Adaptive positive position feedback for multi-modal vibration control of a flexible beam

The multi-modal vibration control of flexible structures is recognised as a significant challenge owing to the well-known phenomenon of spillover and frequency varying. Spillover phenomenon and variation in the modal dynamics may cause instability and degradation in performance. To overcome these defects, an adaptive positive position feedback (PPF) method is proposed for controlling the vibration of a flexible beam with bonded piezoelectric sensors and actuators. Finite element method is used for dynamic modelling of an experimental flexible beam. An online adaptive parameter estimator based on the gradient algorithm with parameter projection and a dead zone is presented to identify the modal frequencies in the presence of disturbances. Multi-modal PPF controller is adjusted with estimated frequencies and is able to damp the target modes quickly. Simulation results show that modal frequencies are estimated quite accurately and the vibration of the structure is significantly suppressed.