Piezoelectric micro-positioning (PMP) platform has been widely used in the field of high precision tracking and positioning in recent years. However, the PMP platform has inherent hysteresis non-linearity, and this characteristic poses challenges for high-precision positioning applications. In this paper, a Bouc–Wen (BW) model and a linear dynamic model are connected in series to describe the rate-dependent hysteresis characteristic of the PMP platform, and the cross-mutation-based two-population differential evolution algorithm and the recursive least square method are used to identify the unknown parameters. In order to eliminate the hysteresis non-linearity, a model reference adaptive controller based on inverse compensation is designed, then the stability of the controller is proved by Lyapunov theory. Finally, a series of comparative experiments are carried out on the PMP platform. The experiment results prove that the proposed rate-dependent BW model has a stronger ability to describe the hysteretic non-linearity than the classic BW model. Comparing with the inverse compensation-based controller and inverse compensation-based proportion-integration-differentiation controllers, the hysteresis inverse compensation-based model reference adaptive controller has better control performance.

近年来，压电微定位（PMP）平台已广泛用于高精度跟踪和定位领域。但是，PMP平台具有固有的磁滞非线性，这一特性对高精度定位应用提出了挑战。本文通过串联Bouc–Wen（BW）模型和线性动力学模型来描述PMP平台的速率相关磁滞特性，基于交叉变异的两种群差分进化算法和递归最小二乘法用于识别未知参数。为了消除磁滞非线性，设计了一种基于逆向补偿的模型参考自适应控制器，并通过Lyapunov理论证明了该控制器的稳定性。最后，在PMP平台上进行了一系列比较实验。实验结果证明，提出的基于速率的BW模型比经典的BW模型具有更大的描述滞后非线性的能力。与基于逆补偿的控制器和基于逆补偿的比例积分微分控制器相比，基于磁滞逆补偿的模型参考自适应控制器具有更好的控制性能。