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

• Published in: International journal of control, automation, and systems Vol. 19; no. 2; pp. 788 - 798
• Main Authors: Eshag, Mohamed Ahmed, Ma, Lei, Sun, Yongkui, Zhang, Kai
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.02.2021; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Boundary control; Control; Engineering; Euler-Bernoulli beams; Feedback control; Mechatronics; Method of lines; Ordinary differential equations; Parameter uncertainty; Partial differential equations; Perturbation; Regular Papers; Robot arms; Robot control; Robotics; Robust control; Vibration control; 제어계측공학; method of lines (MOL); partial differential equation (PDE); Distributed parameter system; global sliding-mode boundary control (GSMBC); vibration control; Euler-Bernoulli beam
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0070-0

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 non-homogenous 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.