迟滞与蠕变耦合压电系统的建模及补偿方法

Modeling and compensation method of hysteresis-creep coupled piezoelectric system

为了准确地描述压电驱动定位平台复杂的非线性特性,在经典Hammerstein结构模型基础上串联分数阶算子,提出了一种耦合迟滞、动力学和蠕变的非线性数学模型。其中该模型的蠕变、迟滞非线性特性分别采用分数阶算子和PI模型来描述;机械动力学特性使用二阶离散传递函数表示。此外,考虑了耦合模型的参数辨识问题,并通过压电驱动定位试验平台对所提耦合模型进行了验证。在1~100 Hz的正弦波输入电压信号作用下,与不考虑蠕变特性的Hammerstein结构模型相比,该耦合模型在均方根误差指标降低了27%以上,相对误差指标下降了约50%。该试验结果充分表明了所提耦合模型的有效性。在模型建立的基础上设计了逆蠕变和迟滞模型对系统进行前馈补偿,并结合PID控制算法对系统的性能进行调节。仿真结果验证了该复合控制方案在低频和混合频率输入信号下具有良好的跟踪效果。

Here,to correcdy describe complex nonlinear characteristics of a piezoelectric driven positioning platform,a hysteresis-creep coupled nonlinear dynamic model based on the classical Hammerstein structure model series fractional order operator was proposed.Nonlinear characteristics of creep and hysteresis were described with fractional order operator and PI model,respectively.Mechanical dynamic characteristics of the model were expressed with a second-order discrete transfer function.In addition,parametric identification of the coupled model was considered,and the coupled model proposed here was verified with a piezoelectric driven positioning test platform.The results showed that under the action of sine wave input voltage signal of 1-100 Hz,compared with Hammerstein structure model not considering creep characteristics,the RMS error index of the coupled model proposed here decreases by more than 27%,and the relative error index decreases by about 50%,so the effectiveness of the coupled model proposed here is fully verified.Finally,based on the proposed model,reverse creep and hysteresis models were designed to do feedforward compensation for the system,and the PID control algorithm was used to adjust system performance.The simulation results showed that this composite control scheme has good tracking effect under low frequency and mixed frequency input signals.