Boundary control of flexible beams

Abstract

The vibration control of flexible beams is an important problem in engineering applications. Many studies have proposed that the vibration control of these beams; however, the implementation methods in practical applications are few. This dissertation investigates passivity-based boundary control for vibration suppression of flexible beams. This method incorporated an energy principle in the design, rather than a signal processing perspective. An undamped shear beam was used as a beam model, and the controller was implemented through a moving base. The storage function was defined and used to determine the control law in the design process. The finite-gain L2 - stability of the controlled system was then proven. This technique treated the beam model PDE directly without model reduction, so control spillover was avoidable. Since the measurement and actuation in the application were non-collocated, a backstepping observer was needed for the state estimation. The controller was applied at the end of the beam via a moving base, so the beam domain was intact. This technique is readily implementable in applications. The PDE model was solved numerically using the finite-difference method. The computer simulation was used to demonstrate the performance of the controllers under the proposed control scheme. The beam vibration was suppressed satisfactorily with L2 - stability.

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