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The existence of hysteresis phenomenon in piezoelectric actuators of nanopositioners adversely affects their performance, e.g. image distortion in Atomic Force Microscopy. A usual approach to circumnavigate hysteresis nonlinearity is feedforward compensation where the performance depends extensively on the accuracy of the hysteresis model. To achieve accurate modeling of hysteresis in nanopositioners driven by piezoelectric stacks, we used a dual-stack differential driving configuration. Comparing hysteresis in single-stack piezoelectric actuators with dual-stack piezoelectric actuators in differential driving configuration, we observed a more symmetric behavior for the hysteresis in dual-stack differential driving actuators. Then, we modeled the differential driving configuration by utilizing coupled electromechanical equations with hysteresis models applied to them. In particular, Duhem and Prandtl-Ishlinskii (P–I) methods were used for hysteresis modeling. Based on the models and experimental data, we observed that the maximum value of the Duhem modeling error reduced from 9.63% for the nondifferential configuration to 1.85% for the differential configuration. For the P–I method, the maximum modeling error decreased from 7.46% to 2.77%. This observation shows that the dual-actuated differential driving configuration improves hysteresis modeling accuracy. Therefore, this configuration is a suitable choice for the applications where accuracy is of prime importance.

International audience; The paper deals with the characterization of piezoelectric ceramic type sensors integrated in a compact high-speed 2-DOF nano-positioner to measure large signal stage displacement. Such transducers are very attractive because they provide measurements in a wide frequency bandwidth with low noise, they do not require bulky electronic modules and are cost effective compared to traditional sensors. The transducers are installed in series with piezoelectric actuators and thick ceramic insulators are incorporated between them to reduce the cross-talk. The sensor provides accurate position measurements as long as the nano-positioner displacement is within the sensing bandwidth. This is verified by large amplitude sinusoidal excitations of the nano-positioner along both x and y axes within the sensor bandwidth. The sensor can also measure the displacement in response to a single tone sinusoid at frequencies well above the dominant imaginary zeros of the interaction force, which is beyond the sensor bandwidth. Experimental measurements are compared with those obtained using a LASER interferometer sensor. The results allow obtaining precise calibration factors of the piezoelectric ceramic transducers with respect to the input frequencies and accurate displacement/voltage transfer characteristics for closed loop control purposes.

International audience; We address design, implementation, and characterization of semiconductor strain gauges as stage displacement sensors with small footprint for piezo-driven nanopositioners in differential actuation mode. The strain gauges are not collocated with the stage of the nanopositioner. They are attached to piezo stack actuators in both longitudinal and transverse directions. We address two differential configurations for the displacement sensing. The first configuration uses all strain gauges and provides three output signals. Two of them are proportional to the length variations of the piezo actuators, which are considered as conventional non-differential sensing method. The last output in the first configuration is the first proposed differential sensor. In the second configuration, we propose an alternative differential sensor using only the longitudinal strain gauges and a simpler readout circuit. The results indicate that in the differential actuation mode, a differential sensing strategy provides much better accuracy than the conventional non-differential schemes. Using a laser interferometer as an independent collocated sensor for stage displacement, we obtained constant calibration factors both proposed differential sensors and characterized their sensing accuracies.