The input to the system is R(S) and the output of the system is C(S). The system is of type
Right Answer is: 0
SOLUTION
The total open-loop gain from the given figure
G(s) = 1/s(s + 2)
Now, the closed-loop transfer function is
$\begin{array}{l}T(s) = \dfrac{{G(s)}}{{1 + G(s).H(s)}}\\\\= \dfrac{{\dfrac{1}{{s(s + 2)}}}}{{1 + \dfrac{3}{{s(s + 2)}}}}\\\\= \dfrac{1}{{({s^2} + 2s + 3)}}\end{array}$
As seen from the closed loop transfer function, there is no pole at origin therefore the type of the system is zero.