中文摘要：

压电陶瓷驱动器电压位移之间的非线性特点严重影响着它的位移控制精度，建立压电陶瓷驱动器非线性模型是纳米级微位移测控中的关键环节。采用支持向量机回归的方法，通过引入核函数和损失函数将非线性回归转化成线性问题并提高回归精度，建立了一种新的压电陶瓷驱动器外环非线性模型，并就模型的准确性与其它建模方法进行了比较。试验证明，所建的基于支持向量回归的压电陶瓷驱动器非线性模型很好的描述了压电陶瓷驱动器外环非线性特点，误差控制在2％以内，并且建模过程简单，准确性高。

英文摘要：

This paper is to model the nonlinearity of piezoelectric actuator. Due to the inherent nonlinearity, piezoelectric actuator always causes position error in the open-loop system and instability in the closed-loop system; to remedy this problem, a new nonlinear model of piezoelectric actuator using support vector machine for regression is presented by introducing a kernel function and a loss function to turn nonlinear regression into linear regression. For validating the nonlinear model based on support vector machines for regression, this paper also establishes another nonlinear model using the polynomial curve fitting based on the theory of least squares, and modeling experiments on nonlinear characteristic of a piezoelectric actuator are carried out; the comparison between presented model simulation results and experiment value shows that the nonlinear model based on support vector machine for regression commendably describes the nonlinear characteristic of piezoelectric actuator, the maximal error is less than 2%, the process of modeling is explicit, and the computation is simple.