Precise, Long-Time Displacement Self-Sensing of Piezoelectric Cantilever Actuators Based on Charge Measurement Using the Sawyer–Tower Circuit

Previous studies show that near linearity exists between displacement and charge of piezoelectric actuators, while studies under higher fields are lacking and long-time displacement self-sensing is still a challenge. Here we indicate that precise, long-time displacement self-sensing can be accomplished using the Sawyer–Tower circuit, where a high-impedance electrometer and a non-leaky capacitor are used to measure the charge. Calibrating the results on a piezoelectric unimorph cantilever shows that the displacement resolution of charge self-sensing is \sim3 nm, much better than that of \sim40 nm for the calibrating laser sensor. Testing results under a unipolar field up to 2 kV/mm with different periods indicate that a direct proportional relationship holds between charge and displacement with the maximum error of 4.65%. The self-sensing time can be over 20 min or even longer if a higher-impedance electrometer is used.