adaptive flight control of a sensor guided mk-82 jdam kevin a. wise, ph.d. senior technical fellow...
TRANSCRIPT
Adaptive Flight Control of a Sensor Guided MK-82 JDAM
Kevin A. Wise, Ph.D.Senior Technical Fellow
Integrated Defense Systems
SAE Mtg, 12 October 2006, Williamsburg VA
2
Outline
• Joint Direct Attack Munition (JDAM)
• Laser-JDAM MK-82
• Adaptive Control Overview
• Flight Test Results
• Movies
• Open Problems in Adaptive Control of Aircraft and Weapons
• Summary
3
JDAM Tail-kit
• JDAM (Joint Direct Attack Munition) is a tail-kit for “dumb” bombs that provides:– Actuated fins
– Guidance and control software
– GPS/INS navigation
– Strakes to improve aero
4
BLU-109(2,000 lb)
MK-84(2,000 lb)
MK-83, BLU-110(1,000 lb) MK-82, BLU-111
(500 lb)*
The JDAM Weapon FamilyAffordable, Accurate, Autonomous, Adverse Weather
*Currently in Developmental Test and Evaluation
6
Baseline JDAM Free-FlightTimeline
Sep
arat
ion
Ph
ase
Imp
act
Ph
ase
Altitude
Time
T=0•Release•Start Guidance
T=1 sec•Unlock Fins•Start Autopilot
T=3 sec•Start GPS Search
T=22-30 sec (24 sec typ)•First Navigation Update
T=1 sec to go•Drive AOA to Zero
Target Impact
Roll Over toPull Downon Target
Optimal Guidance PhaseOptimal Guidance Phase
Tra
nsf
er A
lign
men
t
7
Guidance Law Control of Impact Angle
Impact Angle Commands: 30, 40, 50, 60, 70
0
5000
10000
15000
20000
0 10000 20000 30000 40000
Down Range (ft)
Alt
itu
de
(ft)
Target
Release
8
Baseline Control:Feedback Gains Designed Using
Optimal Control + Projection Theory
Optimal Robust Servomechanism Linear Quadratic Regulator (RSLQR)
Augment Dynamics With Integral Control For Perfect
Command Tracking
Optimal Projection To Output Feedback Architecture
z = Az + B• ~ ~
u=-KSFx= -R-1BTPx
ATP+PA+Q-PBR-1BTP = 0~ ~~ ~
Model:
ARE:
CLAW:
S-Plane
X
XX
X
X
00
• Select Dominant Eigenstructure (r,Xr), r<n
• Project Gains (Static)K=KSFXr(CXr)-1
u=-Ky• Analyze Output Feedback
Design• Iterate LQR To Achieve
Desired Bandwidth
X
XX
• AUTOGAIN Tunes LQR Parameters
• Convergence Criteria Focus On Stability/Actuator Rates
• LQR Design Charts Describe Tuning Process
• Preserve Excellent Stability Properties Of State Feedback Using Output Feedback
• Eliminates Sensor H/W Required For State Feedback
X
X
zRn
9
JDAM Greatest Hits Vol 1
Buried Target
Delay Fuze forUndergroundDetonation
Surface Target
Approved for Public Release 9 Oct 1998
10
JDAM Greatest Hits Vol 2
11
AOA Collapsed to Zero at Impact
MK-84 JDAM Just Before Impact
Hole Shows Fins, Strakes, Strap
Tensioning Screws, Launch Lugs
Approved for Public Release 9 Oct 1998
12
Laser JDAM Program
• Laser JDAM adds a laser seeker to the baseline MK-82– Laser designator is used to paint target– Weapon flies optimal GPS/INS to fixed coordinates until
laser sensor is in range– After laser acquisition, weapon guides to target
• Added seeker hardware + raceway for wire harness cause Laser MK82 aerodynamics to differ from the baseline
• Adaptive control augmented to the baseline MK-82 autopilot for the MK82 Laser to compensate for the differences
13
Adaptive Control Transitioned ToAdvanced Weapon Systems
Adaptive Control Transitioned ToAdvanced Weapon Systems
• Adaptive Control Based upon Earlier Aircraft Application–Extended to Munitions (00-02) with GST–Boeing IRAD Improvements Focus on System ID,
Implementation, and Actuator Saturation Issues–Design Retrofits Onto Existing Flight Control Laws–Flight Proven on MK-82 L-JDAM, (04-06)–Transitioned To Production JDAM
93 94 95 96 97 98 99 00 01 02 03
Technology Transition Timeline
Intelligent Flight Control System (NASA/Boeing)
F-15 ACTIVE
04
MK-82 L-JDAM
Reconfigurable Control For Tailless
Fighters (AFRL-VA/Boeing)
X-36
MK-84 JDAM
Adaptive Control For Munitions
(AFRL-MN/GST//Boeing)MK-84
AFOSR Adaptive Control of UCAVs I,II
Boeing IRAD
Adaptive Flight Control
05
• Ongoing NASA/Boeing IFCS• Other Transitions
Boeing funds MIT (Dr. A. Annaswamy) to initiate research in
V&V of adaptive systems
Boeing Collaborates With Prof. N.
