中文摘要：

为了提高精密定位系统中压电陶瓷的控制精度,研究了压电执行器的动态模型及逆模型。根据Weierstrass第一逼近定理,提出了以多项式函数逼近Duhem模型中的分段连续函数f（·）和g（·）,并应用递推最小二乘算法辨识Duhem模型的参数α 及f（·）和g（·）的多项式系数,建立了压电陶瓷执行器的非线性参数化动态模型。利用辨识结果建立压电陶瓷执行器的动态逆模型,避免对压电陶瓷执行器进行复杂的模型求逆;介绍了通过逆补偿和PID复合控制对压电陶瓷系统进行的控制。实验结果表明：仅通过逆补偿,可在0~200 μm使得控制绝对误差小于0.8 μm;在前馈逆补偿和PID环控制下,绝对误差可小于40 nm,结果验证了算法的有效性。该算法结构简单,适应性强,便于工程实现。

英文摘要：

The dynamic model and inverse model of a piezoceramic actuator were proposed to improve its control precision in a precision position system. According to the Weierstrass approximation theorem, the polynomials f（·） and g（·） in the Duhem function was developed, and the dynamic modeling of nonlinear parameters of the piezoceramic actuator was given by using recursive least squares to identify the model parameters and polynomial coefficients in the Duhem model. Then, an inverse dynamic modeling of the piezoceramic actuator was established based on identified results to simplify the unknown parameter computation process greatly. Finally, the dynamic inverse compensation was incorporated in a closed-loop PID controller to control the piezoceramic actuator. Experimental results indicate that the maximum absolute error with the inverse compensation is less than 0.8 μm and that with the inverse compensation and PID is less than 40 nm in an amplitude range of 200 μm. The experimental result shows that the proposed identification scheme has improved the nonlinear characteristic of the piezoceramic actuator effectively.