Correct Answer - Option 1 : 2

Transfer Function:

The transfer function of a control system is defined as the ratio of the Laplace transform of the output variable to Laplace transform of the input variable assuming all initial conditions to be zero.

G(s) = C(s) / R(s)

Where G(s) = Transfer Function

C(s) = Laplace Transform of output

R(s) = Laplace Transform of input

- Order of the system can be defined as the value of the highest exponent that appears in the denominator of the closed-loop transfer function.
- Total number of poles of the closed loop system gives the order of the system

The type of the system is defined as the number of poles at the origin of the open-loop transfer function G(s) H(s).

For an open-loop transfer function as shown:

\(G\left( s \right)H\left( s \right) = \frac{{{b_m}{s_m} + {b_{m - 1}}{s^{m - 1}} + \ldots + {b_0}}}{{{s^c}({a_n}{s^n} + {a_{n - 1}}{s^{n - 1}} + \ldots + {a_0})}}\)

The above system is a type ‘c’ system with an order of n + c.

**Explanation:**

**Type 2 system number of poles At the origin 2**