CALIFORNIA PATH PROGRAM
INSTITUTE OF TRANSPORTATION STUDIES
UNIVERSITY OF CALIFORNIA, BERKELEY
Brake System Modeling, Control and
Integrated Brake/Throttle Switching:
Phase I
J.K. Hedrick, J.C. Gerdes,
D.B. Maciuca, D. Swaroop
Universtiy of California, Berkeley
California PATH Research Report
UCB-ITS-PRR-97-21
This work was performed as part of the California PATH Program of the
University of California, in cooperation with the State of California Business,
Transportation, and Housing Agency, Department of Transportation; and the
United States Department of Transportation, Federal Highway Administration.
The contents of this report reflect the views of the authors who are responsible
for the facts and the accuracy of the data presented herein. The contents do not
necessarily reflect the official views or policies of the State of California. This
report does not constitute a standard, specification, or regulation.
Report for MOU 101
May 1997
ISSN 1055-1425
CALIFORNIA PARTNERS FOR ADVANCED TRANSIT AND HIGHWAYS
This paper uses Postscript Type 3 fonts.
Although reading it on the screen is difficult
it will print out just fine.
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Pressure (kPa)
2000
1500
1000
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2500
2000
1500
1000
500
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500
1000
1500
2000
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Brake Pressure (kPa)
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3000
Brake Hydraulic Pressure (kPa)
2500
2000
1500
1000
Master Cylinder
500
Wheel (simulated)
Wheel (measured)
0
−500
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (seconds)
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0.45
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Slow and Step Input Forces
400
350
Slow Input
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300
250
200
Step Input
150
100
50
0
0
1
2
3
4
5
6
Time (seconds)
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6.5
Vac (sim)
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5.5
5
4.5
4
3.5
3
0
1
2
3
4
5
6
Time (seconds)
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Experimental and Simulated Master Cylinder Pressures − Slow Apply
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3.5
Pressure (Pa)
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2.5
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1.5
1
0.5
0
−0.5
0
1
2
3
4
5
6
Time (seconds)
7
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5
4.5
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3.5
3
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1
2
3
4
5
6
Time (seconds)
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3
4
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Net Engine Torque (Nm)
400
300
200
100
0
−100
150
5000
100
4000
3000
50
2000
1000
Manifold Pressure (kPa)
0
0
Engine Speed (rpm)
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Throttle Characteristic Table Data
1
0.9
Throttle Characteristic, TC
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
Throttle Angle (degrees)
70
80
90
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140
120
maodot (kg/s)
100
80
60
40
20
0
150
5000
100
4000
3000
50
2000
1000
0
Manifold Pressure (kPa)
0
Engine Speed (rpm)
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Time (seconds)
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Velocity of Synthetic Lead Vehicle
23
Velocity (m/s)
22.5
22
21.5
21
20.5
20
0
2
4
6
8
10
12
Time (seconds)
14
16
18
20
16
18
20
16
18
20
Acceleration of Synthetic Lead Vehicle
Acceleration (m/s/s)
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
Time (seconds)
14
Calculated Value of asynth for Follower
Acceleration (m/s/s)
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
Time (seconds)
14
{-|~}EOC-oC
{@how#Gk[6!|~jCr|KkM#h#T|~~wMb#E
h
Spacing Error During Maneuver
Spacing Error (meters)
0.01
0.005
0
−0.005
−0.01
0
2
4
6
8
10
12
Time (seconds)
14
16
18
20
16
18
20
16
18
20
Actual and Desired Manifold Pressures
Manifold Pressure (kPa)
100
80
60
40
20
0
0
2
4
6
8
10
12
Time (seconds)
14
Actual and Desired Brake Pressures
Caliper Pressure (kPa)
600
500
400
300
200
100
0
0
2
4
6
8
10
12
Time (seconds)
14
{|}ETGC o¡T
\{@h~zw#x¢M
£¤¤r|~¥¢¦y¨§4©¥#|~ª-@h#¬«CGy@h|@®
¯y°
Velocity of Lead Vehicle
24
Velocity (m/s)
23
22
21
20
19
0
2
4
6
8
10
12
Time (seconds)
14
16
18
20
14
16
18
20
16
18
20
Acceleration of Lead Vehicle
Acceleration (m/s/s)
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
Time (seconds)
Calculated Value of asynth for Follower
Acceleration (m/s/s)
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
Time (seconds)
14
±-²~³E´µ¶¸·¤¹~ ºT»±R¼y½~½~¼o¾¿¶µG¢MÀ¾ÂÁM¶#ÃÅÄG¾!²ÄÆÇ¢¦¶Àh¶#ÆC²½¶ÈwÁµÀyb¶#ļEµÅÉ
¯ Spacing Error During Maneuver
Spacing Error (meters)
0.015
0.01
0.005
0
−0.005
−0.01
−0.015
0
2
4
6
8
10
12
Time (seconds)
14
16
18
20
16
18
20
16
18
20
Actual and Desired Manifold Pressures
Manifold Pressure (kPa)
100
80
60
40
20
0
0
2
4
6
8
10
12
Time (seconds)
14
Actual and Desired Brake Pressures
Caliper Pressure (kPa)
600
500
400
300
200
100
0
0
2
4
6
8
10
12
Time (seconds)
14
±-²~³E´µ¶¸·C¹~ o·C»±@¼h½~½~¼o¾¿¶µ6¢À¾»x¢¦¶Àh¶#ÆC²½¶v§©¥¶Ã²~µ¶#Bx@ÀhÃÆ¶#¬«0GÄ´@Ày½2xüy½~²~R®
¯hÊ
Velocity of Lead Vehicle
Velocity (m/s)
30
25
20
15
0
5
10
15
Time (seconds)
20
25
20
25
20
25
Acceleration of Lead Vehicle
Acceleration (m/s/s)
1
0
−1
−2
−3
0
5
10
15
Time (seconds)
Calculated Value of asynth for Follower
Acceleration (m/s/s)
1
0
−1
−2
−3
0
5
10
15
Time (seconds)
±-²~³E´µ¶¸·C¹ »Ë+̤ĵ¶Íd¶K±@¼h½½¼o¾w¶#µ6¢MÀ¾ÂÁM¶#ÃÄ6¾!²ÄÆÇ¢M¶#Àhζ#ÆT²~Ͻ~¶wÁMµÀb¶#ÏļEµÉ
¯¡
Spacing Error During Maneuver
Spacing Error (meters)
0.03
0.02
0.01
0
−0.01
−0.02
0
5
10
15
Time (seconds)
20
25
20
25
20
25
Actual and Desired Manifold Pressures
Manifold Pressure (kPa)
100
80
60
40
20
0
0
5
10
15
Time (seconds)
Actual and Desired Brake Pressures
Caliper Pressure (kPa)
2000
1500
1000
500
0
0
5
10
15
Time (seconds)
±²³E´Tµ¶·¤¹~ ¯ »G±@¼h½½~¼z¾w¶#µ¥¢À¾»GË+ÌCĵ¶Íª¶Ð¾!²ÄÆ;¢¦¶ÀyÎѧ©¥¶Ã²~µ¶#ÎÓÒÔÎ@ÀhÃÆT¶#Î2«2GÏÄ´@Ày½-Ò
üh½²ÎR®
¯º
Spacing Errors for 10 Followers in Platoon
0.015
0.01
Spacing Error (meters)
0.005
0
4
−0.005
3
2
−0.01
1
−0.015
−0.02
0
5
10
15
Time (seconds)
20
25
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