Matched piezoelectric double sensor/actuator pairs for beam motion control

This paper presents a study of an arrangement consisting of two matched pairs of piezoelectric transducers bonded on a cantilever beam for vibration control. A single pair of transducers when used as a matched actuator and sensor in practice, is known not to have a strictly positive real (SPR) response due to coupling between in-plane motion and out-of-plane motion. The stability and performance of the matched single pair are thus limited when direct velocity feedback control is applied. An arrangement using four piezoelectric transducer layers arranged as two matched pairs has been suggested to overcome this problem. Theoretically, when the actuator pair and the sensor pair are connected out-of-phase, the response becomes SPR since in-plane motion cannot be excited. A smart beam with matched double piezoelectric sensor/actuator pairs has been implemented. Triangularly shaped sensors and actuators were bonded on each side of the beam. However, this matched double sensor/actuator pair could not excite pure out-of-plane flexural motion of the beam, due to the direct inter-layer coupling between the sensor and actuator which were bonded directly on to each other. Therefore, the four-layer smart beam does not provide an SPR response.