Design Impact of Piezoelectric Actuator Nonlinearities

Abstract

Data are presented illustrating the need for inclusion of piezoelectric actuator nonlinearities if accurate system modelsaredesired.Thedescribing function approach wasused inthisinvestigation asanexample.Whereastheuse of the describing functions does improve overall accuracy of the system model, it is demonstrated that the extreme sensitivity ofthedescribing functionstoamplitudeatlowactuatordisplacementsstillcompromiseson theaccuracy of system models that include voltage-controlled piezoelectric actuators. It is also demonstrated that using chargefeedback control with piezoelectricactuators makes the use of the nonlinearmodel elements lesspressing since the charge control describing functions are much nearer unity than their voltage-control counterparts. Nomenclature A = actuator cross-sectional area, m 2 C = capacitance, F c D = stiffness at constant electric displacement, Pa c E = stiffness at constant electric e eld, Pa D = electric displacement, C/m 2 d = piezoelectric constant, m/V E = electric e eld, V/m F = force,N g = piezoelectric constant, m 2 /C Kamp = voltage-feedback amplie er gain, V/V Kas = combined actuator, e exure, and amplie er gain, m/V KD = controller derivative gain, V/V KOL = open-loop system gain, m/V Kp = controller proportional gain, V/V Ksg = strain-gauge position feedback subsystem, V/m k = spring constant, N/m L = moment arm effective length, m m = driven mass, kg N = fundamental frequency representation of system nonlinearities n = number of layers in stack actuator Q = charge,C R = resistance, A S = strain T = stress, Pa t = piezoelectric material thickness, m Va = power amplie er input voltage, V x = displacement, m