A decomposition-based learning approach to hysteresis-dynamics system control: Piezoelectric actuator example

In this paper, a decomposition-based learning approach is developed to the control of smart actuators/sensors with both hysteresis and dynamics effects compensated for. The proposed approach integrates off-line learning and online decomposition-synthesis together. Particularly, the off-line learning exploits advantages of iterative learning control in achieving precision tracking while maintaining good robustness, and the online decomposition-synthesis explores the benefits of uniform B-splines in decomposing arbitrary trajectory with few elements, and an inverse-Preisach-based superimposition approach to extend superimposition to nonlinear hysteresis operator. The proposed approach extends the decomposition based control scheme recently developed for linear time invariant (LTI) system to hysteresis compensation. A Hammerstein model is employed to decouple the hysteresis and the dynamics effect. It is shown that arbitrary tracking precision can be achieved by having enough number of elements in the decomposition, and the compensation factors are optimized to maximize the hysteresis compensation through the mapping of the input-output elements. Experiments conducted on the control of a piezoelectric actuator are presented to illustrate the approach.