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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16μm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1μm,相对误差小于10%,证明了控制策略的有效性.
The Hammerstein model was used to model Giant Magnetostrictive Actuators (GMA). The modified models of Prandtl-Ishlinskii (MPI), Modified Prandtl-Ishlinskii (MPI) and Autoregressive model with AR exogenous input represents the static nonlinear part and the linear dynamic part of the Hammerstein model, and gives the identification method of the model.The model can well describe the rate-dependent hysteresis nonlinearity of GMA in the frequency range of 1 ~ 100 Hz. A combined control strategy based on feedforward inverse compensation and Proportional-Integral-Derivative (PID) feedback is proposed.The single-frequency and complex-frequency sinusoidal reference input signals with amplitude of 16μm are tracked in real time, the root mean square error Less than 1μm, the relative error is less than 10%, which proves the effectiveness of the control strategy.