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    This study addresses flexible crane arm control challenges, including deformation and attitude tracking, by developing novel controllers. The proposed method ensures system stability despite input nonlinearities and output constraints.

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    Area of Science:

    • Robotics and Control Systems
    • Mechanical Engineering
    • Applied Mathematics

    Background:

    • Flexible crane arms present significant control challenges due to inherent nonlinearities and external constraints.
    • Modeling inaccuracies and complex dynamics, such as input backlash-saturation and output asymmetrical constraints, hinder precise deformation reduction and attitude tracking.
    • Existing control strategies often struggle to simultaneously address these multifaceted issues effectively.

    Purpose of the Study:

    • To develop a robust control strategy for deformation reduction and attitude tracking of a rotated and extended flexible crane arm.
    • To effectively handle input backlash-saturation and output asymmetrical constraints.
    • To ensure system stability and boundedness under modeling uncertainties.

    Main Methods:

    • Formulation of the flexible crane arm system model using Hamilton's principle, resulting in partial and ordinary differential equations.
    • Application of radial neural networks (RNNs) to approximate uncertain system parameters.
    • Utilization of the backstepping technique for controller design, combined with a barrier Lyapunov function (BLF) to manage output constraints and ensure stability.

    Main Results:

    • The proposed control strategy successfully reduces deformation and achieves attitude tracking for the flexible crane arm.
    • The controller effectively compensates for input nonlinearities (backlash-saturation) and adheres to output asymmetrical constraints.
    • Uniformly ultimate boundedness and stability of the arm system are rigorously proved using a logarithmic barrier Lyapunov function.

    Conclusions:

    • The developed control approach, integrating RNNs and backstepping with BLF, provides an effective solution for complex flexible crane arm systems.
    • Numerical simulations confirm the controller's efficacy in managing nonlinearities and constraints, demonstrating superior performance.
    • This research contributes a robust framework for controlling flexible robotic systems with challenging operational conditions.