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PracticeProblemsMidterm_solu

# S3 2s2 k 1s 2k 0 1 k1 2 2k 1 so the closed loop

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Unformatted text preview: ation is1 Routh table 1 + GD = 0 , is then given by 1 2 1 2k 1+ k+1 2k Routh table is then given by s+2 s2 + s 1 ✓ ◆ k 1+ =0 s , s3 + 2s2 + (k + 1)s + 2k = 0. s3 + 2s2 + (k + 1)s + 2k = 0. 1 k+1 2 2k 1 So the closed-loop system is stable iff k > 0 . 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. w r y D(s) − x u G(s) v H(s) Solution: Since we are interested in the transfer function with input r, set all the other inputs in the Solution: Since we are interestedvin 0). By deﬁnition of e, we see that E/R =,1setYall .the other inputs in the block diagram to be zero (w = = the transfer fun...
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