Question

10 For the system has a gain equal to 0.5, the percent overshoot of the system is: Response 1.2 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 t (s) Kv = 0.5, ? = 0.43, ?n = 1.73 Kv = 1, ? = 0.58, ?n = 1.73 Kv = 1.5, ? = 0.72, ?n = 1.73 Kv = 2, ? = 0.86, ?n = 1.73 Kv = 2.5, ? = 1, ?n = 2 Kv = 3, ? = 1, ?n = 3

          10
For the system has a gain equal to 0.5, the percent overshoot of the system is:
Response
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10
t (s)
Kv = 0.5, ? = 0.43, ?n = 1.73
Kv = 1, ? = 0.58, ?n = 1.73
Kv = 1.5, ? = 0.72, ?n = 1.73
Kv = 2, ? = 0.86, ?n = 1.73
Kv = 2.5, ? = 1, ?n = 2
Kv = 3, ? = 1, ?n = 3

10
For the system has a gain equal to 0.5, the percent overshoot of the system is:
Response
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10
t (s)
Kv = 0.5, ? = 0.43, ?n = 1.73
Kv = 1, ? = 0.58, ?n = 1.73
Kv = 1.5, ? = 0.72, ?n = 1.73
Kv = 2, ? = 0.86, ?n = 1.73
Kv = 2.5, ? = 1, ?n = 2
Kv = 3, ? = 1, ?n = 3

Added by Laura D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ishana K

Step 1

We can use the following formulas: ζ = -ln(% overshoot/100) / sqrt(pi^2 + ln(% overshoot/100)^2) ωn = 4 / (ζ * Tp) where Tp is the time to peak. Using the given information, we can calculate: ζ = -ln(12/100) / sqrt(pi^2 + ln(12/100)^2) ≈ 0.58 Tp = 8 * 0.5 = Show more…

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