Discussion
Identify the type and order of the system \(G(s) = \dfrac{1}{s}\).
Answer: B
The type of a system is the number of poles at the origin in the open loop transfer function, and the order is the highest power of \(s\) in the denominator (the number of poles in all).
\[ G(s) = \frac{1}{s} \]
There is one pole at \(s = 0\), so the type is 1, and the denominator is of degree 1, so the order is 1. This is an integrator. The options with type 0 would need no pole at the origin, and those with order 0 would need a transfer function with no \(s\) in the denominator. The answer is Type 1, Order 1, option B.
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