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A minimum phase output based tracking control of ball and plate systems

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Abstract

This work investigates the trajectory tracking control problem of the ball and plate system. Different from the existing related control approaches that are developed based upon simplified model, our control approach depends on a minimum phase output, which helps to use the input-output feedback linearization approach to design a tracking controller for the original unsimplified nonlinear model. Firstly, a smart output is constructed as the form of the filtered term of ball position plus the plate angle vector. Then the relative degree of system with this output is calculated, and the zero dynamics equation for the tracking problem is computed. Sufficient conditions on design parameters and reference trajectory guaranteeing zero dynamics stable are derived, exhibiting the minimum phase property of output. Relying on this minimum phase output, a tracking control law is proposed with the purpose of regulating the output tracking error to zero. Finally, it is strictly proved by using the input-output feedback linearization theory that the proposed controller is capable of bringing the ball to track the reference trajectory, and the tracking errors are exponentially convergent to zero. Four simulation examples are given to illustrate the effectiveness of the proposed control strategy.

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Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Dehui Kan & Wen**g **e

  2. Chongqing Innovation Center of Industrial BigData Co. Ltd, National Engineering Laboratory for Industrial Big-data Application Technology, Chongqing, 400065, China

    Bin **ng & Linquan Zhu

Authors
  1. Dehui Kan
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  2. Bin **ng
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  3. Wen**g **e
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  4. Linquan Zhu
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Corresponding author

Correspondence to Wen**g **e.

Additional information

This work was supported by Fundamental Research Funds for the Central Universities (No. XDJK2020C036)

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Kan, D., **ng, B., **e, W. et al. A minimum phase output based tracking control of ball and plate systems. Int. J. Dynam. Control 10, 462–472 (2022). https://doi.org/10.1007/s40435-021-00824-1

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  • DOI: https://doi.org/10.1007/s40435-021-00824-1

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