Simultaneous Displacement and Force Estimation of Piezoelectric Stack Actuators Using Charge and Voltage Measurements

Abstract

This article is devoted to simultaneous displacement and force self-sensing using a single piezoelectric stack actuator. Values of displacement and force are estimated from measurements of charge and applied voltage. To calibrate the self-sensing algorithm, a parameter identification procedure is presented that accounts for hysteresis under varying displacement and force conditions using a standard Prandtl–Ishlinskii hysteresis operator. Quasi-static validation experiments are carried out on a custom-built test rig that shows low average estimation errors of $0.5 \%$ and $-0.4\%$ with standard deviations of $2.7\%$ and $3.1\%$ in displacement and force, respectively.