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Partially saturated nonlinear control for gantry cranes with hardware experiments

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Abstract

Gantry cranes are typically underactuated nonlinear dynamic systems with highly coupled system states. We propose in this paper a partially saturated nonlinear controller for gantry crane systems by converting the crane model into an objective (i.e., desired closed-loop) system. The presented scheme guarantees “soft” cart start by introducing a smooth saturated function into the controller. In particular, we first establish an objective system with desired signal convergence and stability performance. Then, on the basis of the objective dynamics’ structure, we derive a partially saturated control law straightforwardly by solving one partial differential equation, without necessity of performing partial feedback linearization operations to the original crane model. The convergence and stability performance of the objective system is assured with Lyapunov-based methods. In order to verify the practical control performance of the proposed method, we implement both numerical simulation and hardware experiments to illustrate that the new method achieves increased performance with respect to existing methods, with lessened control efforts.

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Notes

  1. We focus our controller development on the resultant force \(F(t)\) since, in this work, the model (4) will be utilized for feedforward friction force compensation, as will be shown in the experiments in Sect. 5.

  2. Owing to the smooth property, the hyperbolic tangent function \(\tanh (\cdot )\) in the controller (32) does not affect the uniqueness and existence of the solutions of the closed-loop (objective) system.

  3. It is worthwhile to point out that it is generally assumed that \(-\pi /2 < \theta (t) < \pi /2\) [16–19, 22, 28, 29], which means that the load will not go above the cart in practice. Hence in this sense, we have relaxed this assumption from a mathematical viewpoint, and an almost global asymptotic control result is obtained.

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Acknowledgments

The authors would like to express their sincere thanks to the reviewers and the editor for the valuable suggestions that have greatly improved the quality of the paper. They also greatly acknowledge the financial supports from the National Science and Technology Pillar Program of China (Grant No. 2013BAF07B03), the National Science Fund for Distinguished Young Scholars of China (Grant No. 61325017), the National Natural Science Foundation of China (Grant No. 11372144), and the Academic Award for Doctoral Students from the Ministry of Education of China (Grant No. (190)H0511009).

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  1. Institute of Robotics and Automatic Information System, Nankai University, Tianjin, China

    Ning Sun & Yongchun Fang

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  1. Ning Sun
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Correspondence to Yongchun Fang.

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Sun, N., Fang, Y. Partially saturated nonlinear control for gantry cranes with hardware experiments. Nonlinear Dyn 77, 655–666 (2014). https://doi.org/10.1007/s11071-014-1328-y

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