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6.302 Lab 1D Report - Michael Salib

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Amplitude<br />

0.06<br />

0.05<br />

0.04<br />

0.03<br />

0.02<br />

0.01<br />

<strong>6.302</strong> <strong>Lab</strong> <strong>1D</strong> <strong>Report</strong><br />

<strong>Michael</strong> <strong>Salib</strong><br />

October 31, 2002<br />

Error response to a Ramp<br />

0<br />

0 0.05 0.1 0.15 0.2<br />

Time (sec)<br />

0.25 0.3 0.35 0.4<br />

1


Amplitude<br />

Amplitude<br />

0.06<br />

0.05<br />

0.04<br />

0.03<br />

0.02<br />

0.01<br />

Error Response to a Ramp Input<br />

0<br />

0 0.1 0.2 0.3<br />

Time (sec)<br />

0.4 0.5 0.6<br />

0.014<br />

0.012<br />

0.01<br />

0.008<br />

0.006<br />

0.004<br />

0.002<br />

Integrated Error Response to a Ramp Input<br />

0<br />

0 0.1 0.2 0.3<br />

Time (sec)<br />

0.4 0.5 0.6<br />

<br />

<br />

<br />

ζ =<br />

(ln Po − 1) 2<br />

π 2 + (ln Po − 1) 2<br />

2


ωn =<br />

<br />

<br />

<br />

1<br />

±<br />

<br />

ζ =<br />

ωn =<br />

ωd<br />

√ 1 − ζ 2<br />

<br />

1 − 1<br />

M 2 p<br />

2<br />

ωp<br />

√ 1 − 2ζ 2<br />

3

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