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# Since a hassais 2 smaller than routh table then given

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Unformatted text preview: n of the damping ratio ⇣ . Since A hassais 2 smaller ⇣ than Routh table + then given by B, we have MA > MB where MA is the percent overshoot of A, and MB is k G(s) = 2 similarly. For (s) = 1order .systems with the same denominator (characteristic polynomial), D second + deﬁned s 1 , 1 ks+ + 1 s 2 the percent overshoot is larger with a zero than without a zero, so MC > MA . Hence, the system with 2k 1 the of k percent overshoot is C . Find the rangelargestin which the closed-loop system is stable. 2k So the closed-loop system is r to e := . 27. Find the transfer function from stable iff kr> 0 y for the following feedback system, where 27. Find the transfer function from r to e := r y for the following feedback system, where a 1 10 D(s) = + b, G( s ) = , H (s) = 10 . a 1 s D(s) = + b, G( s ) s + 1 , = H (s) = s + 10 . s s+1 s + 10 We will consider this feedback system for the next six problems. We will consider this feedback system for the next six problems. 6 w r y D(s) − x u G(s) v H(s) Solution: Since we are interested in the transfer function with input r, s...
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