Finite-time boundary control of a one-link Timoshenko arm

This paper addresses the vibration suppression of a flexible arm modeled by a hybrid PDE-ODE model. Flexible arms, known for their speed, efficiency, and safety, are commonly modeled with the Euler–Bernoulli beam. However, this study uses the Timoshenko beam model for improved accuracy, accounting for shear and rotational inertia, making it applicable to more scenarios. A novel finite-time boundary controller is proposed to suppress vibrations within finite time, where the finite-time control is not previously proposed for the Timoshenko arm modeled by the hybrid PDE-ODE model. In particular, the proposed controller simplifies implementation by utilizing boundary sensing and actuation. The paper proves the finite-time stability of the system and validates the controller through numerical simulations. This work offers a practical and innovative solution for efficient vibration suppression in flexible arms.