Constructive Non-linear Control Design With Applications...
Transcript of Constructive Non-linear Control Design With Applications...
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Constructive Non-linear Control Design With
Applications to Quad-Rotor and Fixed-Wing
Aircraft
Nicholas Kottenstette, Joseph Porter
ISIS-Vanderbilt University
December 2, 2009
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Outline
To make (distributed) control system design and synthesis
intuitive and robust via constructive formalisms
Recent Milestones
Fixed-Wing Aircraft Literature Review
Main Idea (back-stepping control)
Quad-rotor Dynamics/ Control/ Simulation
Fixed-Wing Aircraft Dynamics
Airframes Library
Fixed-Wing Control Equations
Velocity Control Subsystem
Body Angular Velocity Control
Angle-of-attack, slide-slip-angle, bank-angle Control
Preliminary Simulations
Future Directions
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Recent MilestonesJournal Papers:
Kottenstette N., Hall J., Koutsoukos X., Antsaklis P., Sztipanovits J., "Digital
Control of Multiple Discrete Passive Plants Over Networks", Int. J. of
Systems, Control and Communications Special Issue on “Progress in
Networked Control Systems”, pp. 1-20 (to appear)
Conference / Workshop Papers:
N. Kottenstette, J. Porter “Digital Passive Attitude and Altitude Control
Schemes for Quadrotor Aircraft”, 7th IEEE International Conference on
Control & Automation (ICCA’09), Christchurch, New Zealand, December
2009. (invited chair Aircraft Control and Aerodynamic Systems)
Kottenstette, N., Chopra, N., "Lm2-stable digital-control networks for
multiple continuous passive plants", NecSys'09, Venice, Italy, September,
2009.
Nicholas Kottenstette, Gabor Karsai, and Janos Sztipanovits, “A Passivity-
based Framework for Resilient Cyber-Physical Systems”, 2nd International
Symposium on Resilient Control Systems (ISRCS 2009), August 11-13,
2009, Idaho Falls, Idaho.
Technical Report:
Kottenstette, N., H. LeBlanc, E. Eyisi, and X. Koutsoukos, "Multi-Rate
Networked Control of Conic Systems", Technical Report, Nashville, TN,
Institute for Software Integrated Systems, Vanderbilt University, 09/2009.
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Fixed-Wing Aircraft Literature Review
Key Fixed-Wing Aircraft Control:
J. Farrell, M. Sharma, and M. Polycarpou, “Backstepping-based flight
control with adaptive function approximation,” Journal of Guidance, Control,
and Dynamics, vol. 28, no. 6, pp. 1089–1102, 2005.
O. Harkegard, “Backstepping and control allocation with applications to
flight control,” Ph.D. dissertation, Linkoping University, 2003.
B. L. Stevens and F. L. Lewis, Aircraft Control and Simulation, 2nd ed. John
Wiley & Sons, Inc., 2003.
S.L. Morris, D.E. Bossert and W.F. Hallgren, Introduction to Aircraft Flight
Mechanics, Performance, Static Stability, Dynamic Stability, and Classical
Feedback Control, AIAA Education Series, 2003.
Key Fixed-Wing Aircraft Formation Control:
G. Campa, Y. Gu, B. Seanor, M. Napolitano, L. Pollini, and M. Fravolini,
“Design and flight-testing of non-linear formation control laws,” Control
Engineering Practice, vol. 15, no. 9, pp. 1077–1092, 2007. [airlib]
Y. Zou, P. Pagilla, and R. Ratliff, “Distributed Formation Flight Control Using
Constraint Forces,” JOURNAL OF GUIDANCE, CONTROL, AND
DYNAMICS, vol. 32, no. 1, 2009.
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Main Idea (back-stepping control)
1( )f x
1( )g x1x
1x
2 ( )f x
2 ( )g x2x
2x1u
1 1 1 1( ) ( )x f x g x u
2 2 2 1( ) ( )x f x g x x
J. Farrell, M. Sharma, and M. Polycarpou, “Backstepping-based flight control with
adaptive function approximation,” Journal of Guidance, Control, and Dynamics, vol. 28,
no. 6, pp. 1089–1102, 2005.
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Recursive Control Strategy
1( )f x
1( )g x1x
1x1u1
1 ( )g x
1( )f x
1k1dx
1dx
111 1 1 1 1 1( ) ( ) ( ) ddu g x k x x f x x
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Ideal Feedback and Feedforward Comp.
