针对压电微定位台固有的率相关迟滞非线性严重限制其微定位精度的问题, 研究了基于Backlash-Like的Hammerstein率相关迟滞非线性模型及其建模方法。以改进的Backlash-Like分段辨识模型描述压电微定位台的静态非线性特性, 结合ARX(Auto Regressive eXogenous)模型, 建立描述压电微定位台的率相关动态迟滞模型。同时, 针对传统的粒子群算法(Particle Swarm Optimization, PSO)进行模型参数辨识时易陷入局部最优的问题, 提出一种具有交叉变异策略的改进型粒子群算法进行模型的参数辨识。实验结果表明: 与传统的Backlash-Like模型相比, 改进的Backlash-Like分段辨识模型在输入电压为60 V, 频率为2 Hz的信号时, 模型辨识的最大误差由0.68 μm下降到了0.104 μm, 最大相对误差由2.69%下降为0.35%。当压电微定位台输入电压为60 V, 频率分别为30 Hz, 60 Hz和90 Hz的单频信号时, Hammerstein率相关迟滞模型较Backlash-Like分段辨识模型, 均方根误差由0.393 1~0.700 6 μm下降至0.054 1~0.190 4 μm, 相对误差由1.721%~3.087%下降至0.236%~0.831%。验证了基于改进Backlash-Like的Hammerstein率相关迟滞模型较传统的Backlash-Like静态迟滞模型能精确地描述压电微定位台的率相关动态迟滞特性, 具有较好的频率泛化能力, 提高了压电微定位平台的定位精度。

The inherent rate-dependent hysteresis non-linearity of a piezoelectric micro-positioning station seriously limits its micro-positioning accuracy. To solve this problem, the Hammerstein rate-dependent hysteresis nonlinear model based on Backlash-Like hysteresis and its modeling method were investigated in this study. An improved Backlash-Like piece-wise identification model was first utilized to describe the static nonlinear characteristics of the piezoelectric micro-positioning station. Combined with the Auto Regressive eXogenous(ARX) model, a rate-dependent dynamic hysteresis model was then established to describe the piezoelectric micro-positioning station. In addition, to solve the problem in which the traditional Particle Swarm Optimization (PSO) method easily falls into a local optimum, an improved PSO method using a cross-mutation strategy was proposed to identify the parameters of the model. The experimental results show that, compared to the traditional Backlash-Like model, the maximum error of model identification is reduced from 0.68 μm to 0.104 μm and the maximum relative error is reduced from 2.69% to 0.35% when the input voltage is 60 V and the voltage frequency is a single-frequency signal of 2 Hz. In addition, when the input voltage of the piezoelectric micro-positioning station is 60 V and the voltage frequency is a single-frequency signal of 30, 60, and 90 Hz, as compared with the Backlash-Like piece-wise identification model, the root mean square error of the Hammerstein rate-dependent hysteresis model decrease from 0.338 7-0.700 6 to 0.035 1-0.190 4, and the relative error decrease from 1.478%-3.087% to 0.153%-0.831%. It was verified that the rate-dependent hysteresis model based on the improved Backlash-Like model could more accurately describe the rate-dependent dynamic hysteresis characteristics of a piezoelectric micro-positioning station as compared with the traditional Backlash-Like static hysteresis model. In addition, the model showed better frequency generalization, and the positioning accuracy of the piezoelectric micro-positioning platform was improved.