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Linear Systems Simulation Part II and III
Perform the required tasks as described in this document
Required tasks:
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A professionally written report as one Master Doc file
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MATLAB/Simulink files
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It is your responsibility to convince me, with the results you provide, that your system
works properly.
Objective To evaluate the effect of pole and zero location upon the time response of first- and
second- order systems.
Minimum required software packages
Prelab
MATLAB, Simulink, and the Control System Toolbox
a
: Evaluate settling time and rise time for the following
s a
values of a : 1, 2, 3, 4. Also, plot the poles.
b
.
2. Given the transfer function, G(s) 2
s as b
(a) Evaluate percent overshoot, settling time, peak time, and rise time for the following values:
a = 4, b = 25. Also, plot the poles.
1. Given the transfer function, G(s)
(b) Calculate the values of a and b so that the imaginary part of the poles remains the same, but
the real part is increased 2times over that of (a), and repeat Prelab 2(a).
(c) Calculate the values of a and b so that the imaginary part of the poles remains the same, but
the real part is decreased ½ time over that of (a), and repeat the Prelab 2(a).
3.
(a) For the system of Prelab 2(a), calculate the values of a and b so that the real part of the poles
remains the same, but the imaginary part is increased 2 times over that of Prelab 2(a), and repeat
Prelab 2(a).
(b) For the system of Prelab 2(a), calculate the values of a and b so that the real part of the poles
remains the same, but the imaginary part is increased 4 times over that of Prelab 2(a), and repeat
Prelab 2(a).
4.
(a) For the system of Prelab 2(a), calculate the values of a and b so that the damping ratio
remains the same, but the natural frequency is increased 2 times over that of Prelab 2(a), and
repeat Prelab 2(a).
(b) For the system of Prelab 2(a), calculate the values of a and b so that the damping ratio
remains the same, but the natural frequency is increased 4 times over that of Prelab 2(a), and
repeat Prelab 2(a).
5. Briefly describe the effects on the time response as the poles are changed in each of Prelab 2, 3,
and 4.
Lab
1. Using Simulink, set up the systems of Prelab 1 and plot the step response of each of the 4
transfer functions on a single graph by using the Simulink LTI Viewer. Also, record the values of
settling time and rise time for each step response.
2. Using Simulink, set up the systems of Prelab 2. Using the Simulink LTI Viewer, plot the step
response of each of the 3 transfer functions on a single graph. Also, record the values of percent
overshoot, settling time, peak time, and rise time for each step response.
3. Using Simulink, set up the systems of Prelab 2(a) and Prelab 3. Using the Simulink LTI Viewer,
plot the step response of each of the 3 transfer functions on a single graph. Also, record the values
of percent overshoot, settling time, peak time, and rise time for each step response.
4. Using Simulink, set up the systems of Prelab 2(a) and Prelab 4. Using the Simulink LTI Viewer,
plot the step response of each of the 3 transfer functions on a single graph. Also, record the values
of percent overshoot, settling time, peak time, and rise time for each step response.
Postlab
1. For the first-order systems, make a table of calculated and experimental values of settling time,
rise time, and pole location.
2. For the second-order systems of Prelab 2, make a table of calculated and experimental values of
percent overshoot, settling time, peak time, rise time, and pole location.
3. For the second-order systems of Prelab 2(a) and Prelab 3, make a table of calculated and
experimental values of percent overshoot, settling time, peak time, rise time, and pole location.
4. For the second-order systems of Prelab 2(a) and Prelab 4, make a table of calculated and
experimental values of percent overshoot, settling time, peak time, rise time, and pole location.
5. Discuss the effect of pole location upon the time response for both first- and second-order
systems. Discuss any discrepancies between your calculated and experimental values.
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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.
25
. Evaluate the percent overshoot, settling time,
s 4s 25
peak time, and rise time. Also, plot the poles.
(a) Given the transfer function, G(s)
2
(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.
(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?
3. 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?
4. Given the transfer function, G(s)
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.
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
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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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