1
$\begingroup$

$\frac{\mathrm dw(t)}{\mathrm dt}+2w(t)=y(t)$ $\frac{\mathrm dy(t)}{\mathrm dt}+3y(t)=2w(t)+f(t)$ The input to the system is $~f(t)$ and the output is $~y(t).$

The initial conditions are $~w(0)=0,\quad y(0)=1$.

Write a state space formulation of this system and solve using the

state space methods for an input $~f(t)=\delta(t)$


solving the system gives

w = -e^-t + e^t y = -e^-t + 3e^t 

This solution checks out when plugged into the first equation, but I am unsure of what to do with the second equation to check my work. Anywho, why not plug it in? I get

10e^t = f 

Either I did the problem right and don't know how to check it or I did the problem wrong. In order to match the f, I need a delta function in there somewhere.

  • 0
    Since $10 e^t \ne f$, there must be something wrong with your solution. In this case, there should be terms in $e^{-t}$ and $e^{-4t}$, but no $e^t$.2012-08-24

0 Answers 0