Lab4_jaleti
.pdf
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Physics
Date
Apr 3, 2024
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Uploaded by SuperIronDragonfly3078
Lab 4: The swing up pendulum. (Answer Sheet)
∗
Name:
∗
Part of this write-up and figures were taken directly from Quanser’s lab manuals, Quanser Inc.
1
Joshita
Alexi
1
Total energy
1.1
Experiment: the controller using
E
.
Figure 1: Simulink model used with QUARC to run swing-up controller
In this experiment, we will design a controller of the form
u
= sat
u
max
⇣
k
e
(
E
-
E
r
) ˙
↵
cos(
↵
)
⌘
.
(1.1)
1. Run the setup
swingup.m file in Matlab.
2. Open and run the QUARC Swingup.slx in Matlab. This should look like Figure 1.
3.
Be ready to hit the stop button at any time in case the pendulum goes wild.
Place your critical value (minimum value to make the pendulum stand up)
E
r
with
k
e
= 1
here:
Place your best
k
e
and
E
r
here:
2
Er
=
3500
m5
~
34
seconds
for
pendulum
to
stand
up
We
=
60
M5s
Er
=
50 mJ
For your best
k
e
and
E
r
place the graph of the pendulum angle here:
For your best
k
e
and
E
r
place the graph of the pendulum energy
E
here:
3
1.2
Experiment: the controller
E
with the sign function.
In the final experiment, we will design a controller of the form
u
= sat
u
max
⇣
k
e
(
E
-
E
r
)sign( ˙
↵
cos(
↵
))
⌘
.
(1.1)
1. Run the setup
swingup.m file in Matlab.
2. Run the QUARC file Swingup
sign.slx in Matlab. This should look like Figure 1.
3.
Be ready to hit the stop button at any time in case the pendulum goes wild.
Place your best
k
e
and
E
r
here:
For your best
k
e
and
E
r
place the graph of the pendulum angle here:
4
ke
=
30 M5/5
Er
=
85M]
2
Kinetic energy
2.1
Experiment: the controller using
E
c
.
Figure 2: Simulink model used with QUARC to run swing-up controller
In this experiment, we will design a controller of the form
u
c
= sat
u
max
⇣
k
e
(
E
c
-
E
r
) ˙
↵
cos(
↵
)
⌘
(2.1)
1. Run the setup
swingup.m file in Matlab.
2. Open the Swingup
center.slx in Matlab. This should look like QUARC model presented
in Figure 2. Hit monitor and tune to run this file.
3.
Be ready to hit the stop button at any time in case the pendulum
goes wild.
Place your critical value (minimum value to make the pendulum stand up)
E
r
with
k
e
= 1
here:
Place your best
k
e
and
E
r
here:
5
Er
=
50
~
13
.
922
seconds
for
pendulum
to
stand
up
Ke
=
10
M5
,
s
Er
=
20
m5
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