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

Abstract

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.

Modeling of Hysteresis in Piezoelectric Actuator Based on Segment Similarity

“…In fact, hysteresis responses follow certain laws relying on the inherent characteristics of the piezoelectric materials. Some properties of hysteresis in PZA can be seen via experiments and have been proposed and validated in previous studies [6,[16][17][18]. In this section, these properties are presented and explained in the following subsections.…”

“…The hysteresis nonlinear relationship between input signal and output displacement is a memory effect of PZAs, which depends not only on the instantaneousness of the input but also the history of its operation [6,16,17]. Although the hysteresis trajectories are complicated, they are not random.…”

“…[18], the curve of output displacement is closed between two consecutive turning points, 1(3) and 2. It should be noted that all the descending trajectories originated from the first ascending curve that originate from initial state do not target the initial point but converge to a single point on the third region of the hysteresis plane [17]. …”

“…Bashash and Jalili disclose and demonstrate the underlying intellectual behavior of hysteresis. Based on this, several memory-based constitutive mathematical modeling frameworks have been developed [6,16,17].However, the calculation is bulky. Nguyen and Choi [18] store two discretized first-order datasets of ascending and descending curves in advance and then use congruency property to get high-order hysteretic curves.…”

Study on the Time-Scale Similarity of Bouc-Wen Hysteresis Model

“…Besides, several approaches for modeling the hysteresis based on empirical observations have been developed [5][6][7]. But these empirical models are not rate-dependent and the memory-based hysteresis model still needed many memory units.…”