Passivity-based adaptive integral control for underactuated mechanical systems and its application in tower cranes

Authors

Shuaixin Hou, Lijun Sun, Tianfei Chen, Xiaoping Liu, Na Wang, Renhan Wu, Cungen Liu

Abstract

This study proposes a novel adaptive integral controller integrated with the interconnection and damping assignment passivity-based control framework for underactuated mechanical systems, and applies it to tower cranes. First, an underactuated system model with uncertainties is constructed based on Port-controlled Hamiltonian structure. Subsequently, using a state transformation, an adaptive integral controller is designed to realize real-time estimation of unknown parameters and reduce steady-state errors. The stability of the closed-loop system under uncertainties is rigorously proven via the Lyapunov candidate function based on the Hamiltonian energy. Then, a constructive approach without additional parameter constraints is presented to obtain the solution of partial differential equations. Finally, the proposed controller is applied to an underactuated tower crane system, and the control parameters are determined by the pole placement method to reduce time and effort spent on parameter tuning. Experimental results demonstrate that, under the action of the proposed controller, the mean absolute tracking errors of the jib and the trolley remain within 0.9251 deg and 0.0175 m, and the mean absolute swing angles of the load are effectively suppressed within 0.1399 deg and 0.2239 deg, which fully complies with the performance specifications for industrial applications.

Keywords

adaptive integral control, partial differential equations, passivity-based control, tower cranes with uncertainties, underactuated mechanical systems

Citation

• Journal: Applied Mathematical Modelling
• Year: 2027
• Volume: 163
• Issue:
• Pages: 117268
• Publisher: Elsevier BV
• DOI: 10.1016/j.apm.2026.117268

BibTeX

@article{Hou_2027,
  title={{Passivity-based adaptive integral control for underactuated mechanical systems and its application in tower cranes}},
  volume={163},
  ISSN={0307-904X},
  DOI={10.1016/j.apm.2026.117268},
  journal={Applied Mathematical Modelling},
  publisher={Elsevier BV},
  author={Hou, Shuaixin and Sun, Lijun and Chen, Tianfei and Liu, Xiaoping and Wang, Na and Wu, Renhan and Liu, Cungen},
  year={2027},
  pages={117268}
}

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