Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Piezo actuators are used in high-precision systems that require nanometer accuracy. In this paper, we consider a nano-motion stage driven by a walking piezo actuator, which contains four bimorph piezo legs. We propose a (model-based) optimization method to derive waveforms that result in optimal driving properties of the walking piezo motor. A model of the stage and motor is developed incorporating the switching behavior of the drive legs, the contact deformation, and stick-slip effects between the legs and the stage. The friction-based driving principle of the motor is modeled using a set-valued friction model, resulting in a model in terms of differential-algebraic inclusions. For this model, we developed a dedicated numerical time-stepping solver. Experiments show a good model accuracy in both the drive direction and the perpendicular direction. The validated model is used in an optimization, resulting in waveforms with optimal driving properties of the stage at constant velocity. Besides the model-based optimization, also a direct experimental data-based waveform optimization is performed. Experiments with the optimized waveforms show that compared to existing sinusoidal and asymmetric waveforms in literature the driving properties can be significantly improved by the model-based waveforms and even further by the data-based waveforms.