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

Authors: Zhen Yu; Yu Guo; Li-ping Wu; Wei Yao; Guang-yan Li

Addresses: School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China ' School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China ' School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China ' School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China ' School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

Abstract: 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.

Keywords: smart beams; flexible beams; positive position feedback; PPF; adaptive parameter estimation; multi-modal vibration control; flexible structures; spillover; modal dynamics; instability; performance degradation; piezoelectric sensors; piezoelectric actuators; finite element method; FEM; dynamic modelling; simulation.

DOI: 10.1504/IJMIC.2015.072625

International Journal of Modelling, Identification and Control, 2015 Vol.24 No.3, pp.224 - 234

Received: 11 Apr 2015
Accepted: 11 Apr 2015
Published online: 22 Oct 2015 *

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