A Polynomial-Based Linear Mapping Strategy for Feedforward Compensation of Hysteresis in Piezoelectric Actuators

A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis response of piezoelectric actuators. These properties, namely, targeting turning points, curve alignment, and wiping-out effect, are applied in a linear mapping strategy to develop a mathematical framework for modeling the hysteresis phenomenon. More specifically, the locations of turning points are detected and recorded for the prediction of future hysteresis trajectory. An internal trajectory is assumed to follow a multiple-segmented path via a continuous connection of several curves passing through every two consequent turning points. These curves adopt their shapes via a linear mapping strategy from the reference hysteresis curves with polynomial configurations. Experimental implementation of the proposed method demonstrates slight improvement over the widely used Prandtl–Ishlinskii hysteresis operator. However, to maintain the level of precision during the operation, a sufficient number of memory units must be included to record the turning points. Otherwise, in the event of memory saturation, two memory-allocation modes, namely, “open” and “closed” strategies, can be implemented. It is shown that the closed memory-allocation strategy demonstrates better performance by keeping the most important target points. The proposed modeling framework is adopted in an inverse model-based control scheme for feedforward compensation of hysteresis nonlinearity. The controller is experimentally implemented on a three-dimensional nanopositioning stage for surface topography tracking, a problem typically encountered in scanning probe microscopy applications.