中文摘要：

为了克服压电叠堆的迟滞特性,实现压电叠堆的精确控制,建立了压电叠堆控制系统,研究了该系统所用到的神经网络、分数阶微积分等算法。首先,搭建了采集压电叠堆位移数据的硬件系统,并对含有噪声的位移数据进行了滤波处理;利用径向基函数（RBF）神经网络对压电叠堆建模,得到了模型参数。然后,利用RBF神经网络建模得到的Jacobain信息来整定分数阶PI~μD~λ控制器中的参数对压电叠堆进行控制。最后,与RBF整数阶PID对压电叠堆的控制效果进行了对比。结果显示：RBF建模误差仅为位移实测数据的0.22%,RBF神经网络分数阶PIμDλ控制系统输出稳定,很好地跟随了给定。得到的结果表明RBF神经网络分数阶PI~μD~λ控制器控制性能良好,在压电叠堆的控制中比RBF整数阶PID控制器表现得更加稳定、精确。

英文摘要：

To overcome the hysteresis characteristics of a piezoelectric stack and to control the piezoelectric stack more accurately,a control system for the piezoelectric stack was established and corresponding algorithms such as neural network,fractional order differential and integral calculus were investigated.First,a hardware platform was set up to collect displacement data of the piezoelectric stack and a wavelet algorithm was used to removal noise.The Radial Basis Function（RBF）neural network model of piezoelectric stack was built to obtain model parameters.Then,the Jacobain information obtained by RBF neural network model was used to set controller parameters of a fractional order PIμDλto control the piezoelectric stack.Finally,the comparative work between RBF fractional orderPIμDλand traditional RBF integer order PID was performed to demonstrate the effectiveness of the proposed control methodology.The results show that the RBF model error is only 0.22% that of measured displacement data.The output of fractional order PIμDλcontrol system is stable and has a good follow to the input.It concludes that the RBF neural network fractional order PIμDλcontroller has good control performance,and it is more stable and accurate to RBF integer order PID in the control process of piezoelectric stacks.