Dynamic H∞ Feedback Boundary Control for a Class of Parabolic Systems with a Spatially Varying Diffusivity

Zhou, Yanjiu; Cui, Baotong; Lou, Xuyang

doi:10.1007/s12555-019-0926-3

Cited by 6 publications

(1 citation statement)

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“…The control problem of distributed parameter systems, whose dynamics is described by PDEs, has been investigated in the literature 16 – 21 . Boundary control technique, wherein the control input is exerted to the PDE through its boundary conditions 22 – 25 , is a powerful tool for handling these systems. Contrary to the stationary beam, the vibration of the cantilever beam with a moving base can be suppressed via the control input applied at the base (i.e., the clamped end of the beam) or the beam’s tip.…”

Section: Introductionmentioning

confidence: 99%

Vibration control of a nonlinear cantilever beam operating in the 3D space

Pham

Nguyen

Yoon³

et al. 2022

Sci Rep

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This paper addresses a control problem of a nonlinear cantilever beam with translating base in the three-dimensional space, wherein the coupled nonlinear dynamics of the transverse, lateral, and longitudinal vibrations of the beam and the base’s motions are considered. The control scheme employs two control inputs applied to the beam’s base to control the base’s position while simultaneously suppressing the beam’s transverse, lateral, and longitudinal vibrations. According to the Hamilton principle, a hybrid model describing the nonlinear coupling dynamics of the beam and the base is established: This model consists of three partial differential equations representing the beam’s dynamics and two ordinary differential equations representing the base’s dynamics. Subsequently, the control laws are designed to move the base to the desired position and attenuate the beam’s vibrations in all three directions. The asymptotic stability of the closed-loop system is proven via the Lyapunov method. Finally, the effectiveness of the designed control scheme is illustrated via the simulation results.

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