ME5659_LecSuppl_RootMore

ME5659_LecSuppl_RootMore - (a) L ( s ) = 1 s ( s + 1)( s +...

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3. For the characteristic equation 1+ K s ( s +1)( s +5) =0: (a) Draw the real-axis segments of the corresponding root locus. (b) Sketch the asymptotes of the locus for K →∞ . (c) For what value of K are the roots on the imaginary axis? (d) Verify your sketch with a MATLAB plot. Solution: (a) The real axis segments are 0 >σ> 1; 5 (b) α = 6 / 3= 2; φ i = ± 60 , 180 (c) K o =30 Root Locus Real Axis Imag Axis -15 -10 -5 0 5 -10 -5 0 5 10 Solution for Problem 5.3
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4. Real poles and zeros. Sketch the root locus with respect to K for the equation 1+ KL ( s )=0 and the following choices for L ( s ) .B es u r et
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Unformatted text preview: (a) L ( s ) = 1 s ( s + 1)( s + 5)( s + 10) (b) L ( s ) = ( s + 2) s ( s + 1)( s + 5)( s + 10) (c) L ( s ) = ( s + 2)( s + 6) s ( s + 1)( s + 5)( s + 10) (d) L ( s ) = ( s + 2)( s + 4) s ( s + 1)( s + 5)( s + 10) Solution: All the root locus plots are displayed at the end of the solution set for this problem. (a) = 4; i = 45; 135; o = 1 . 77 (b) = 4 . 67; i = 60; 180; o = 5 . 98 (c) = 4; i = 90; o > none (d) = 5; i = 90; o > none Root Locus Real Axis Imag Axis Root Locus Real Axis Root Locus Real Axis Root Locus Real Axis-10-5-6-4-2 2 4 6-10-5-6-4-2 2 4 6-10-5-6-4-2 2 4 6-10-5-6-4-2 2 4 6 Solution for Problem 5.4...
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ME5659_LecSuppl_RootMore - (a) L ( s ) = 1 s ( s + 1)( s +...

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