GATE EC 2020 Set 1 — Question 65
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Control Systems → Time-Domain Analysis → Steady-State Error & Constants
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Question
Consider the following closed loop control system
where and . If the steady state error for a unit ramp input is 0.1, then the value of is ________.

Correct answer
30 to 30
Solution
The open-loop transfer function of the system is given by:This is a Type 1 system. For a unit ramp input , the Laplace transform is . The steady-state error for a Type 1 system with a unit ramp input is given by:where is the velocity error constant, defined as:Given that the steady-state error , we have:Therefore, the value of is 30.
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