基于近似偏最小一乘的闭环系统辨识新方法

本文基于近似最小一乘准则和主成分分析,针对反馈通道模型阶次低于前向通道模型阶次且反馈通道不存在噪声的闭环系统,进行了近似偏最小一乘递推辨识算法的推导.为解决最小一乘准则函数不可微的问题,本文算法用确定性可导函数近似代替残差绝对值.近似偏最小一乘辨识算法可以克服基于最小二乘准则的辨识算法在受到满足(SαS)分布的尖峰噪声干扰时残差平方项过大的缺点,具有目标函数可导,计算简单的优点.同时,通过主成分分析去除数据向量各元素之间的线性相关,可以得出模型参数的唯一解.仿真实验表明,本文算法可以对反馈通道模型阶次低于前向通道模型阶次的闭环系统进行直接辨识,抑制了尖峰噪声对辨识结果的影响,具有优良的稳健性,可以更好地应用于闭环系统辨识.

Identification of closed-loop system by partial least absolute deviation

Based on approximate least absolute deviation criterion and principal component analysis, a recursive partial approximate least absolute deviation (PALAD) identification algorithm is deduced for closed-loop system whose model order of feedback channel is lower than that of the forward channel and there is no noise in the feedback channel. To solve the non-differentiable problem of the least absolute deviation, a deterministic derivable function is established to approximate the absolute value under certain situations in this paper. The proposed method can overcome the disadvantage of large square residual of least square criterion when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable distribution(SS). By adopting principal component analysis to eliminate the linear correlation among the elements of data vector, the unique solution of model parameters can be easily acquired by the proposed method. The simulation experiments show that the proposed method can be directly used to identify closed-loop system whose model order of feedback channel is lower than that of the forward channel. Moreover, the proposed algorithm can restrain the impact of impulse noise effectively, has strong robustness and can be better applied to closed-loop identification..