High performance motion trajectory tracking can be achieved on a piezoelectric stack actuator stage by the combination of a new hysteresis model, judicious modeling of the dominant dynamics, and adaptive robust control design.
A new hysteresis model for piezoelectric actuators is proposed. Inspired by the similarity between pre-sliding friction and piezoelectric hysteresis, the Dahl friction model is extended with non-local memory to model piezoelectric hysteresis. Asymmetry in hysteresis loops is accommodated with a shaping function, which eliminates the need for having different parameters for different branches of the hysteresis loops. All parameters of the hysteresis model can be identified from the outer-loop alone, and the identified model reduces hysteresis nonlinearity from 14 percent of the actuator range to less than 1 percent.
A low-order dynamic model is developed by recognizing the domain switching dynamics of the actuator as the dominant dynamics when the resonant frequency of the stage is far beyond the application bandwidth. The piezoelectric dynamics is well approximated by a feed-through gain and a first-order nonlinear dynamics driven by the input with hysteretic disturbances.
Based on the parameterized model, an adaptive robust controller is designed to achieve (a) guaranteed transient error under the assumption of bounded uncertainties and disturbances; and (b) asymptotic tracking in the presence of parametric uncertainties only. Good tracking performance is achieved for large amplitude trajectories up to 100 Hz even when the hysteresis is entirely attenuated as an unknown disturbance. With additional model compensation from the hysteresis model, the final tracking errors are more than two orders of magnitude smaller than previously reported in literature on an identical actuator.
For single-loop periodic trajectories, performance can be improved without using an explicit hysteresis model. By approximating the unknown but periodic uncertainty with harmonic basis functions and adapting their amplitudes online, non-parametric uncertainty from unknown hysteresis is significantly reduced. Experimental results demonstrate tracking error down to the sensor noise level for sinusoidal trajectories up to 100 Hz with moderate amplitudes and less than one percent for large amplitudes.
|Commitee:||Hu, Jianghai, Meckl, Peter H., Raman, Arvind|
|School Location:||United States -- Indiana|
|Source:||DAI-B 76/02(E), Dissertation Abstracts International|
|Keywords:||Adaptive control, Dahl friction model, Hysteresis, Piezoelectric actuator, Repetitive control, Robust control|
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