PROBLEM: A unity feedback system with the forward transfer functionKG(s)s(s7)is operating with a closed-loop step response that has 15% overshoot. Do thefollowinga. Evaluate the settling time.b. Design a lead compensator to decrease the settling time by three timesChoose the compensator's zero to be at -10.ANSWERS:a. T 1.143ss10b. Glead(s)K = 476.3s25.52The complete solution is at www.wiley.com/college/nise.

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Asked Dec 1, 2019
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PROBLEM: A unity feedback system with the forward transfer function
K
G(s)
s(s7)
is operating with a closed-loop step response that has 15% overshoot. Do the
following
a. Evaluate the settling time.
b. Design a lead compensator to decrease the settling time by three times
Choose the compensator's zero to be at -10.
ANSWERS:
a. T 1.143s
s10
b. Glead(s)
K = 476.3
s25.52
The complete solution is at www.wiley.com/college/nise.
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PROBLEM: A unity feedback system with the forward transfer function K G(s) s(s7) is operating with a closed-loop step response that has 15% overshoot. Do the following a. Evaluate the settling time. b. Design a lead compensator to decrease the settling time by three times Choose the compensator's zero to be at -10. ANSWERS: a. T 1.143s s10 b. Glead(s) K = 476.3 s25.52 The complete solution is at www.wiley.com/college/nise.

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Expert Answer

Step 1

The closed-loop transfer function of the given system is:-

G(s)
1+G(s) H(s)
K
s(5+7)
=0
K
1+
s(s+7)
K
= 0
s(s+7)+K
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G(s) 1+G(s) H(s) K s(5+7) =0 K 1+ s(s+7) K = 0 s(s+7)+K

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Step 2

Comparing with the standard form we get:-

K and 250, =7
Overshoot 15%
=0.15
take natural log on bith sides
ev-
In(0.15)
n
ET
0.60
0.517
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K and 250, =7 Overshoot 15% =0.15 take natural log on bith sides ev- In(0.15) n ET 0.60 0.517

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Step 3

Substituting the val...

2Ea,7
7
2x0.517
=6.76
K 45.83
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2Ea,7 7 2x0.517 =6.76 K 45.83

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