为了降低率相关迟滞特性对压电作动器的影响, 研究了基于Hammerstein模型的建模方法和实时跟踪控制策略。以改进的Prandtl-Ishlinskii(MPI)模型表示静态非线性部分, 以外因输入自回归模型(Autoregressive Model with Exogenous Input ARX)表示动态线性部分, 建立了能够描述压电作动器率相关迟滞特性的Hammerstein模型。基于所建Hammerstein模型, 设计了基于前馈自适应逆补偿和PI反馈的复合控制策略。最后, 设计并实现了基于前馈逆补偿和PI反馈的复合控制策略来对比和验证所设计的控制策略的有效性。验证实验显示: 采用文中设计的控制策略实时跟踪100 Hz以内, 幅值为11 μm的单一频率信号和扫频信号以及变幅值的复合频率信号和正弦扫描信号时, 均方根误差为0.280 8~0.437 3μm, 相对误差为0.016 5~0.024 4, 并且具有良好的实时性能。与基于前馈逆补偿和PI反馈的复合控制策略相比, 提出的基于前馈自适应逆补偿和PI反馈的复合控制策略具有更高的跟踪精度。

A modeling method and a real-time trajectory tracking control strategy were proposed based on Hammerstein model to overcome the effect of rate-dependent hysteresis on piezoelectric actuators. First, by using modified Prandtl-Ishlinskii(MPI) model and the Autoregressive Model with Exogenous Input(ARX) to represent the static nonlinear part and the linear dynamic part of the Hammerstein model, respectively, a Hammerstein model was proposed to describe the rate-dependent hysteresis of piezoelectric actuators. Then, based on the proposed Hammerstein model,a compound control strategy with feed-forward adaptive inverse compensation and PI feed-back was designed. Finally, to verify the effectiveness of the proposed control strategy, a compound control strategy with feed-forward inverse compensation and PI feed-back was designed to compare with the proposed scheme. The experiments on the real-time tracking for single frequency signals and sweep signals with the amplitudes of 11 μm, compound frequency signals and sinusoidal scanning signals with variable amplitudes were performed in a frequency of 100 Hz, obtained results show that the root mean square error and the relative error between the reference input and the output of piezoelectric actuator are 0.280 8-0.437 3 μm and 0.016 5-0.024 4 respectively. As compared with the compound control strategy with feed-forward inverse compensation and PI feed-back, the proposed control strategy has better tracking accuracy and real-time ability.