Vibration Control of a Flexible Beam

An Euler–Bernoulli beam [1–3] is a model that can be used to describe many mechanical flexible systems such as flexible robotic manipulator [4], flexible spacecraft [5], flexible marine riser [6] and moving strip [7]. These physical processes, cannot be modeled by ODEs since the state of the system depends on more than one independent variable [8]. In practice, most of the flexible systems exhibit vibration in the presence of disturbances. Since vibration has been known to reduce the system quality, lead to limited productivity and result in premature fatigue failure, vibration suppression of the beam-like structure has broad applications and has received great attention in the recent years. The chapter is motivated by the industrial applications in boundary control of vibrating flexible structures. Examples of practical applications where vibrating beams are exposed to undesirable spatiotemporally varying disturbances include flexible production risers used for offshore oil transportation, free hanging underwater pipelines, and drilling pipe for drilling mud transportation. The unknown spatiotemporally varying disturbances of the beam lead to the appearance of oscillations, which make the control problems of such systems relatively difficult.