GATE EC 2024 Set 1 — Question 38
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Control Systems → Compensators & Controllers → Root Locus Design
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Question
A satellite attitude control system, as shown below, has a plant with transfer function cascaded with a compensator , where and are positive real constants.
In order for the closed-loop system to have poles at , the value of must be __________.
In order for the closed-loop system to have poles at , the value of must be __________.
Correct answer
(B) 1
Solution
The open-loop transfer function of the cascaded system is .
Given and .
So, .For a unity negative feedback system, the characteristic equation is .
We are given that the closed-loop system has poles at .
These two poles form a quadratic factor:
Since is a factor of the characteristic equation, we can perform polynomial division or compare coefficients. Let the third pole be .
Then the characteristic equation can be written as .
Expanding this, we get:
Comparing the coefficients with :
Both and are positive real constants, as required by the problem statement.The final answer is
Given and .
So, .For a unity negative feedback system, the characteristic equation is .
We are given that the closed-loop system has poles at .
These two poles form a quadratic factor:
Since is a factor of the characteristic equation, we can perform polynomial division or compare coefficients. Let the third pole be .
Then the characteristic equation can be written as .
Expanding this, we get:
Comparing the coefficients with :
1.Coefficient of : .
2.Coefficient of : .
3.Constant term: .
Since , we have , which implies .Both and are positive real constants, as required by the problem statement.The final answer is
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