原子力显微镜中微悬臂梁分布参数系统的Hammerstein模型
Hammerstein model for distributed parameter system of micro-cantilever in atomic-force microscope

为提高原子力显微镜(atomic force microscope, AFM)中微悬臂梁分布参数模型的精度, 本文提出了包含非 线性时空特性的改进模型, 在此基础上简化控制器的结构. 首先加入非线性补偿项修正传统分布参数模型; 然后采 用Karhunen-Loève(K–L)方法提取系统主导空间基函数, 实现系统输出的时空变量分离. 利用求解得到的时间系数 和系统激励, 建立系统时域Hammerstein模型, 使系统无限维偏微分方程模型转化为时域有限维常微分方程形式, 控 制器的设计无需考虑空间耦合的影响; 最后, 利用最小二乘支持向量机结合奇异值分解法辨识模型中的参数. 与传 统分布参数模型进行仿真和实验结果比较, 验证了方法的有效性.
To improve the accuracy of the distributed-parameter model of the micro-cantilever in an atomic-force microscope (AFM), we propose a modified model which contains the nonlinear spatial-temporal properties. On this basis, the structure of the controller is simplified and a nonlinear compensation term is added to correct the traditional distributed parameter model. Next, the Karhunen-Loève (K–L) decomposition method is applied to extract the dominant spatial basis function of the system, achieving the space-time decomposition. Then, a temporal Hammerstein model is identified by the temporal coefficients obtained from the decomposition and the input signal, which transforms the infinite dimensional partial differential equation model into the finite-dimensional ordinary differential equation model, making it possible to design the controller without considering the space coupling. Finally, we use the leas t-squares-support-vector-machine algorithm and the singular-value decomposition method to identify the parameters of the model. Simulation and experimental comparisons with the traditional distributed parameter model are given to validate the effectiveness of the proposed method.