GATE EC 2017 Set 1 — Question 18
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Control Systems → Time-Domain Analysis → Steady-State Error & Constants
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Question
The open loop transfer function where is an integer, is connected in unity feedback configuration as shown in the figure.
Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter is _________.

Correct answer
0.99 to 1.01
Solution
1.Steady State Error for Step Input: For a unity feedback system, the steady state error for a unit step input is , where . For , must be . This implies that the system must be at least Type 1, so .
2.Steady State Error for Ramp Input: The steady state error for a unit ramp input is , where . Given , we have .
3.Solve for :
For to be a finite non-zero value (), the power of in the denominator must be zero. Thus, , which gives .4.Verification: If :
This matches the given error . Therefore, .Continue learning with Success Tracker
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