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    This study proposes novel saturated controllers to ensure global asymptotic stability for uncertain multiple integrators with nonlinear perturbations. The controllers enhance system robustness by maintaining convergence domains and achieving large saturation levels.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Robotics and Automation

    Background:

    • Multiple integrator systems are fundamental in control theory but challenging due to uncertain parameters and nonlinear perturbations.
    • Ensuring global asymptotic stability under these conditions requires advanced control strategies that can handle parameter variations and nonlinearities.

    Purpose of the Study:

    • To address the global asymptotic stability problem for multiple integrators with uncertain parameters and high-order nonlinear perturbations.
    • To develop and analyze novel modified nested saturated controllers capable of managing these complex system dynamics.

    Main Methods:

    • Introduction of a modified saturation function with tunable positive parameters.
    • Design and comprehensive analysis of three types of modified nested saturated controllers with distinct parameter assignments.
    • Utilizing derivatives calculation and M-matrix-based comparison theory for control scheme validation.

    Main Results:

    • Demonstrated that the proposed controllers maintain an invariable global convergence domain for each state, even with saturation.
    • Achieved a large saturation level by effectively adjusting the positive tunable parameters.
    • Verified the feasibility and effectiveness of the proposed control designs through simulations on an active magnetic bearing (AMB) system.

    Conclusions:

    • The developed modified nested saturated controllers effectively guarantee global asymptotic stability for uncertain multiple integrators with high-order nonlinear perturbations.
    • The controller design offers robustness and adaptability, crucial for real-world applications like active magnetic bearing systems.