3. Design of Piezoelectric Actuators with Guaranteed Performances Using the Performances Inclusion Theorem

This chapter presents the design of piezoelectric actuators by using the performances inclusion theorem (PIT). The main objective is to seek for the dimensions of a cantilevered actuator such that its performances will lie within some specifications imposed a priori. For that, these specifications are transcribed into an interval transfer function, called interval reference model, while an interval model of the actuator is also provided. Then, from the PIT, a problem of finding the dimensions is yielded such that this latter model is enclosed in the reference model. The problem is seen as a set-inversion problem that can be solved with interval tools such as the SIVIA (Set Inversion Via Interval Analysis) algorithms. The designed piezoelectric actuator is afterwards fabricated and characterized. The experimental characterizations demonstrate the efficiency of the proposed technique.