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Robust Boundary Vibration Control of Uncertain Flexible Robot Manipulator with Spatiotemporally-varying Disturbance and Boundary Disturbance

Mohamed Ahmed Eshag, Lei Ma*, Yongkui Sun, and Kai Zhang
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.788-798, 2021

Abstract : In this paper the vibration control problem is addressed for the Euler-Bernoulli beam with system parameters uncertainties, spatiotemporally-varying disturbance, and boundary disturbance. By using global sliding-mode boundary control (GSMBC) through method of lines (MOL), a robust boundary control design is suggested to diminish the perturbations of uncertain Euler-Bernoulli beam and to compensate the influence of the spatiotemporally varying disturbance and boundary disturbance. Dynamics of the Euler-Bernoulli beam are described by nonhomogenous hyperbolic partial differential equation (PDE) and ordinary differential equations (ODEs). MOL is employed to acquire the beam dynamics represented by ODE system in lieu of PDE system, therefore a precise solution is obtained by solving the resulting ODE system. Then, GSMBC is established for mitigating the vibrations of the beam affected by system parameters uncertainties, spatiotemporally-varying disturbance, and boundary disturbance. Chattering phenomena is avoided by using exponential reaching law supported by a relay function. Exponential convergence and stability robustness of the closed-loop system are assured by Lyapunov direct approach. In the end, simulation outcomes show that the GSMBC-based MOL scheme is valid for vanishing the vibrations of the uncertain Euler-Bernoulli beam efficiently.

Keyword : Distributed parameter system, Euler-Bernoulli beam, global sliding-mode boundary control (GSMBC), method of lines (MOL), partial differential equation (PDE), vibration control.

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