基于Simulink电路模拟仿真求解Bagley-Torvik方程

Solvingbagley-torvik equation based on simulink circuit simulation

针对定常系数的分数阶Bagley-Torvik方程,提出一种新颖的求解方法——电路模拟仿真法.该方法的核心思想是利用分抗逼近电路构造微积算子s~μ(-1<μ<0)去代替分数导数算子_0D■(-1<μ<0).将分抗逼近电路阻抗函数转换为Simulink中的传输函数模块,然后运用传输函数模块搭建仿真框图求解分数阶微分方程.将电路模拟仿真法与传统的数值逼近求解法进行对比,对比结果表明,电路模拟仿真法求解结果稳定可靠;并且可根据仿真框图搭建实际电路对分数阶微分方程进行实时求解.

A novel solution method, circuit simulation method, is proposed for the Bagley-Torvik equation with constant coefficient. The core idea of this method is to construct micro-product operator: s^μ(-1<μ<0) by the classical fractional approximation circuit to replace the fractional derivative: 0 Dt^μ(-1<μ<0). The circuit simulation method converts the impedance function of impedance approximation circuit into the transfer function module in Simulink which is then used to build the simulation block diagram to solve the fractional differential equation. Comparing the circuit simulation method with the traditional numerical method, namely the numerical approximation method and the Green's function method. The comparison results show that the solving results of circuit simulation method is stable and reliable, and the actual circuit based on the simulation block diagram can be built to solve the fractional differential equation in real time.