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PracticeProblemsMidterm_solu

# Since a rst smaller than never has an overshoot m is

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Unformatted text preview: 2s + 5 s + 2s + 10 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 6...
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