.

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Acknowledgements

This research was funded by the National Natural Science Foundation of China, under Grant numbers 71071078 and 70671035.

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Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, No. 263 Kaiyuan Road, Luolong District, Luoyang, 471023, PR China

    Qun Chen & Zong-Xiao Yang

  2. College of Physics and Electronic Information, Luoyang Normal University, No. 6 Jiqing Road, Yibin District, Luoyang, 471934, PR China

    Qun Chen

  3. Institute of Systems Science and Engineering, Henan University of Science and Technology, No. 48 Xiyuan Road, Jianxi District, Luoyang, 471003, PR China

    Zong-Xiao Yang

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  1. Qun Chen
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  2. Zong-Xiao Yang
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Correspondence to Qun Chen or Zong-Xiao Yang.

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Chen, Q., Yang, ZX. Adaptive RBF-PIDSMC control method with estimated model parameters for a piezo-actuated stage. Microsyst Technol 27, 69–77 (2021). https://doi.org/10.1007/s00542-020-04907-5

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  • DOI: https://doi.org/10.1007/s00542-020-04907-5

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