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Problem 5.42PP
Plot the loci for the 0* locus or negative K for each of the following: 
(a) The examples given in Problem 1
(b) The examples given in Problem 2
(c) The examples given in Problem 3
(d) The examples given in Problem 4
(e) The examples given in Problem 5
(e) The examples given in Problem 5
(f) The examples given in Problem 6 
Problem 1
For the characteristic equation 
K1+ - ■ = 0,
j2(j +1)(j + 5 ) ■
(a) Draw the real-axis segments of the corresponding root locus.
(b) Sketch the asymptotes of the locus for K -
(c) Sketch the locus
(d) Verify your sketch with a Matlab plot.
Problem 2
Real poles and zeros. Sketch the root locus with respect to K for the equation 1 + KL(s) = 0 and 
the listed choices for L(s). Be sure to give the asymptotes, and the arrival and departure angles 
at any complex zero or pole. After completing each hand sketch, verify your results using Matlab. 
Turn in your hand sketches and the Matlab results on the same scales.
(a) Us) - j(,+i)(,+5)(,+io)
(b) Ks) =
(c) Us) —
fd) Ks) = f+ray
Problem 3
Complex poles and zeros. Sketch the root locus with respect to K for the equation 1 + KL(s) = 0 
and the listed choices for L(s). Be sure to give the asymptotes and the arrival and departure 
angles at any complex zero or pole. After completing each hand sketch, verify your results using 
Matlab. Turn in your hand sketches and the Matlab results on the same scales.
W «*> = ?T5Ti5
(b) t ( j ) _
Problem 4
Multiple poles at the origin. Sketch the root locus with respect to K for the equation 1 + KL(s) = 0 
and the listed choices for L(s). Be sure to give the asymptotes and the arrival and departure 
angles at any complex zero or pole. After completing each hand sketch, verify your results using 
Matlab. Turn in your hand sketches and the Matlab results on the same scales.
(b) W =
( - ( j - l ) t ( jW + 3 ]
S tep -by-s tep s o lu tio n
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