Control and Guidance law for Guided Bomb
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Transcript of Control and Guidance law for Guided Bomb
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Conventional Guidance & Control Design
.Mohammed Osman,
Project AssociateDept. of Aerospace Engineering
Indian Institute of Science - Bangalore
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21-Jan-2011 G & C of Air-dropped Bomb 2
Conventional Guidance & Control Philosophy
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21-Jan-2011 G & C of Air-dropped Bomb 3
PN Guidance Law
cos( ( )) cos( ( ))c t t m mV r V V
sin( ( )) sin( ( ))t t m mV r V V
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21-Jan-2011 G & C of Air-dropped Bomb 4
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21-Jan-2011 G & C of Air-dropped Bomb 5
Outer Loop - Latax Generation
V r r V r r
( . ) ( . )r V r r r r
( . )r Vr r
. 0r
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21-Jan-2011 G & C of Air-dropped Bomb 6
Outer Loop - Latax Generation Required information are relative velocity and distance
between Target and Munitions, Munitions flight path angles
Then LOS rate in inertial frame
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21-Jan-2011 G & C of Air-dropped Bomb 7
Outer Loop - Latax Generation Transform LOS rate from Inertial frame to velocity frame using
and
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21-Jan-2011 G & C of Air-dropped Bomb 8
Outer Loop -Command Transfer Loop Desired Angle of Attack (AOA)
generation in Pitch and Yaw plane, for tracking Latax commands in Pitch and Yaw plane.
Given data is in Body frame, convert it to velocity frame for Lift slope calculation.
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21-Jan-2011 G & C of Air-dropped Bomb 9
Outer Loop -Command Transfer Loop Compare below Flight path equation for calculations of desired
Corresponding equations in 6-DOF
Corresponding equations in 3-DOF
and
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21-Jan-2011 G & C of Air-dropped Bomb 10
Outer Loop -Command Transfer Loop
Solve first equation for directly Solve second equation for by numerical assuming
Drag (D) is constant. By CGC we can control and , so we can keep
bound on and
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21-Jan-2011 G & C of Air-dropped Bomb 11
Body Rate Generation- AOA Tracking
Desired AOA Tracking Desired Body rates Generation Desired Body rates Tracking
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21-Jan-2011 G & C of Air-dropped Bomb 12
Body Rate Generation- AOA Tracking
Rearrange below equation to get desired body rate
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21-Jan-2011 G & C of Air-dropped Bomb 13
Desired Body Rate Generation Final expression for desired Body rates with roll stabilization are
Here we took desired roll rate zero for roll stabilization
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21-Jan-2011 G & C of Air-dropped Bomb 14
Body Rate Tracking Loop In this loop using DI method we can get required control
surface deflections
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21-Jan-2011 G & C of Air-dropped Bomb 15
Body Rate Tracking Loop
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21-Jan-2011 G & C of Air-dropped Bomb 16
Parameters and Simulation Initial Conditions Taken
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Results
Dr. Radhakant Padhi (PI), Associate Prof.
Mohammed Osman, Project Associate
Mayuri Tatiya, Project AssistantDept. of Aerospace Engineering
Indian Institute of Science - Bangalore
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21-Jan-2011 G & C of Air-dropped Bomb 18
02000
40006000
8000
-1000
-500
0
500
10000
500
1000
1500
2000
2500
3000
Downrange (m)Crossrange (m)
Altitu
de (m
)
Simulation Results
-1000 0 1000 2000 3000 4000 5000 6000 -1000
0
1000
0
500
