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A neural network-based inversion method of a feedback linearization controller applied to a hydraulic actuator

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Abstract

In this work, we use a neural network as a substitute for the traditional analytic functions employed as an inversion set in feedback linearization control algorithms applied to hydraulic actuators. Although very effective and with strong stability guarantees, feedback linearization control depends on parameters that are difficult to determine, requiring large amounts of experimental effort to be identified accurately. On the other hands, neural networks require little effort regarding parameter identification, but pose significant hindrances to the development of solid stability analyses and/or to the processing capabilities of the control hardware. Here, we combine these techniques to control the positioning of a hydraulic actuator, without requiring extensive identification procedures nor losing stability guarantees for the closed-loop system, at reasonable computing demands. The effectiveness of the proposed method is verified both theoretically and by means of experimental results.

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Correspondence to Fábio Augusto Pires Borges.

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Technical Editor: Victor Juliano De Negri.

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Appendix

Appendix

  1. (1)

    Normalization Equations.

    Input normalization function: Table 9

    Table 9 Neural network normalization
    $$N(x) = \frac{0,9 - 0,1}{{X_{\max } - X_{\min } }}\left( {x - X_{\min } } \right) + 0,1$$
    (33)

    Output normalization function:

    $$D(y) = \frac{y - 0,1}{{0,9 - 0,1}}\left( {X_{\max } - X_{\min } } \right) + X_{\min }$$
    (34)
  2. (2)

    Weights for neural network when Tables 10, 11, 12, 13

    Table 10 Weights Layer 1 to Layer 2
    Table 11 Weights Layer 2 to Layer 3 (neuron 1–6)
    Table 12 Weights Layer 2 to Layer 3 (neuron 7–10)
    Table 13 Weights Layer 3 to Layer 4

    \(\dot{y}\ge 0.\)

  3. (3)

    Weights for neural network when Tables 14, 15\(\dot{y}<0.\)

    Table 14 Weights Layer 1 to Layer 2
    Table 15 Weights Layer 2 to Layer 3

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Borges, F.A.P., Perondi, E.A., Cunha, M.A.B. et al. A neural network-based inversion method of a feedback linearization controller applied to a hydraulic actuator. J Braz. Soc. Mech. Sci. Eng. 43, 248 (2021). https://doi.org/10.1007/s40430-021-02957-y

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