Discussion
For a unity feedback control system having an open-loop transfer function
\[G(S) = \dfrac{K(S + 2)}{S^{2}(S^{4} + 7S + 12)}\]
The error constant \(K_p\), \(K_v\) and \(K_a\) respectively are
Answer: A
The error constants are \(\infty\), \(\infty\) and \(K/6\), the first option. The system has two poles at the origin, so it is of type 2, and for type 2 the position and velocity constants are infinite.
\[K_p = \lim_{s \to 0} G(s) = \infty\]
\[K_v = \lim_{s \to 0} sG(s) = \infty\]
\[K_a = \lim_{s \to 0} s^2 G(s)\]
\[K_a = \dfrac{2K}{12} = \dfrac{K}{6}\]
The other options give a finite \(K_p\) or \(K_v\), which belongs to a type 0 or type 1 system.
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