A self-balancing robot is an inverted-pendulum example problem. The idea is to keep the robot upright by driving the wheels towards the leaning angle theta. When the robot is tilting forward, the wheels should be driven forward with a specific acceleration to counter the tilting. This will keep the robot in an upright position at all times. The block diagram of the system shown in Figure 3 with transfer function of G(s) = 1/s(s+1)(s2+4s+20) and H(s) = 1. a) Sketch the root locus by indicating the poles and zeros location on the loci. b) Locate the asymptotes on the root locus in (a). c) Determine the range of K to keep the system stable. d) Identify the jco axis crossing on the root locus in (a).
A self-balancing robot is an inverted-pendulum example problem. The idea is to keep the robot upright by driving the wheels towards the leaning angle theta. When the robot is tilting forward, the wheels should be driven forward with a specific acceleration to counter the tilting. This will keep the robot in an upright position at all times. The block diagram of the system shown in Figure 3 with transfer function of G(s) = 1/s(s+1)(s2+4s+20) and H(s) = 1. a) Sketch the root locus by indicating the poles and zeros location on the loci. b) Locate the asymptotes on the root locus in (a). c) Determine the range of K to keep the system stable. d) Identify the jco axis crossing on the root locus in (a).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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A self-balancing robot is an inverted-pendulum example problem. The idea is to keep the
robot upright by driving the wheels towards the leaning angle theta. When the robot is tilting
forward, the wheels should be driven forward with a specific acceleration to counter the
tilting. This will keep the robot in an upright position at all times. The block diagram of the
system shown in Figure 3 with transfer function of G(s) = 1/s(s+1)(s2+4s+20) and H(s) = 1.
a) Sketch the root locus by indicating the poles and zeros location on the loci.
b) Locate the asymptotes on the root locus in (a).
c) Determine the range of K to keep the system stable.
d) Identify the jco axis crossing on the root locus in (a).
Transcribed Image Text:Input
R(s)
Actuating
signal
E (s)
Forward
transfer
function
KG(s)
H(s)
Feedback
transfer
function
Output
C(s)
Figure 3: A Feedback Control System Block Diagram
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