GATE 2017 EC – Question 28
The open loop transfer function $G(s) = \dfrac{(s + 1)}{s^p(s + 2)(s + 3)}$ where $p$ is an integer, is connected in unity feedback configuration as shown in the figure.
[Figure: A unity feedback loop with $G(s)$ in the forward path.]
Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter $p$ is ________.
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Correct answer: 1
Explanation
A steady state error of zero for a step input means the system has at least one integrator. A finite non-zero error for a ramp means exactly one integrator, so the system is of type 1 and $p = 1$. Check: $K_v = \lim_{s \to 0} sG(s) = \frac{1}{2 \times 3} = \frac{1}{6}$, so the ramp error is $\frac{1}{K_v} = 6$.