1000
1500
2000
2500
3000
Crossrange (m)
X: 5189Y: 500Z: 0
Downrange (m)
Altitu
de (m
)
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21-Jan-2011 G & C of Air-dropped Bomb 19
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60200
300
400
500
u (m/
s)
0 10 20 30 40 50 60-50
0
50
100
v (m/
s)
0 10 20 30 40 50 60-50
0
50
100
Time (sec)
w (m
/s)
02000
40006000
800010000
0
500
1000
1500
0
2000
4000
6000
8000
10000
Downrange (m)Crossrange (m)
Altitu
de (m
)
Free fall
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21-Jan-2011 G & C of Air-dropped Bomb 20
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60-1
0
1
p (de
g/s)
0 10 20 30 40 50 60-50
0
50
q (de
g/s)
0 10 20 30 40 50 60-40
-20
0
20
Time (sec)
r (de
g/s)
0 10 20 30 40 50 60-1
0
1
p* (d
eg/s
)0 10 20 30 40 50 60
-50
0
50
q* (d
eg/s)
0 10 20 30 40 50 60-40
-20
0
20
Time (sec)
r* (de
g/s)
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21-Jan-2011 G & C of Air-dropped Bomb 21
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60-1
0
1
p-p* (
deg/s
)
0 10 20 30 40 50 60-40
-20
0
20
q-q* (
deg/s
)
0 10 20 30 40 50 60-5
0
5
10
r-r* (
deg/s
)
0 10 20 30 40 50 600.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Time (sec)
Mach
Num
ber
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21-Jan-2011 G & C of Air-dropped Bomb 22
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60-10
0
10
20
(d
eg)
0 10 20 30 40 50 60-10
-5
0
5
10
15
Time (sec)
(de
g)
0 10 20 30 40 50 60-2
-1
0
1
2
3
Time(sec)
Pitch
lata
x (g)
0 10 20 30 40 50 60-3
-2
-1
0
1
Time(sec)
Yaw
latax
(g)
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21-Jan-2011 G & C of Air-dropped Bomb 23
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60-10
-5
0
5
e (d
eg)
0 10 20 30 40 50 60-1
0
1
a (d
eg)
0 10 20 30 40 50 60-4
-2
0
2
Time (sec)
r (de
g)
Comnd
0 10 20 30 40 50 60-10
-5
0
5
e (d
eg)
0 10 20 30 40 50 60-1
0
1
a (d
eg)
0 10 20 30 40 50 60-4
-2
0
2
Time (sec)
r (de
g)
Actual
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21-Jan-2011 G & C of Air-dropped Bomb 24
Numerical Results: Target at (9705,1000)
0 10 20 30 40 50 60-20
0
20
40
(de
g)
0 10 20 30 40 50 60-100
-50
0
50
(de
g)
0 10 20 30 40 50 60-20
0
20
40
Time (sec)
(d
eg)
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21-Jan-2011 G & C of Air-dropped Bomb 25
Numerical Results: Target at (11000,0)
0 10 20 30 40 50 60200
300
400
500
u (m/
s)
0 10 20 30 40 50 60-0.1
0
0.1
v (m/
s)
0 10 20 30 40 50 60-50
0
50
100
Time (sec)
w (m
/s)
020004000600080001000012000
-1
-0.5
0
0.5
1
0
2000
4000
6000
8000
10000
Downrange (m)
Crossrange (m)
Altitu
de (m
)
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21-Jan-2011 G & C of Air-dropped Bomb 26
Numerical Results: Target at (11000,0)
0 10 20 30 40 50 60-1
0
1
p (de
g/s)
0 10 20 30 40 50 60-10
0
10
20
q (de
g/s)
0 10 20 30 40 50 60-0.2
0
0.2
0.4
Time (sec)
r (de
g/s)
0 10 20 30 40 50 60-1
0
1
p-p* (
deg/s
)0 10 20 30 40 50 60
-40
-20
0
20
q-q* (
deg/
s)
0 10 20 30 40 50 60-10
-5
0
5
r-r* (
deg/s
)
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21-Jan-2011 G & C of Air-dropped Bomb 27
Numerical Results: Target at (11000,0)
0 10 20 30 40 50 60-10
0
10
20
(d
eg)
0 10 20 30 40 50 60-10
-5
0
5
Time (sec)
(d
eg) Achieved
Commnded
0 10 20 30 40 50 60-3
-2
-1
0
1
Time(sec)
Pitch
lata
x (g)
0 10 20 30 40 50 60-0.5
0
0.5
1
Time(sec)
Yaw
latax
(g)
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21-Jan-2011 G & C of Air-dropped Bomb 28
Numerical Results: Target at (11000,0)
0 10 20 30 40 50 60-10
-5
0
5
e (d
eg)
0 10 20 30 40 50 60-1
0
1
a (d
eg)
0 10 20 30 40 50 60-0.05
0
0.05
0.1
Time (sec)
r (de
g)
Actual
0 10 20 30 40 50 60-0.02
-0.01
0
0.01
(d
eg)
0 10 20 30 40 50 60-100
-50
0
50
(de
g)
0 10 20 30 40 50 60-0.01
0
0.01
0.02
Time (sec)
(d
eg)
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21-Jan-2011 G & C of Air-dropped Bomb 29
Thanks for the Attention….!!