Problem 1. i) Sketch the root locus for the feedback system in Fig. 1 with the given transfer functions. ii) Find all information about the root locus (such as asymptotes, break-in and away points, angle of departure and arrival), if applicable. iii) Find a critical gain if it exists.
Problem 1. i) Sketch the root locus for the feedback system in Fig. 1 with the given transfer functions. ii) Find all information about the root locus (such as asymptotes, break-in and away points, angle of departure and arrival), if applicable. iii) Find a critical gain if it exists.
Introductory Circuit Analysis (13th Edition)
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![Problem 1. i) Sketch the root locus for the feedback system in Fig. 1 with the given transfer functions. ii)
Find all information about the root locus (such as asymptotes, break-in and away points, angle of
departure and arrival), if applicable. iii) Find a critical gain if it exists.
Compensator
G(s)
a) G₂ (s)
b) Gp(s)
c) G₂ (s):
d) G(s) =
e) Gp(s) =
5+5
s(s+2)(s+4)'
1
RG)
s²-45+20
(s+2)(s+4)*
s(s+2)(s+4)'
S42
(s+3)(s²+2s+2)"
Sensor
HG)
MG)
Fig. 1.
Ge(s)k, H(s) = 1
Ge(s)k, H(s) = s +3
Ge(s)=k, H(s) = 1
1
s(s+5)(s+6)(s²+2s+2)'
Ge(s)k, H(s) = 1
G₂G)
C(₂)
Ge(s)=k, H(s) = s +3
Note. Sketch the root locus for positive gain.
Note. Compute angle of departure or arrival only at complex conjugate poles or zeros.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8140eaa-f328-42bd-ad78-05bf6a53ea49%2Fd51741ee-658c-4ed2-b64f-2df88208e74c%2Fnls7gcj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1. i) Sketch the root locus for the feedback system in Fig. 1 with the given transfer functions. ii)
Find all information about the root locus (such as asymptotes, break-in and away points, angle of
departure and arrival), if applicable. iii) Find a critical gain if it exists.
Compensator
G(s)
a) G₂ (s)
b) Gp(s)
c) G₂ (s):
d) G(s) =
e) Gp(s) =
5+5
s(s+2)(s+4)'
1
RG)
s²-45+20
(s+2)(s+4)*
s(s+2)(s+4)'
S42
(s+3)(s²+2s+2)"
Sensor
HG)
MG)
Fig. 1.
Ge(s)k, H(s) = 1
Ge(s)k, H(s) = s +3
Ge(s)=k, H(s) = 1
1
s(s+5)(s+6)(s²+2s+2)'
Ge(s)k, H(s) = 1
G₂G)
C(₂)
Ge(s)=k, H(s) = s +3
Note. Sketch the root locus for positive gain.
Note. Compute angle of departure or arrival only at complex conjugate poles or zeros.
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