The block diagram of a closed-loop control system is given figure. What is the type of this system?

Concept:

The Type of the system is the number of poles present at the origin.

The Order of the system is the total number of poles.

Ex: Transfer function \(G\left( s \right)=\frac{K}{{{s}^{2}}\left( 1+sT \right)}\)

The number of poles present at the origin = 2

So the type of the system = 2

And since the total number of poles = 3

Analysis:

\(G\left( s \right)H\left( s \right) = \frac{2}{{s\left( {{s^2} + 2s + 2} \right)}}\) 

∵ there is one pole at the origin, the type of the system is 1.