Discussion
A feedback control system has open loop transfer function is :
\[ G(s) = \frac{5(s+3)(s+5)}{s^{2}(s+1)(s^{2}+7s+12)} \]
The system order and type number respectively is :
Answer: B
The order and type are 5 and 2.
The order is the highest power of \(s\) in the denominator of the transfer function. Here the denominator is \(s^{2}(s+1)(s^{2} + 7s + 12)\), of degree \(2 + 1 + 2 = 5\).
The type is the number of open-loop poles at the origin, the power of the factor \(s\) alone in the denominator: \(s^{2}\), so type 2. A type 2 system has zero steady-state error to step and ramp inputs.
The options with order 2 count only the \(s^{2}\) factor, and 2, 5 gives the two numbers in the wrong order.
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