分数阶系统的一种频域辨识算法.pdf

第 38卷增刊( ) 东南大学学报 ( 自然 科学版 ) V ol38 Sup( ) 2008年 11月 JOURNAL OF SOUTHEA ST UN IVERSITY ( Natural Science E ition) N ov. 2008 彭 程 王 永 ( , 230027) : 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 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 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 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. : 分数阶系统; 频域辨识; 线性最小二乘; 拟退火 : TP273 : A : 1001- 0505( 2008)( ) 002304 Frequency dom ain identification algorithm for fractional order system s Peng Cheng W ang Y ong ( D epartm ent of A utom ation, University o f Science an Techno logy of China, H efei 230027, China) Abs tract: The problem of i entify ing fractional or er transfer functions from frequency response ata has been stu ie . The fractional erivative or er an the enom inator coefficients appear nonlinearly in the fractional or er transfer function mo el, w h ile the num erator coefficients appear linearly. Base on this fact, a frequency omain i entification algorithm ispropose . The fractional erivative or er an the enom inator coefficients are estmi ate using smi ulate annealing, an the numerator coefficients are erive by solving the linear least squares problem. A ll param eters, inclu ing the fractional erivative or er, can be estmi ate using the propose algorithm. Smi u lation examp lesw ith noise- free an noisy frequency response ata em on strate the effectiveness of the propose algo rithm. K ey w ord s: fractional or er system s; frequency omain i entification; linear least squares; smi ula te annealing . [ 1