Dual-stage repetitive control with Prandtl–Ishlinskii hysteresis inversion for piezo-based nanopositioning

The positioning performance of piezo-based nanopositioning systems is limited by dynamic and hysteresis effects in the piezoactuator. Herein, a high-performance, dual-stage repetitive controller (dual-RC) with a feedforward hysteresis compensator is proposed for tracking periodic trajectories, such as the scanning-type motion, in nanopositioning systems. Firstly, a discrete-time dual-RC is created by cascading a conventional RC with an odd-harmonic RC. The favorable gain characteristics of the dual-RC coincide with the odd harmonics of the scanning-type periodic reference trajectory, thus offering good robustness and low tracking error. Secondly, a new inverse-hysteresis compensator is developed based on the Prandtl–Ishlinskii hysteresis model. The structure of the inverse model mimics the structure of the forward model, where the parameters of the inverse model can be easily identified from measured input–output data. Finally, the controllers are applied to a custom-designed high-speed nanopositioner, and simulations and experimental results are provided to illustrate the performance improvement of the proposed control scheme compared to industry-standard PID control and conventional RC. High-speed positioning results (tracking of triangle scan trajectories) at rates of 1 kHz, 1.5 kHz, and 2 kHz are shown. Compared to a conventional RC, the tracking error of the dual-RC is 48% lower at 1 kHz and 33% lower at 2 kHz scanning frequency. It is also shown that by compensating for hysteresis, the performance of the RC system designed based on the linear dynamics can be enhanced. 2011 Elsevier Ltd. All rights reserved.