Keywords: piezoelectric actuator and sensor networks, active control, dynamic shape control.

In the present paper we study the active control of continuous structures using piezoelectric actuators and sensor networks. As a starting point the method of dynamic shape control is shortly reviewed. In this method one seeks for a continuously distributed strain induced actuation, which exactly compensates the force induced vibrations of a structure. Given the spatial distribution and the time variation of the external forces, the continuous strain induced actuation can be computed from a convolution integral formulation. In the case where the time variation is not known, a collocated distributed strain-type sensing is computed and feedback control is implemented. In most practical applications a continuous distribution of the actuation is not feasible. More likely, one has to work with a network of strain induced actuators with a constant intensity within their domain. In the latter case, we assume the time variations applied to the individual members of the network to be identical. The distributed nature of such an actuation is then achieved through proper placement and weight assignment to the network members.

In the second part of the paper, we develop a method for the design of strain induced actuator networks as well as for collocated strain-type sensor networks. In the first step, we assume the time variation of the previously computed continuous strain induced actuation to be applied impulsively; likewise, the time variation of the actuator network is also applied impulsively. For this latter case, we show that the problem of computing locations and weights for the actuator network members reduces to the problem of computing weights for the collocated sensor network. We solve the latter sensor network problem by applying a method we have previously developed for the design of dense strain-type sensor networks. As an outcome we find locations and weights for the individual members of both, the sensor and actuator networks, because the two networks are collocated. The computation of the time variation for the actuator network remains. In the case of the time variation of the external forces, the disturbance, is known, we apply a feedforward control; in contrast, a feedback control is implemented for an unknown disturbance.

Finally, a cantilever beam under a tip force excitation is studied. In particular, we use collocated piezoelectric actuator and sensor networks to implement our method. It is shown that it is of utmost importance to ensure the sensor signal accurately measures the entity to be controlled, because the effectiveness of control strongly depends on this accuracy.

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