19 April 2008 Limit of feedback gains of collocated sensor and actuator pairs for beams
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This paper presents an approach to define an optimal piezoactuator length to actively control structural vibration. The optimal ratio of the piezoactuator length against beam length when a pair of piezoceramic actuator and accelerometer is used to suppress unwanted vibration with direct velocity feedback (DVFB) control strategy is not clearly defined so far. It is well known that direct velocity feedback (DVFB) control can be very useful when a pair of sensor and actuator is collocated on structures with a high gain and excellent stability. It is considered that three different collocated pairs of piezoelectric actuators (20, 50 and 100 mm) and accelerometers installed on three identical clamped-clamped beams (300 * 20 * 1 mm). The response of each sensor-actuator pair requires strictly positive real (SPR) property to apply a high feedback gain. However the length of the piezoactuator affects SPR property of the sensor-actuator response. Intensive simulation and experiment shows the effect of the actuator length variation is strongly related with the frequency range of SPR property. A shorter actuator gave a wider SPR frequency range as a longer one had a narrower range. The shorter actuator showed limited control performance in spite of a higher gain was applied because the actuation force was relatively small. Thus an optimal length ratio (actuator length/beam length) was suggested to obtain relevant performance with good stability with DVFB strategy. The result of this investigation could give important information in the design of active control system to suppress unwanted vibration of smart structures with piezoelectric actuators and accelerometers.
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Young-Sup Lee, Young-Sup Lee, Sang-Kwon Lee, Sang-Kwon Lee, } "Limit of feedback gains of collocated sensor and actuator pairs for beams", Proc. SPIE 6928, Active and Passive Smart Structures and Integrated Systems 2008, 69282I (19 April 2008); doi: 10.1117/12.782151; https://doi.org/10.1117/12.782151

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