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.

压电致动器（PAs）越来越多地用于要求在微米和纳米级上进行高速且精确定位的工业和研究应用中，例如原子力显微镜。这是由于它们的高定位分辨率，紧凑性和快速响应性。但是，有两个主要因素会严重限制其性能，即磁滞和结构共振。为了克服这些限制，同时避免使用基于反演的前馈补偿器，我们提出了一种用于高速放大PA（APA）轨迹跟踪的新型学习控制器。为了进一步增强APA抵抗传感器噪声和其他干扰的鲁棒性，在反馈回路中添加了一个简单的比例积分（PI）控制器。所提出的反馈-前馈控制器可以补偿上述现象，而无需访问APA的“复杂”数学模型。使用系统无源性和有限增益稳定性的概念，我们证明了闭环系统是稳定的，并且跟踪误差对于连续参考输入是有界的。这些结果通过使用具有变化频率的正弦参考输入在实验上得到证实。控制器能够以相对较小的跟踪误差跟踪频率高达500 Hz（非常接近APA的谐振频率）的参考信号。为了进一步评估建议的控制器的质量，我们将其跟踪性能与以前建议的控制器进行了比较。我们表明，我们的控制器始终能够实现较小的跟踪误差，并且两个控制器之间的性能差距会随着频率的增加而增加。通过将前馈-反馈控制器的跟踪性能与PI的跟踪性能进行比较，我们最终展示了使用前馈学习控制器的优势。结果显示出明显的性能改进，并且该改进在更高的频率下变得更加明显。