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Angle of Twist: Problem Solving01:13

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Method to Measure Tone of Axial and Proximal Muscle
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A Generalized Supertwisting Algorithm.

Keqi Mei, Shihong Ding, Xinghuo Yu

    IEEE Transactions on Cybernetics
    |August 1, 2022
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    Summary
    This summary is machine-generated.

    A new generalized supertwisting algorithm (GSTA) enhances control system performance by replacing discontinuous terms with fractional powers. This innovation ensures finite-time convergence of sliding variables, outperforming conventional methods.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Robotics

    Background:

    • Conventional Supertwisting Algorithm (STA) limitations in performance.
    • Need for improved convergence properties in sliding mode control.

    Purpose of the Study:

    • Introduce a Generalized Supertwisting Algorithm (GSTA).
    • Develop a constructive design strategy for GSTA.
    • Enhance the performance of conventional STA.

    Main Methods:

    • Replacing the discontinuous term in STA with a fractional power term.
    • Utilizing strict Lyapunov analysis for theoretical verification.
    • Finite-time convergence analysis.

    Main Results:

    • GSTA reduces to conventional STA when fractional power is -1/2.
    • Sliding variables achieve finite-time convergence to an arbitrarily small region.
    • Demonstrated superiority of GSTA through simulation studies.

    Conclusions:

    • GSTA offers fundamental performance improvements over conventional STA.
    • The fractional power term is key to enhanced convergence.
    • The proposed method is rigorously verified and practically demonstrated.