Gain-scheduled control of a smart beam with identification of a crack

Kiyoshi Takagi; Muneharu Saigo

doi:10.1117/12.658385

27 March 2006 Gain-scheduled control of a smart beam with identification of a crack

Kiyoshi Takagi, Muneharu Saigo

Proceedings Volume 6166, Smart Structures and Materials 2006: Modeling, Signal Processing, and Control; 61661A (2006) https://doi.org/10.1117/12.658385
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2006, San Diego, California, United States

Abstract

This study deals with damage detection and vibration control of a smart beam and proposes a method for crack identification when the vibration of the beam is suppressed using active control. A finite-element model of a cracked beam is established by applying fracture mechanics methods. This model is applied to a cantilever beam, and the natural frequencies are determined for different crack lengths and locations. First, the crack length and locations are identified by using the relationship between the crack and the natural frequency of the beam. However, the crack length and locations are difficult to identify when the vibration is suppressed by active control, because the natural frequency is obtained by fast Fourier transform (FFT) of the vibration data. This study proposes a crack identification algorithm under vibration control where crack detection is repeated more than once. Furthermore, the gain-scheduled controller design considers both the crack length and the location. Once cracks are present in structures, control performance becomes worse because both the eigenvalue and eigenvector of the beam vary. A linear parameter-varying (LPV) model considering the crack length and locations is developed for the gain-scheduled controller design. To obtain the LPV model, the discrepancy between the state-space representations of the reduced-order model and the LPV model is measured by its Frobenius norm. This norm is minimized by simultaneously optimizing the coefficient functions and the state-space representations contained in the model. The efficiencies of this crack identification method and the gain-scheduled controller design are verified by simulation and experiment.

Citation Download Citation

Kiyoshi Takagi and Muneharu Saigo "Gain-scheduled control of a smart beam with identification of a crack", Proc. SPIE 6166, Smart Structures and Materials 2006: Modeling, Signal Processing, and Control, 61661A (27 March 2006); https://doi.org/10.1117/12.658385

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KEYWORDS

Vibration control

Finite element methods

Sensors

Actuators

Damage detection

Matrices

Transducers

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