Simultaneous quasi-static displacement and force self-sensing of piezoelectric actuators by detecting impedance

This article extends the conventional permittivity change based displacement self-sensing technique for piezoelectric actuators to an impedance change based displacement-force self-sensing technique. The presented methodology evaluates changes in capacitance and resistance at an electrical resonance frequency and uses a third order polynomial fit to estimate displacement and force. Experimental validations show a mean error of 1.8%, and an error standard deviation of 1.9% for displacement and a mean error of 1.7%, and an error standard deviation of 1.8% for force.