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Experiment 2 - EE 342 Experiment 2 Step Response DATE...

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EE 342: Experiment 2 Step Response DATE: 01/21/2010 Authors: Gurpal Bhoot, Mason Borda, Jong Park Lab Partners: None
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Motomatic : EE 4617 i. Settings of the Resistors: R f R 1 R 2 R 3 System 1 15KΩ 30KΩ 30KΩ System 2 6.5KΩ 30KΩ 30KΩ System 3 15KΩ 30KΩ 30KΩ 300KΩ ii. Resulting Theoretical Values: ω n ζ K System 1 15.17 rad/s .128 -1 System 2 7.06 rad/s .197 -1 System 3 10.73 rad/s .2 -1 ω n = K2KpKaKmτmN ζ = + 1 K3KTKaKm2ωnτm K = - K1K2 iii. Resulting Theoretical Values: ω d v p (∞) τ r τ p O p τ s System 1 9.71 rad/s 6 V 148.7 ms 289 ms 86.8 % 1.54 s
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System 2 6.92 rad/s 6 V 255.6 ms 453.9 ms 53.18% 2.17 s System 3 10.51 rad/s 6 V 168.4 ms 299 ms 52.66% 1.40 s ω d = - 1 ζ2 ω n v p (∞) = 6 V (given) τ r = - - π cos 1ζωd = - - - π cos 1ζ1 ζ 2ωn = - - (. ) - (. ) * . π cos 1 128 1 128 2 15 17 rads = 148.7 ms τ p = πωd = - π1 ζ 2ωn = - . * . π1 0452 10 87 rads = π . 10 86 rads = 289 ms O p = exp( - πζ - 1 ζ 2 ) * 100 = exp( - π (. ) 128 - (. ) 1 128 2 ) * 100 = .666 * 100 …………………………………………………….. = 66.6% τ s ≤ - ( . ln 0 05 - ) 1 ζ 2 ζωn = - ( . ln 0 05 - ( . ) . ( . ) 1 0 128 2 0 128 15 17 rads = 1.54 s iv. Experimental Values: ω d v p (∞) τ r τ p O p τ s System 1 13.66 rad/s 6.1 V 180 ms 300 ms 65.55 % 0.99 s
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