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.
This paper reports damage detection and vibration control of a new smart board designed by mounting piezoelectric fibers with metal cores on the surface of a CFRP composite. Damage to the board is identified on the assumption that the piezoelectric fibers used as sensors and actuators are broken simultaneously at the damaged location. When such damage-induced breakage occurs, the piezoelectric fibers expand and contract between the root and the damaged position on the cantilever beam. Damaged positions are detected by focusing attention on this property. Furthermore, this deterioration of sensors and actuators caused by breaks in the piezoelectric fibers is a consideration in the design of the gain-scheduled controller. First, the length of the piezoelectric fibers is measured to derive a finite-element method (FEM) model of the cantilever beam. If the fiber length is shortened due to a break, there is a decrease not only in actuator performance but also in the sensor output. Thus, peak gain of the FEM model is calculated for the length of every piezoelectric fiber. Damage detection is based on the computed relation between peak gain and the damage position. Furthermore, a reduced-order model that considers only the first mode is derived for the controller design and transformed into a linear fractional transformation (LFT) representation for the gain-scheduled controller design. The position of the damage is the contributing parameter in the variation. Next, the gain-scheduled controller is designed using LFT representation. Finally, the simulation and experimental results of the damage detection and the gain-scheduled control are presented. These results show that our gain-scheduled controller can improve control performance when damage cause a break in the piezoelectric fiber.
This paper addresses the active vibration control of a new smart board designed by mounting piezoelectric fibers with a metal core on the surface of the CFRP composite. These complex fibers function as sensors and actuators in the CFRP board. A finite element model of a cantilever and a reduced order model for controller design were established. The piezoelectric fibers are uneven in the actuator outputs.Therefore, the linear fractional transformation (LFT) is formulated considering the unevenness of the actuator outputs as the perturbation. Next, the controller is designed by using mu synthesis, considering the perturbation and robust stability. The control performance of the proposed method is verified by experiment and demonstrates that piezoelectric fibers can be effectively used in vibration control.