GATE EC 2021 Set 1 — Question 58
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Control Systems → Compensators & Controllers → PID Controllers
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Question
A unity feedback system that uses proportional-integral (PI) control is shown in the figure.
The stability of the overall system is controlled by tuning the PI control parameters and . The maximum value of that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is _________.

Correct answer
3.125 to 3.125
Solution
The open-loop transfer function is .
The characteristic equation is :Using the Routh-Hurwitz criterion:
To find the maximum , we maximize . Setting gives .
Substituting into the equation: .
Thus, .
The characteristic equation is :Using the Routh-Hurwitz criterion:
- :
- :
- :
- :
- :
To find the maximum , we maximize . Setting gives .
Substituting into the equation: .
Thus, .
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