摘要
介绍了分数阶线性定常系统的状态方程描述 ,并给出了其稳定性定理的一个证明 .然后给出了线性定常分数阶系统的一个有效辨识算法 .其基本思想是利用分数阶泊松滤波器把分数阶导数和滤波计算合并起来 ,只需计算 1步就可以得到滤波后的分数导数 ,再利用最小二乘法进行系统辨识 .还把辅助变量方法运用到分数阶系统的辨识上 ,这样即使系统中存在有色噪声 ,仍可以获得参数的无偏估计 .最后给出了一个粘弹性系统的辨识实例 ,说明了上述方法的有效性 .
The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.
基金
TheNationalHighTechnologyResearchand DevelopmentProgramofChina (863Program) (No .2 0 0 3AA5 170 2 0 )
theNationalNaturalScienceFoundationofChina (No .5 0 2 0 60 12 )
theDevelopingFoundationofShanghaiScienceandTechnologyCommittee(No .0 1160 70
关键词
分数阶系统
状态空间描述
系统辨识
分数阶泊松滤波器
最小二乘法
辅助变量法
fractional order systems
state-space representation
system identification
fractional order Poisson filter
least square method
instrumental variable method
