In this paper, a detailed review on the dynamics of axially moving systems is presented. Over the past 60 years, vibration control of axially moving systems has attracted considerable attention owing to the board applications including continuous material processing, roll-to-roll systems, flexible electronics, etc. Depending on the system’s flexibility and geometric parameters, axially moving systems can be categorized into four models: String, beam, belt, and plate models. We first derive a total of 33 partial differential equation (PDE) models for axially moving systems appearing in various fields. The methods to approximate the PDEs to ordinary differential equations (ODEs) are discussed; then, approximated ODE models are summarized. Also, the techniques (analytical, numerical) to solve both the PDE and ODE models are presented. The dynamic analyses including the divergence and flutter instabilities, bifurcation, and chaos are outlined. Lastly, future research directions to enhance the technologies in this field are also proposed. Considering that a continuous manufacturing process of composite and layered materials is more demanding recently, this paper will provide a guideline to select a proper mathematical model and to analyze the dynamics of the process in advance.
In this paper, a neural network-based robust anti-sway control is proposed for a crane system transporting an underwater object. A dynamic model of the crane system is developed by incorporating hoisting dynamics, hydrodynamic forces, and external disturbances. Considering the various uncertain factors that interfere with accurate payload positioning in water, neural networks are designed to compensate for unknown parameters and unmodeled dynamics in the formulated problem. The neural network-based estimators are embedded in the anti-sway control algorithm, which improves the control performance against uncertainties. A sliding mode control with an exponential reaching law is developed to suppress the sway motions during underwater transportation. The asymptotic stability of the sliding manifold is proved via Lyapunov analysis. The embedded estimator prevents the conservative gain selection of the sliding mode control, thus reducing the chattering phenomena. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.
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