Ignoring the initial conditions in the identification of fractional order systems (FOS) usually results in incorrect parameter estimations. In this paper, we present a method for the online identification of FOS with nonzero initial conditions. The initial conditions are treated as extra parameters and identified together with the system parameters. To reduce the complexity involved with calculating the fractional order derivatives of input and output signals, generalized operational matrices of block pulse functions are adopted. A recursive least squares identification method and a bias compensated recursive least squares identification method are designed to estimate the parameters of FOS without and with noise, respectively. Identification examples are given and the results demonstrate that the identification accuracy is significantly improved if the nonzero initial conditions are considered.

在识别分数阶系统（FOS）时忽略初始条件通常会导致错误的参数估计。在本文中，我们提出了一种在非零初始条件下在线识别FOS的方法。初始条件被视为额外参数，并与系统参数一起识别。为了降低计算输入和输出信号的分数阶导数所涉及的复杂性，采用了块脉冲函数的通用运算矩阵。设计了一种递归最小二乘辨识方法和一个偏置补偿的递归最小二乘辨识方法，分别估计了有噪声和无噪声时FOS的参数。