超磁致伸缩作动器的率相关建模与跟踪控制

利用Hammerstein模型对超磁致伸缩作动器(GMA, Giant Magnetostrictive Actuators)进行建模, 分别以改进的Prandtl-Ishlinskii(MPI, Modified Prandtl-Ishlinskii)模型和外因输入自回归模型(ARX, Autoregressive model with exogenous input)代表Hammerstein模型中的静态非线性部分和线性动态部分,并给出了模型的辨识方法.此模型能在1~100 Hz频率范围内较好地描述GMA的率相关迟滞非线性特性.提出了前馈逆补偿和比例-微分-积分(PID, Proportional-Integral-Derivative)反馈相结合的复合控制策略.实时跟踪幅值为16 μm的单一频率和复合频率正弦参考输入信号, 均方根误差小于1 μm, 相对误差小于10%, 证明了控制策略的有效性.

Rate-dependent modeling and tracking control of giant magnetostrictive actuators

A Hammerstein model was proposed to model giant magnetostrictive actuators (GMA). A modified Prandtl-Ishlinskii(MPI) model and an autoregressive model with exogenous input (ARX) were used to represent the static nonlinear part and the linear dynamic part of the Hammerstein model respectively. Model identification method was also given. The proposed model can describe the rate-dependent hysteresis of GMA from 1 Hz to 100 Hz well. A compound controller containing inverse compensator and proportional-integral-derivative (PID) feedback was designed for tracking control. Real time trajectory tracking of single frequency and composite frequency sinusoidal reference inputs with the amplitude of 16 μm was conducted. The root-mean-square error was less than 1μm and the relative error was less than 10%, which verify the effectiveness of the control strategy.