System type equals the number of pure integrators (poles at the origin) in the open-loop transfer function G(s)H(s). Here the denominator contains s², so there are two poles at the origin and the system is Type 2.
Formula / Key Relation
G(s)H(s)=K(s+2)/[s²(s+3)(s+4)]
Number of poles at s=0 = 2
⇒ Type 2
Detailed Explanation
Concept & Reasoning
Finite poles such as roots of s²+7s+12=(s+3)(s+4) do not affect system type. Likewise the zero at −2 does not reduce the count unless it exactly cancels a pole at the origin, which it does not. Type determines steady-state error constants for step, ramp and parabolic inputs.
How to Solve It in the Exam
Count uncancelled poles at the origin only.
Important Exam Point
Do not count total denominator order.
Related Revision Path
This question sits in the revision path Control Systems → Steady-State Error → System Type .
Quick Trick
Count uncancelled poles at the origin only.
Common Mistake
Calling it Type 4 because the overall denominator is fourth order.
Exam Tip
Do not count total denominator order.
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