Optimal Design of Piezoelectric Cantilevered Actuators With Guaranteed Performances by Using Interval Techniques

Piezoelectric materials are well recognized for the development of systems and actuators working at the micro/nano-scale such as microsystems. This recognition is thanks to the high resolution, high bandwidth, and high force density that they can offer. However, piezoelectric actuators are typified by low range of displacement relative to other actuators like magnetic or thermal actuators. To obtain the sufficient range of displacement with a piezoelectric actuator, either we use high input voltages or we redesign the actuator to have larger dimensions. The former solution may lead to the destruction of the actuators and the latter is not congruent with the objectives of microsystems where the dimensions should be miniaturized. Furthermore, increasing the dimensions of the actuators reduces their rapidity and bandwidth. This paper proposes an approach based on interval analysis to design piezoelectric actuators with cantilever structures. The aim consists in reducing their dimensions while still satisfying some specified performances in term of output range and in term of resonant frequency (and thus bandwidth). The problem of the design is formulated as a set-inversion problem which can be solved using interval techniques. The obtained results, validated with prototype fabrication and experimental characterization, demonstrate the efficiency and the interests of the proposed method for designing systems and actuators working at the micro/nano-scale in general.