Boundary control of harmonic disturbances on flexible cantilever beams using piezoelectric patch actuators

Abstract

This work addresses the control of vibrations in flexible structures caused by external harmonic disturbances using a boundary control method. The research is motivated by practical systems where beam-like structures require vibration suppression to prevent fatigue and system damage, or to increase efficiency. Importantly, this paper addresses a practical constraint of the actuation points being at the boundaries only. The method presented here is an open-loop control scheme which requires knowledge of the harmonic disturbance and a model of the flexible system. The controller uses the model, developed using the Rayleigh–Ritz method, to predict the reaction of the beam to the known input disturbance and compute an optimized control input which reduces the steady state vibration in the system. By properly choosing the cost function, the controller can be used to reduce the total vibration or to reduce the vibration in certain spatial locations. The method's vibration reduction capabilities are studied over a range of frequencies; data collected from experiments on a physical beam model is used to validate the predicted behavior of the system.