Question #26: A) Where the input to the closed loop system shown in the figure below is a unit step function, answer the following: X(s) K, Y(s) (s+2) K2 A-1) What is the value of the time taken by the system to settle within 2% of its final value? What must be the range of the gain value K=K,K2 in order to obtain (10% < percentage overshoot < 30%)? Verify that the range found above for K K,Ke will produce a stable response? (Hint: use Routh Hurwitz criterion). If the steady state error = 0, what must be the value of Ke? А-2) А-3) A-4) B-1) Explain with the aid of a diagram the difference between an underdamped and an overdamped second order system response to a unit step input?

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Question #26:
A)
Where the input to the closed loop system shown in the figure below is a
unit step function, answer the following:
X(s)
K,
1
Y(s)
(s+2)
K2
A-1) What is the value of the time taken by the system to settle within 2% of its
final value?
A-2) What must be the range of the gain value K = K,K2 in order to obtain
(10% < percentage overshoot < 30%)?
A-3) Verify that the range found above for K- K,K2 will produce a stable
response? (Hint: use Routh Hurwitz criterion).
A-4) If the steady state error = 0, what must be the value of K2?
B-1) Explain with the aid of a diagram the difference between an underdamped
and an overdamped second order system response to a unit step input?
Transcribed Image Text:Question #26: A) Where the input to the closed loop system shown in the figure below is a unit step function, answer the following: X(s) K, 1 Y(s) (s+2) K2 A-1) What is the value of the time taken by the system to settle within 2% of its final value? A-2) What must be the range of the gain value K = K,K2 in order to obtain (10% < percentage overshoot < 30%)? A-3) Verify that the range found above for K- K,K2 will produce a stable response? (Hint: use Routh Hurwitz criterion). A-4) If the steady state error = 0, what must be the value of K2? B-1) Explain with the aid of a diagram the difference between an underdamped and an overdamped second order system response to a unit step input?
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