Matlab solve a first-order transfer functin using differential equation and step responce simulation

爱安敝之

于 2022-12-03 17:37:29 发布

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分类专栏：学习 matlab Matrix 文章标签： matlab 开发语言矩阵

本文链接：https://blog.youkuaiyun.com/libizhide/article/details/128157282

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本文介绍了一种利用微分方程而非传递函数来模拟随时间变化的信号的方法。通过一个具体的例子展示了如何在MATLAB中实现这一过程，并对比了输入与输出信号的变化。此方法适用于一阶系统，但不适用于二阶系统。

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Most of the time, we use transfer function to simulate the signal relating to time by using tf() and lsim(). In this paper, I try to use differential equation to solve it.

Main

Transfer funtion:
$0.5y˙+y=F(t)0.5\dot{y}+y=F(t)$
Input :
$\space (t>0) \\ F(t)=75 \space (t\le0)$
matlab code

syms y(t) inp;
ode = 0.5*diff(y,t)+y== inp;
cond = y(0) == 75;
ySol(t,inp) = dsolve(ode, cond);
x=[0:0.1:10];
result=ySol(x,100);
input=x*0+100;
input(1)=75;
plot(x, result);
hold on;
plot(x, input);
legend({'Output','Input'},'Location','southwest');
xlabel('Time') 
ylabel('Amplitude') 
hold off;

result 1

ySol(t, inp) =
inp - exp(-2*t)*(inp - 75)

result 2

在这里插入图片描述

Note

This method is not suitable for second order system practically. I guess primarily because of its complexcity of the differential equation.
This method is useful for periodic input.