# The input to the system is R(S) and the output of the system is C(S). The system is of type

Consider the system in the figure shown. The input to the system is R(S) and the output of the system is C(S). The system is of type

#### 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.

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