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
21-Jan-2011 G & C of Air-dropped Bomb 2
Conventional Guidance & Control Philosophy
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
21-Jan-2011 G & C of Air-dropped Bomb 4
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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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
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
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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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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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
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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Body Rate Generation- AOA Tracking
Rearrange below equation to get desired body rate
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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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Body Rate Tracking Loop In this loop using DI method we can get required control
surface deflections
21-Jan-2011 G & C of Air-dropped Bomb 15
Body Rate Tracking Loop
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Parameters and Simulation Initial Conditions Taken
Results
Dr. Radhakant Padhi (PI), Associate Prof.
Mohammed Osman, Project Associate
Mayuri Tatiya, Project AssistantDept. of Aerospace Engineering
Indian Institute of Science - Bangalore
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
)
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
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)
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
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)
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
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)
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
)
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
)
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)
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)
21-Jan-2011 G & C of Air-dropped Bomb 29
Thanks for the Attention….!!
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