HW06_solutions

# HW06_solutions - Winter 2009 1(Problem 8-5(a G s H s = o K...

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Winter 2009 1. (Problem 8-5) (a) GsHs Ks ss s ( ) ( ) ( ) ( ) = + + + 8 5)( 6 Asymptotes: K > 0: 90 270 o and K < 0: 0 and 180 Intersect of Asymptotes: σ 1 0 5 6 8 3 1 15 = − − = − ( ) . Breakaway-point Equation: 2 35 176 240 0 3 2 + + + = Breakaway Points: 2 55724, 9 7098 .2178, . . Root Locus Diagram: (The book’s notation is used here for the complementary root locus. However, Prof. Grizzle’s notation is okay as well. Using that notation, all the arrows for the complementary root locus would be in the reverse to the arrows in this diagram).

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Winter 2009 2. (Problem 8-5) (d) GsHs Ks ss s ( ) ( ) ( ) ( ) = + + + 2 2 2 2 Asymptotes: K > 0: 90 270 o , K < 0: 0 180 , Intersect of Asymptotes: σ 1 0 1 1 2 3 1 0 = − − = j ( ) Breakaway-point Equation: 2 8 8 4 0 3 2 + + + = Breakaway Points: 28393 . The other two solutions are not breakaway points. Root Locus Diagram
Winter 2009 3. (Problem 8-5) (e) ( ) 2 ( 5) () () 22 Ks GsHs ss s + = ++ Asymptotes: K > 0: 90 270 o , K < 0: 0 180 , Intersect of Asymptotes: σ 1 0 1 1 5) 3 1 15 = − − = j ( . Breakaway-point Equation: 2 17 20 10 0 3 2 s + + + = Breakaway Points: 7.2091 The other two solutions are not breakaway points.

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HW06_solutions - Winter 2009 1(Problem 8-5(a G s H s = o K...

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