基于粒子群和辅助变量法的分数阶系统辨识

Identification of Fractional Order System Based on PSO and Recursive Instrumental Variable Methods

  • 摘要: 针对噪声环境下分数阶系统的频域辨识问题,提出了一种结合粒子群优化算法和递推辅助变量法的辨识方法.首先将递推辅助变量法扩展到分数阶系统的频域辨识中,再将辅助变量法的抗噪声特性和粒子群算法的全局寻优能力相结合,采用粒子群算法辨识系统的阶次参数,并利用辅助变量法估计系统的分子分母多项式系数,完成了噪声环境下分数阶系统的阶次和分子分母多项式系数的整体辨识.仿真实验和对电网络阻抗的辨识实例表明了本文提出的辨识方法不仅适用于同元次分数阶系统,也适用于一般形式的分数阶系统.

     

    Abstract: To identify the frequency domain in fractional order systems in noisy environments, we propose an identification method that combines the particle swarm optimization (PSO) algorithm with the recursive instrumental variable (RIV) method. First, we extend the RIV method to identify the frequency domain of a fractional order system. Then, we combine the anti-interference performance of the RIV method with the global optimization capability of PSO. We apply the PSO algorithm to estimate the order and apply the RIV method to identify the multinomial coefficients. Experimental results and the identification example of an electric network show that the proposed method is applicable to commensurate, as well as general, fractional order systems.

     

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