Hovakimyan at VaTech on limited
actuation
• Gen I, flown 1999, 2003• Gen II, 2002 – 2006
•flight test 4th Q 2005• Gen III, 2006
06
14
Adaptive Augmentation• Retrofits onto an existing autopilot (baseline A/P unchanged)
• Baseline A/P commands incremented/decremented as needed
• Uses a reference model representing the desired closed-loop dynamics
• Adaptive increment makes airframe behave like the reference model
• Adaptation dormant while airframe response matches reference model to within pre-specified tolerance
BaselineAutopilot
AdaptiveControl
ReferenceModel
OptimalGuidance
Airframe
-
+ +
+• Provides robustness to
modeling errors (aero uncertainties)
15
MK-82/L Adaptive Autopilot
• Baseline JDAM autopilot– LQR PI with output projection
– High confidence design, tested extensively and in production
– Constructed using wind-tunnel data and gain-scheduling
• Adaptive augmentation– Developed for the Laser JDAM demonstration program
– Allowed baseline MK-82 autopilot (and gains) to be applied to MK-82 Laser
– Later added to the MK-82 baseline autopilot
– Autopilots of both MK-82 variants now use the same autopilot architecture and gains (including the adaptive components)
– Direct-adaptive control
– No off-line training
16
Generalized Plant and Baseline ControllerOpen-Loop Dynamics
Generalized Plant and Baseline ControllerOpen-Loop Dynamics
1 2
p c
p p p p p
c c c c c
p p p
T T Tx p x c r
x A x B u f x
x A x B r t B F y
y C x D u
u K x K x K r t
21
2 2 1
0 0
0
p pp pp
c p c c p cc c
p p
DC
A Bx xu f x r
B F C A B F D Bx x
Bx x BA
y C x D u C x Du
1 2px A x B u f x B r t
control failures
moment uncertainties
guidance commands
extended system state
inner-loop commands
Tff x x x
system state controller state
17
Reference Model and Adaptive ControlReference Model and Adaptive Control
• Set uncertainties to zero:
• Use baseline A/P:
• Formulate Closed – Loop System Dynamics
– defines nominal closed-loop dynamics achievable under baseline A/P– forms desired dynamics for adaptive augmentation with uncertainties
• Control:
10 , 0m m p mf x
T Tbl x ru u K x K r t
1 2 1
ref ref
T Tref x ref r ref ref
A
e
B
r fx A B K x B B K r t x B tA r
Baseline A/P Adaptive Augmentation
ˆ ˆ ˆT T T T Tbl ad x r x r pu u u K x K r t k x k r t x
ˆ ˆ ˆT T
Tx x r r pu K k x K k r t x
Reflects Desired Weapon
Dynamics
18
Parameter Adaptation
• Theoretical Basis– 2nd Theorem of Lyapunov– Barbalat Lemma– Universal Approximation Property of RBF NN
• Adaptive laws yield bounded tracking performance with all signals bounded, in the presence of uncertainties, (UUB)
– using Dead-zone modification, (enforces robustness to noise) freezes adaptation if:
– using Projection Operator, (bounds adaptive parameters)
– using e – modification, (adds damping and bounds adaptive parameters)
– using μ– modification, (protects against control saturation)
1
1
1
ˆ ˆProj ,
ˆ ˆProj ,
ˆ ˆProj ,
Tx x x
Tr r z
Tp
k k x e P B
k k r t e P B
x e P B
limt
refx x C
refx t x t
Control Weapon Response Through Reference Model.
