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Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems

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Abstract

The robust control problem for a class of underactuated mechanical systems called acrobots is addressed. The goal is to drive the acrobots away from the straight-down position and balance them at the straight-up unstable equilibrium position in the presence of parametric uncertainties and external disturbance. First, in the swing-up area, it is shown that the time derivative of energy is independent of the parameter uncertainties, but exogenous disturbance may destroy the characteristic of increase in mechanical energy. So, a swing-up controller with compensator is designed to suppress the influence of the disturbance. Then, in the attractive area, the control problem is formulated into a H ∞ control framework by introducing a proper error signal, and a sufficient condition of the existence of H ∞ state feedback control law based on linear matrix inequality (LMI) is proposed to guarantee the quadratic stability of the control system. Finally, the simulation results show that the proposed control approach can simultaneously handle a maximum ±10% parameter perturbation and a big disturbance simultaneously.

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Xu-zhi Lai  (赖旭芝), Chang-zhong Pan  (潘昌忠) & Min Wu  (吴敏)

  2. Hunan Engineering Laboratory for Advanced Control and Intelligent Automation (Central South University), Changsha, 410083, China

    Xu-zhi Lai  (赖旭芝), Chang-zhong Pan  (潘昌忠) & Min Wu  (吴敏)

  3. School of Computer Science, Tokyo University of Technology, Tokyo, 192-0982, Japan

    Jin-hua She  (佘锦华)

  4. School of Engineering, University of Guelph, Guelph, N1G 2W1, Canada

    Chang-zhong Pan  (潘昌忠) & Simon X. Yang

Authors
  1. Xu-zhi Lai  (赖旭芝)
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  2. Chang-zhong Pan  (潘昌忠)
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  3. Min Wu  (吴敏)
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  4. Jin-hua She  (佘锦华)
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  5. Simon X. Yang
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Corresponding author

Correspondence to Xu-zhi Lai  (赖旭芝).

Additional information

Foundation item: Projects(61074112, 60674044) supported by the National Natural Science Foundation of China

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Lai, Xz., Pan, Cz., Wu, M. et al. Robust stabilization and disturbance attenuation for a class of underactuated mechanical systems. J. Cent. South Univ. 19, 2488–2495 (2012). https://doi.org/10.1007/s11771-012-1301-1

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  • DOI: https://doi.org/10.1007/s11771-012-1301-1

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