For the following control system, apply the Root Locus techniques to design a PD compensator so that the settling time is 0.5 seconds and the system operates at 18% overshoot. Controller Plant R(s) + E(s) HD K Gc(s) 1 $3+20s²+75s C(s) The root locus of the uncompensated system operating at 18%OS is shown below. QUESTIONS: Uncompensated system: a) Find the coordinates of the dominant poles for which the system operates at 18% OS b) Find the Gain to have 18% OS c) Find the settling time of the uncompensated system d) Find the angle q (cos q = z) Design of the Compensator: e) Find the position of the Desired Pole to have Ts = 0.5 second and continue having 18% OS f) Use trigonometry to find the angle and position of the compensator, this find qZc and Zc g) Give the transfer function of the compensator Root Locus

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For the following control system, apply the Root Locus techniques to design a PD compensator so that the
settling time is 0.5 seconds and the system operates at 18% overshoot.
Controller
Plant
R(s) +
E(s)
K
Gc(s)
1
$3+20s²+75s
The root locus of the uncompensated system operating at 18%OS is shown below.
QUESTIONS:
Uncompensated system:
a) Find the coordinates of the dominant poles for which the system operates at 18% OS
b) Find the Gain to have 18% OS
c) Find the settling time of the uncompensated system
d) Find the angle q (cos q = z)
C(s)
Design of the Compensator:
e) Find the position of the Desired Pole to have Ts = 0.5 second and continue having 18% OS
f) Use trigonometry to find the angle and position of the compensator, this find qZc and Zc
g) Give the transfer function of the compensator
Root Locus
0.479
Transcribed Image Text:For the following control system, apply the Root Locus techniques to design a PD compensator so that the settling time is 0.5 seconds and the system operates at 18% overshoot. Controller Plant R(s) + E(s) K Gc(s) 1 $3+20s²+75s The root locus of the uncompensated system operating at 18%OS is shown below. QUESTIONS: Uncompensated system: a) Find the coordinates of the dominant poles for which the system operates at 18% OS b) Find the Gain to have 18% OS c) Find the settling time of the uncompensated system d) Find the angle q (cos q = z) C(s) Design of the Compensator: e) Find the position of the Desired Pole to have Ts = 0.5 second and continue having 18% OS f) Use trigonometry to find the angle and position of the compensator, this find qZc and Zc g) Give the transfer function of the compensator Root Locus 0.479
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