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Bifurcation and chaos for a novel model of trigonal centrifugal governor with non-smooth control

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Abstract

The traditional Watt’s centrifugal governors with a flywheel ball cause research challenges in both model design and analytical approach. The development of the new model and the new control scheme for the centrifugal governor system, however, has received little attention. The three-dimensional differential equations of motion for trigonal centrifugal governor (TCG) model are presented with the aid of Euler–Lagrange’s equation and the theorem of angular momentum. A novel TCG system with new-style nonlinearities of quotient (*/*) function, radical (the square root \(\sqrt{*}\)) function, and non-smooth control strategy (|*|) is proposed. To display the complex relationship of parameter dependence relationship, the mechanical properties of nonlinear restoring force surfaces and non-smooth torque surfaces are plotted. Then, various dynamical behaviors for the autonomous system are examined, including the equilibrium bifurcation, potential energy, Hamilton energy, equilibrium stability, and phase portraits. Additionally, the numerical simulation of chaotic phase portraits are used to validate the theoretical chaotic criteria, and the three-dimensional Melnikov’s method is newly defined and employed to obtain the analytical chaotic thresholds for the non-autonomous TCG system. Last but not least, an experimental setup is established to verify the theoretical analysis and numerical findings. Thus, a wide range of mechanical engineering and control system applications could use the new proposed TCG system.

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Data availability

These datasets generated during the current study are available from the corresponding authors on reasonable request.

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Funding

This work was supported by the State Key Laboratory of Robotics and System (HIT) (Grant no. SKLRS-2022-KF-19).

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Authors and Affiliations

  1. School of Civil Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Yanwei Han

  2. School of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Zijian Zhang

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  1. Yanwei Han
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  2. Zijian Zhang
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Correspondence to Yanwei Han.

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Han, Y., Zhang, Z. Bifurcation and chaos for a novel model of trigonal centrifugal governor with non-smooth control. Nonlinear Dyn 111, 5249–5268 (2023). https://doi.org/10.1007/s11071-022-08115-w

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