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# How many roots of the following polynomial equation

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Unformatted text preview: 25. How many roots of the following polynomial equation are in the RHP? s 5 + 3s 4 + 5s 3 + 7s 2 + 9s + 1 = 0 Solution: Routh table is given by 25. How many roots of the following polynomial equation are in the LHP? 1 3 8 -11 318 4 59 7 s5 + 3s4 + 5s3 + 7s2 + 9s + 1 = 0 1 26 Solution: Routh table is given by 4 1 59 3 71 8 26 -11 4 Since there two sign changes in the ﬁrst column, there are two poles in the RHP. 2 318 4 26. Consider the unity feedback system of the plant G(s) and controller D(s): Since there two sign changes in the ﬁrst column, there are two poles in the RHP. Since there is no zero entry in the + 2 column, there is no root on the imaginary axis. The degree of the polynomial is ﬁve, s ﬁrst k G( s ) = 2 , D (s) = 1 + . so there are ﬁve roots. Thus, the number of roots in the LHP is ﬁve minus two, 3 . s +s 1 s 26. Consider the unity feedback system of the plant G(s) and controller D(s): Find the range of k in which the closed-loop system is stable. Solution: The characteristic equation is k s+2 G (s ) = s2 + s 1 , D (s ) = 1 + . s✓ ◆ s+2 k Find the range , 1 + GD = 0 of k in which the closed-loop system is stable. , 1+ 2 1+ =0 s +s s Solution: The characteristic equ...
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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.

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