A novel digital charge-based displacement estimator for sensorless control of a grounded-load piezoelectric tube actuator

• A grounded-load digital charge-based displacement estimator (GDCDE) is presented.
• An artificial neural network (ANN) was also designed to estimate the piezoelectric tube's displacement using the piezoelectric voltage at low frequencies of excitation.
• A complementary filter combines the proposed GDCDE and the ANN to estimate displacement over a wide bandwidth and to overcome drift.
• The discrepancy between the desired and estimated displacement is fed back to the piezoelectric actuator using proportional control.

Piezoelectric tube actuators are widely used in nanopositioning applications, especially in scanning probe microscopes to manipulate matter at nanometer scale. Accurate displacement control of these actuators is critical, and in order to avoid the expense and practical limits of highly accurate displacement sensors, sensorless control has recently attracted much attention. As the electrical charge on these actuators is an accurate indicator of their displacement exhibiting almost no hysteresis over a wide range of frequencies, it suggests that charge measurement can replace displacement sensors. However, charge-based methods suffer from poor low frequency response and voltage drop across the sensing capacitor. In this paper, a displacement estimator is presented that complements a digitally implemented charge amplifier with an artificial neural network (ANN) designed and trained to estimate the piezoelectric tube's displacement using the piezoelectric voltage at low frequencies of excitation where the charge methods fail. A complementary filter combines the grounded-load digital charge amplifier (GDCDE) and the ANN to estimate displacement over a wide bandwidth and to overcome drift. The discrepancy between the desired and estimated displacement is fed back to the piezoelectric actuator using proportional control. Experimental results highlight the effectiveness of the proposed design.