Feedback-feedforward control for high-speed trajectory tracking of an amplified piezoelectric actuator

Piezoelectric actuators (PAs) are increasingly used in industrial and research applications requiring high speed and accurate positioning at the micro and nano scales such as atomic force microscopy. This is due to their high positioning resolution, compactness, and fast response. There are, however, two main factors that significantly limit their performance, namely hysteresis and the structural resonance. To overcome these limitations, while avoiding using inversion-based feedforward compensators, we propose, a new learning controller for high speed amplified PA (APA) trajectory tracking. To further enhance the robustness of the APA against sensor noise and other disturbances, a simple proportional and integral (PI) controller is added in the feedback loop. The proposed feedback-feedforward controller compensates for the above-mentioned phenomena without requiring access to the 'complex' mathematical model of the APA. Using the notions of system passivity and finite gain stability, we show that the closed-loop system is stable, and the tracking error is bounded for continuous reference inputs. These results are experimentally confirmed using a sinusoidal reference input with varying frequencies. The controller is able to track reference signals with frequencies up to 500 Hz (very close to the resonance frequency of the APA) with relatively small tracking errors. To further assess the quality of the proposed controller, we compare its tracking performance against a previously proposed controller. We show that our controller consistently achieves smaller tracking errors and the performance gap between the two controllers increases with an increase in frequency. We finally show the advantage of using the feedforward learning controller by comparing the tracking performance of our feedforward-feedback controller against that of the PI. The results show a clear performance improvement and that this improvement becomes even more evident at higher frequencies.