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已知某LTI系统的微分方程为 y"(t)+5y'(t)+6f(t)=2f'(t)+8f(t) 激励信号为f(t)=e-tu(t),初始
已知某LTI系统的微分方程为
y"(t)+5y'(t)+6f(t)=2f'(t)+8f(t)
激励信号为f(t)=e-tu(t),初始状态为y(0-)=3,y'(0-)=2,求零输入响应、零状态响应和全响应。
![](https://static.youtibao.com/asksite/comm/h5/images/m_q_a.png)
对微分方程两边取拉普拉斯变换,得
s2Y(s)-sy(0-)-y'(0-)+5[sY(s)-y(0-)]+6Y(s)=2sF(s)+8F(s)
分别对上两式进行反变换得
yzi(t)=(11e-2t-8e-3t)u(t),
yzs(t)=(3e-t-4e-2t+e-3t)u(t)
y(t)=yzi(t)+yzs(t)=(3e-t+7e-2t-7e-3t)u(t)
![](https://static.youtibao.com/asksite/comm/h5/images/solist_ts.png)