note11 - MEEN 364 Notes for session on November 17, 2004....

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MEEN 364 Notes from Session on November 17, 2004 Notes for session on November 17, 2004. (1) In (a) and (b) use Routh’s stability criterion to determine how many roots with positive real parts the characteristic equations have. In (c), find the range of a and b that makes the system stable: a) s 4 + 53s 3 + 7s 2 + 41s + 5 = 0 b) s 5 + 12s 4 + 10s 3 + 24s 2 + 16 = 0 c) s 3 + 2bs 2 + (4 - b )s + ( 3a - 4) = 0 Solution: a) The Routh array for this polynomial is: s 4 : 1 7 5 s 3 : 53 41 0 s 2 : 53 7 1 41 330 53 53 ⋅−⋅ = 53 5 1 0 5 53 = 0 s 1 : 330 53 41 53 5 515 330 53 330 =− 330 53 0 53 0 0 330 53 −⋅ = 0 s 0 : 515 330 5 330 53 0 5 515 330 = 0 0 Since we have 2 sign changes, the number of roots with positive real parts are 2. b) The Routh array for this polynomial is: s 5 : 1 10 0 s 4 : 12 24 16 s 3 : 12 10 1 24 8 12 ⋅− = 12 0 1 16 4 12 3 ⋅ −⋅ = − 0 s 2 : ( ) 824 12 43 26 8 = 816 120 16 8 = 0 1
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MEEN 364 Notes from Session on November 17, 2004 s 1 : () 26 4 3 8 16 488 26 78 ⋅− − ⋅ =− 26 0 8 0 0 26 ⋅−⋅ = 0 s 0 : 488 78 16 26 0 16 488 78 −⋅ = 0 0 There are again two changes of sign on the first column, so c)
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This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.

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note11 - MEEN 364 Notes for session on November 17, 2004....

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