有理幂次分数阶线性电路方程的W域解法  

W-Domain Solution of Fractional Linear CircuitEquations with Rational Powers

作　　者：梁贵书[1] 蒋铭珏 LIANG Guishu;JIANG Mingjue(School of Electrical and Electronic Engineering,North China Electric Power University,Baoding 071003,China)

机构地区：[1]华北电力大学电气与电子工程学院,河北保定071003

出　　处：《华北电力大学学报（自然科学版）》2021年第1期56-61,84,共7页Journal of North China Electric Power University：Natural Science Edition

基　　金：河北省自然科学基金资助项目(E2018502121);北京市自然科学基金资助项目(3192039).

摘　　要：电气工程领域中的很多设备都表现出分数阶的本质,充分利用分数阶微积分能更好地描述这种分数阶现象。对于分数阶电路,电路方程的求解是至关重要。对于含有多个分数阶幂次的电路方程,现有的方法求解非常困难。通过对传统的Laplace变换改进,提出了一种新的变换——W变换。这种变换可适用于有理幂次分数阶方程的求解。针对W域有理象函数的特点,给出了其部分分式展开形式,简化了时域解的表达式。最后,通过实例验证了方法的正确性以及可行性。The phenomenon that fractional order is implied in many electrical engineering devices and system can be well described by fractional calculus.Equation solution is key to fractional circuit,but it is very difficult for existing methods to solve circuit equations with multiple fractional powers.This paper refined the traditional Laplace transform,and proposed a new method for fractional circuits—W transform,which is applied to solve the fractional circuits with rational powers.According to the characteristics of rational image functions in W domain,part of its fraction expansion method is given,which simplifies the equation of time-domain solution.Finally,examples are given to verify the correctness and feasibility of W transform.

关 键 词：有理阶次分数阶方程 W变换 部分分式展开法 

分 类 号：TN711.[电子电信—电路与系统]