Robust Boundary Vibration Control of Uncertain Flexible Robot Manipulator with Spatiotemporally-varying Disturbance and
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
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 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 spatiotemporallyvarying 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. Keywords: Distributed parameter system, Euler-Bernoulli beam, global sliding-mode boundary control (GSMBC), method of lines (MOL), partial differential equation (PDE), vibration control.
1.
INTRODUCTION
Distributed parameter systems (DPSs) are widely used in a many engineering fields such as drill ropes, moving strips, and marine risers [1–4]. The Euler-Bernoulli beam is a DPS which is composed of one non-homogenous hyperbolic partial differential equation (PDE) and four ordinary differential equations (ODEs). By considering the unknown disturbances and uncertainties of the EulerBernoulli beam, the dynamic solution and control design of such system are become difficult. Thus, it is becoming more challenge and received more attention [4–7]. Global sliding-mode control (GSMC) has a dynamic sliding surface formula containing both linear sliding surface and nonlinear exponential decay functions. These functions have benefits in robustness alongside the system uncertainties and unknown disturbances. The shortcomings of the sliding-mode control (SMC) are overcome
in GSMC by eliminate the attaining motion phase and then assurances that the whole system performance is robust [8]. GSMC plays a spirited role in lumped parameter system (LPS), including nonlinear systems [9], uncertain nonlinear system, linear time delay system [10], and the hypersonic slide automobile [11]. For the sake of LPS, GSMC is widely used for t
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