Identification of flexible structure model for piezoelectric vibration control

Abstract

Modern structures are light and compliance. Therefore, they are strongly influenced by external and internal perturbations. To reduce the structure vibrations the active vibration controls systems are designed. When active control of flexible structures is sought, three items must be individually and simultaneously considered. 1) The creation of reduced-order models. 2) Placement of sensors and actuators. 3) Countermeasures for spillover. All these problems are particularly important in the case of active system with parameter-distributed piezoelectric sensors and actuators. The glued piezoelectrics and their amplifiers change the structure parameters and should be taken into account in the model of the open-loop system. In the paper we consider an identification method which leads directly to the reduced-order model of the open-loop system. Analytical and experimental investigations were carried out for flexible beam with fixed one end and with opposite free end. Piezoelectric strips were glued on both sides of the beam: one works as a sensor and second one as an actuator. It means that we have designed single input single output system. It is appeared that used amplifier works as a low-pass filter which cuts-off the high-frequency dynamic effects. The frequency response function (FRF) was recorded and model of open-loop system was adjusted to experimental results. Taking into account the theory of reduced-order model of flexible structures we can state that resonances are connected with poles while anti-resonances with zeros of system transfer function. The resonance and anti-resonance frequencies were used directly in the model while damping coefficients were calculated by using of the least-square sum method. In the next step some control laws were used to damp the vibration of the beam. The proper control law was chosen with help of computer simulations. The active control loop rapidly accelerates the vanishing of the impulse-excited transient vibrations of the structure. Experimental results confirmed the analytical considerations. W artykule opisano badania eksperymentalne aktywnego układu tłumienia drgań na przykładzie konstrukcji modelowanej jako belka. Elementem pomiarowym i elementem wykonawczym są wstęgi piezoelektryczne. W wyniku zastosowanej procedury identyfikacyjnej otrzymano model matematyczny układu otwartego. Różni się on w sposób istotny od znanych modeli analitycznych. Zaprojektowano dwa prawa sterowania. Dla jednego z nich zbadano eksperymentalnie działanie aktywnego układu tłumienia drgań. Wykazano, że poprawnie przeprowadzony proces identyfikacji dynamiki obiektu w znakomity sposób upraszcza proces projektowania układu sterowania drganiami.