3. Consider unity negative feedback applied to the system: k G(s) s(s? + 4s + 5) (a) Find the value of k required to yield a steady state error of 10% in response to a unit ramp input. (b) Use a method other than the Routh-Hurwitz method to determine the limiting value of k = klim for closed-loop stability. (c) What is the frequency of oscillation of the system at k = klim?

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3. Consider unity negative feedback applied to the system:
k
G(s) =
s(s2 + 4s + 5)
(a) Find the value of k required to yield a steady state error of 10% in response to a unit
ramp input.
(b) Use a method other than the Routh-Hurwitz method to determine the limiting value
of k = klim for closed-loop stability.
(c) What is the frequency of oscillation of the system at k = klim?
(d) What is the exact location of the real pole(s) for k = klim.
(e) Give a complete sketch of the root locus (0 Sks 00) for this system assuming a unity
feedback configuration. Make sure you show all the significant features on your sketch.
Give particular attention to the angle of departure from the complex poles.
(f) Indicate on your root locus diagram the point at which the damping ratio of the
dominant poles is 0.5.
Transcribed Image Text:3. Consider unity negative feedback applied to the system: k G(s) = s(s2 + 4s + 5) (a) Find the value of k required to yield a steady state error of 10% in response to a unit ramp input. (b) Use a method other than the Routh-Hurwitz method to determine the limiting value of k = klim for closed-loop stability. (c) What is the frequency of oscillation of the system at k = klim? (d) What is the exact location of the real pole(s) for k = klim. (e) Give a complete sketch of the root locus (0 Sks 00) for this system assuming a unity feedback configuration. Make sure you show all the significant features on your sketch. Give particular attention to the angle of departure from the complex poles. (f) Indicate on your root locus diagram the point at which the damping ratio of the dominant poles is 0.5.
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