分数阶控制系统的仿真方法  

A Simulation Method of Fractional-order Control Systems

作　　者：曾庆山[1] 曹广益[1] 朱新坚[1] 

机构地区：[1]上海交通大学自动化系,上海200030

出　　处：《计算机仿真》2004年第12期84-86,218,共4页Computer Simulation

基　　金：上海市科技发展基金资助项目(011607033)

摘　　要：该文对分数阶控制系统提出了一种数值仿真方法。该方法根据Riemann-Liouville定义的分数阶积分和微分,利用δ函数的过滤性质,得到分数阶积分和分数阶微分的近似计算,推导出了相应的分数阶微分方程的数值求解方法,从而得到了分数阶控制系统的一种仿真算法。利用"短记忆法则"对此仿真方法进行改进,可以减少计算量、提高运行速度。文中给出了一些仿真例子,仿真研究结果表明该方法是有效的,它可适用与不同的分数阶系统。对于分数阶控制系统的仿真研究具有一定的实际意义。A method of numerical simulation for fractional-order control systems is proposed. In terms of Riemann-Liouville's definitions of fractional integral and fractional derivative, the approximation computation of fractional integral and fractional derivative are obtained by using the sifting property of Dirac's delta function. Then the new method of numerical solution of the fractional differential equations is derived and the simulation arithmetic of fractional-order control systems is obtained. By using the Short-Memory Principle, the computational load and running time of the method are reduced. There are some simulation examples shown in the paper. The simulation results show the method is valid and it applies to various fractional systems. It is helpful for the simulation research of fractional-order control systems.

关 键 词：分数阶微积分 分数阶微分 分数阶系统 数值仿真 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]