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2s the systems with no zeros, the percent overshoot is a decreasing function of the damping ratio ⇣ . Since A ﬁrst smaller ⇣ than never has an overshoot, M is the percent overshoot For and MB is
Solution: A has a order system B, we have MA > MB where soAD is not the solution. of A, second order
deﬁned similarly. percent order systems with the same function of the damping ratio ⇣ . Since
systems with no zeros, theFor secondovershoot is a decreasing denominator (characteristic polynomial),
the percent overshoot
A has a smaller ⇣ than B, we is larger with a zero than without a zero, so MC > MA . Hence, the system with B is
have MA > MB where MA is the percent overshoot of A, and M
the largest percent overshoot is C .
deﬁned similarly. For second order systems with the same denominator (characteristic polynomial),
the percent overshoot is larger with a zero than without a zero, so MC > MA . Hence, the system with
the largest percent overshoot is C . 6
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This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.
 Winter '09
 IDAN

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