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Objective To evaluate the effect of additional poles and zeros upon the time response of
second- order systems.
Minimum required software packages
MATLAB, Simulink, and the Control System Toolbox
Prelab
?
1.
(a) Given the transfer function, G(s) ??
25
. Evaluate the percent overshoot, settling time,
s ? 4s ? 25
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peak time, and rise time. Also, plot the poles.
(b) Add a pole at -200 to the system of (a). Estimate whether the transient response in (a) will be
appreciably affected.
(c) Repeat (b) with the pole successively placed at -20, -10, and -2.
2. A zero is added to the system of Prelab 1(a) at -200 and then moved to -50, -20, -10,
-5, and -2. List the values of zero location in the order of the most to the least effect upon the pure
second-order transient response.
3. Given the transfer function, G(s) ??
(25b / a)(s ? a)
: Let a ? 3 and b = 3.01, 3.1, 3.3, 3.5,
(s ? b)(s2 ? 4s ? 25)
and 4.0. Which values of b will have minimal effect upon the pure second-order transient
response?
4. Given the transfer function, G(s) ??
(2500b / a)(s ? a)
: Let a = 30 and b = 30.01, 30.1,
(s ? b)(s2 ? 40s ? 2500)
30.5, 31, 35, and 40. Which values of b will have minimal effect upon the pure second-order
transient response?
Lab
1. Using Simulink, add a pole to the second-order system of Prelab 1(a) and plot the step responses
of the system when the higher-order pole is nonexistent, at -200, -20, -10, and -2. Make your plots
on a single graph using the Simulink LTI Viewer. Normalize all plots to a steady-state value of
unity. Record percent overshoot, settling time, peak time, and rise time for each response.
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2. Using Simulink, add a zero to the second-order system of Prelab 1(a) and plot the step responses
of the system when the zero is nonexistent, at -200, -50, -20, -10, -5, and -2. Make your plots on a
single graph using the Simulink LTI Viewer. Normalize all plots to a steady-state value of unity.
Record percent overshoot, settling time, peak time, and rise time for each response.
3. Using Simulink and the transfer function of Prelab 3 with a = 3, plot the step responses of the
system when the value of b is 3, 3.01, 3.1, 3.3, 3.5 and 4.0. Make your plots on a single graph
using the Simulink LTI Viewer. Record percent overshoot, settling time, peak time, and rise time
for each response.
4. Using Simulink and the transfer function of Prelab 4 with a = 30, plot the step responses of the
system when the value of b is 30, 30.01, 30.1, 30.5, 31, 35, and 40. Make your plots on a single
graph using the Simulink LTI Viewer. Record percent overshoot, settling time, peak time, and rise
time for each response.
Postlab
1. Discuss the effect upon the transient response of the proximately of a higher-order pole to the
dominant second-order pole pair.
2. Discuss the effect upon the transient response of the proximately of a zero to the dominant
second-order pole pair. Explore the relationship between the length of the vector from the zero to
the dominant pole and the zero?s effect upon the pure second-order step response.
3. Discuss the effect of pole-zero cancellation upon the transient response of a dominant secondorder pole pair. Allude to how close the canceling pole and zero should be and the relationships of
(1) the distance between them and (2) the distance between the zero and the dominant second-order
poles.
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