How can I obtain differential equation of the block diagram below ?
The way to find this is by looking at the definition of the transfer function. It is the laplace transform of the output divided by the laplace transform of the input, so we have here:
$\displaystyle \frac{C(s)}{R(s)}=\frac{s^5+2s^4+4s^3+s^2+3}{s^6+7 s^5+3s^4+2s^3+s^2+3}$
From which we have now:
$\displaystyle C(s)\cdot [s^6+7s^5+3s^4+2s^3+s^2+3]=R(s) \cdot [s^5+2s^4+4s^3+s^2+3]$
From which the DE can be found by assuming that the initial conditions are 0.
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