On the dynamics of piezoactuated positioning systems

Piezoelectric actuators (PEAs) are commercially available for producing extremely small displacements. If a PEA is used to drive a positioning mechanism, the combined dynamics is approximated empirically by that of a second-order system. However, the rationale for such an approximation is lacking in the literature, thus leaving some issues unaddressed, such as the scope of and the error associated with the approximation. This paper presents such a rationale for the second-order approximation and a method to quantify the error associated with the approximation, by employing the assumed mode method to solve the governing equation. For the experimental verification, step voltages of 48.2, 64.2, and 75.4 V were used to excite a prototype of the positioning system with a mass ratio of 24.7, 47.7, 87.5, 115.8, and 138.8, respectively; and the measured system step responses were compared to the ones simulated by using the second-order approximation. Also, it is illustrated that the error associated with the approximation can be well characterized and quantified by using the developed method.