基于Hammerstein模型描述的非线性系统辨识新方法

New identification method of nonlinear systems based on Hammerstein models

Hammerstein模型常用来描述pH值或具有幂函数、死区、开关等特性的过程,本文提出了一种辨识此类对象模型结构和参数的新方法,首先将非线性静态部分和线性动态部分分别用非线性基和Laguerre级数表示,然后通过最小二乘法、矩阵特征值分解和矩阵扩维,辨识出两部分参数．并证明了该方法在输出端存在白噪声情况下误差的收敛性．此方法仅需假设输入为持续激励,适用范围广,计算简单,辨识精度高．最后通过pH中和滴定实验验证了以上结论．

Hammerstein models are commonly used to present the pH process or the processes with characteristics such as exponent, dead-zone and switch. A new method for identification Hammerstein models is presented in this paper. Firstly, the nonlinear static part and the linear dynamic part are expressed by nonlinear basis functions and the Laguerre functions, respectively. The parameters of these two parts are then identified by least squares estimation, singular value decomposition and matrix dimension expansion. The convergence of the output error is also proved when white noises exist in the output signal. The proposed approach is based on weak assumptions on persistency of the excitation, so it is suitable for many applications. The operation is easy and the result is accurate. Finally, a simulation on a pH process is given to validate the conclusions.