1x
1x
1k1dx
1dx
11dx 1x
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Recursive Control Strategy
2 ( )f x
2 ( )g x2x
2x1dx1
2 ( )g x
2 ( )f x
2k2dx
2dx
121 2 2 2 2 2( ) ( ) ( ) dd dx g x k x x f x x
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Quad-Rotor Dynamics
( )
( )
( )
0 1 sin( ) tan( ) cos( ) tan( )
[ , , ] , 0 , ( ) 0 cos( ) sin( )
0 sin( ) cos( )0
cos( ) cos( )
[ , , ] , ( )
I
TI I D ab
T
T
v
mv f mge R f
I I
J
r q
p q r r p J
q p
c c c s s
R s s
c s c
( ) ( ) , ( ) ( ) ( ), ( )T T
I
c c s s s s c c c s
s s c s s s c c c
R R I R R R
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Quad-Rotor Control
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Quad-Rotor Simulation
0 10 20 30 40 50 60 70 80-25
-20
-15
-10
-5
0
5
10
15
20
25
time (s)
(m
)
xI
yI
zI
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Quad-Rotor Simulation
0 10 20 30 40 50 60 70 80
-3
-2
-1
0
1
2
3
time (s)
(ra
dia
ns)
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Fixed-Wing Aircraft Dynamics
2 1 1
/
( ) , diag , , , ,
1[ , , ] , , , tan , sin
2
cos( ) 0 sin( )
[ , , ] , ( ) 0 1 0
sin( ) 0 cos( )
T
l m n d
T T T
b b b I I
Ds
T
as Ds Y L ab b s as Y
L
I I qS b c b C C C
w vv u v w V v v v v q V
u V
C
f qS C C C f R f qS C
C
DDin Dq
Yp Yr Y Y
Lin Lq L
0 00 01
0 02
0 0 0 0
e
a r
e
Ds D Do f e
Y Y Yo a
L L Lo f r
l l
m
n
CC C C C C c p
C C C C b C b q C CV
C C C C C c r C
C C
C
C
l llp lr
min mq m
np nr m m
001
0 0 0 02
0 0
a r
e
a r
lo e
m mo f a
n no r
C CC C b C b p
C C C C c q CV
C C C b C b r C C
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Airframes Library
http://www.ae.illinois.edu/m-selig/apasim/Aircraft-uiuc.html
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Airframes Library
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Relevant Fixed-Wing Equations for Control
1
2
3
cos cos
cos sin
cos sin cos sin( )
cos 0 sin cos sin 0
0 1 0 , sin cos 0
sin 0 cos 0 0 1
T
T s
T s
s
s
s
mV F D mg
mV F C mg mVr
mV F L mg mV q p
p p D
q q C qS
r r L
1 3
1 11 2
2 2 2 2
1 2 1 2
1 1
Velocity flight-path angle, , - =sin
Velocity heading-angle, cos sin
Bank-angle, cos sincos
Ds
Y
L
I
I I
I I I I
C
C
C
v
V
v v
v v v v
c s c cc c c s s
1 2 3
cos
( )sin , ( )sin cos , ( ) cos cos
s s c c s
g g h g g h g g h
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Relevant Fixed-Wing Equations for Control
1cos sin cos
1cos sin
1
cos
T
T
sT
gC L F s c c s s
V mV
C L F s s c s cmV
pgCt c L t t s F s s t s t c s c t t c c
mV V
Velocity
ControllerdV TF
Vel-Angle
Controller
,T
d d ,T
d d
0
Aerodynamic
-Angle
Controller
, ,T
d d dp q r
Body-
angular
Velocity
Controller
, ,T
e a r
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Velocity Control Subsystem
Do Din
Dq
D D
Do Din set
( )2
( ) ( )
e
T f v
v e
dT v f d I
mV F qS C C f x
C cf x qS C q C mg h
V
sF f x mg h qS C C m V mK V V
s
set
( )
( )
I
I
KV s
V s s K
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Angle-of-attack, slide-slip-angle, bank-angle Control
1 00 0 0( )
0 0 ( ) 0 1 04
( )
0 0 0 14 4
( )
LqT L
T YYp Yr
a
f x pC cF qSC
f x qmV m
f x rF qSC C b C b
mV m m
a A x a
1
2( ) ( ) , ( ) ( ) ( )c a df x G x G x f x k a a
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Body Angular Velocity Control
set( ) , ( )d dI I k
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Preliminary Simulations
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Future Directions
Short Term:
Finish Flight-Path Heading Angle and Velocity Heading Angle
Controller Design
Evaluate Controller Performance When Subject to Wind
Disturbances
Include 101-[1,4] and 201-[1,4] airframe-configurations
described in WL-TR-97-3059
Long Term:
Use Power-Junction Like Structure to Implement Formation
Control System
Investigate Adaptive Control Structures
Consider Actuator Rate and Dynamic Limitations
Improve back-stepping control synthesis tools