分数阶系统的一种频域辨识算法

研究了利用频率响应数据辨识分数阶传递函数的问题.根据分数阶传递函数模型中,公因子阶次和分母系数是非线性参数,而分子系数则是线性参数,给出了一种频域辨识算法:利用模拟退火算法估计公因子阶次和分母系数,相应的分子系数通过求解线性最小二乘问题得到.该算法可以估计出包括公因子阶次在内的所有模型参数.无噪声和有噪声频率响应数据2种情况下的仿真算例验证了算法的有效性.

Frequency domain identification algorithm for fractional order systems

The problem of identifying fractional order transfer functions from frequency response data has been studied.The fractional derivative order and the denominator coefficients appear nonlinearly in the fractional order transfer function model,while the numerator coefficients appear linearly.Based on this fact,a frequency domain identification algorithm is proposed.The fractional derivative order and the denominator coefficients are estimated using simulated annealing,and the numerator coefficients are derived by solving the linear least squares problem.All parameters,including the fractional derivative order,can be estimated using the proposed algorithm.Simulation examples with noise-free and noisy frequency response data demonstrate the effectiveness of the proposed algorithm.