Uniform Response For Each Weapon
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600 Hz
Vehicle
AZcmd e+ +
--1/sKAZ
+
-
q
Inner Loop
KI
KP
Turn Rate qcmd
3rd OrderElliptic Filter
Fin Mixing
3rd OrderElliptic Filter
MeanFilter
1st Order LagNoise Filter
AZ
Lever Arm * s
+
-
IMU
Actuators
AZ
Cperc
3
100 Hz
a r
adeAdaptive Control cmd
z za a qIncremental Elevator
Command
Adaptive Augmentation of RSLQROptimal Pitch Autopilot
Adaptive Augmentation of RSLQROptimal Pitch Autopilot
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+-
+-
a
r
Error
-
Aycmd=0
+
KPHI
KAY
Vehicle
p 4th OrderElliptic Filter
Fin Mixing
4th OrderElliptic Filter
MeanFilter
1st Order LagNoise Filter
AY
Lever Arm * s
+
-
IMU
Actuators
r 4th OrderElliptic Filter
Transform toStability Axes
ps rs
+
-+
-
Turn Rate rcmd
3
1/s
1/s
KI
KP
600 Hz
AY
Cperc
100 Hz
Inner Loop
e
lead-lag filter
ad ada r Adaptive Control cmd
err y y s sa a p r
Incremental Ail/Rud Commands
Adaptive Augmentation ofRSLQR Optimal Roll-Yaw Autopilot
Adaptive Augmentation ofRSLQR Optimal Roll-Yaw Autopilot
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0 0.02 0.04 0.06 0.08 0.1 0.120
5
10
15
20
25
30
35
40
Mean Aero Perturbation
Nu
mb
er
of
Ca
se
s
Mean Aero Perturbation
Num
ber
of C
ases
0 0.02 0.04 0.06 0.08 0.1 0.120
5
10
15
20
25
30
35
40
Mean Aero Perturbation
Nu
mb
er
of
Ca
se
s
Mean Aero Perturbation
Num
ber
of C
ases
Simulation-Based Evaluation
• Trajectories with both open and closed-loop guidance
• Monte-Carlo Testing:– Aerodynamic uncertainties
Body forces and moments and fin moments (no fin forces)
– c.g. location uncertainty in all three axes
– Winds and turbulence
• Results show adaptive a/pprovides added robustness
Histogram of mean aerodynamic perturbationHistogram of mean aerodynamic perturbation
22
Robustness to Time Delays
• Time delay sensitivity evaluated via simulations (nominal aero)– Sweep through various combinations of input and output time-delay
– Simulation time-histories “eyeballed” to determine goodness and given values based on amount of activity
• Results show more than adequate time-delay margins
5 10 15 20 255
10
15
20
25
30
35
40Nominal A/P Time-Delay Sensitivity
Output Delay (msec)
Inp
ut D
ela
y (m
sec)
5 10 15 20 255
10
15
20
25
30
35
40Adaptive A/P Time-Delay Sensitivity
Output Delay (msec)
Inp
ut D
ela
y (m
sec)
Adaptive a/p Nominal a/p
Nominal hardware time delays below minimum of chart
23
Oct 04 Flight Data (1 of 2)
+30 deg -30 deg
+BETA -BETA
Bank Maneuvers
AOA
Beta
Qbar
Mach
24
Oct 04 Flight Data (2 of 2)
+30 deg -30 deg
+BETA -BETA
Del
e (d
eg)
Del
a (d
eg)
Del
r (d
eg)
Roll Maneuver
Sideslip Maneuvers
25
LJDAM - Jan 05 Fixed Target
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LJDAM – May 05 Moving Target
27
Remote Controlled Target
LJDAM – May 05 Moving Target
28
MK82 Laser SDD-G2
29
MK82 Laser – 40 mph HMVMK82 Laser – 40 mph HMV
30
Lessons Learned
• X-36 RESTORE Flight Test– Stabilized Unstable Airframe Under Significant Failures
– Limited Flight Envelope
• MK-84 JDAM Dynamic Inversion CLAW– Eliminated Gain Scheduling Requirements
– Used Existing Truth Model for Analysis/Comparison
• MK-82 LJDAM Augmented LQR– Retrofit Onto Baseline Control
– Significant Parameter Tuning Required For Performance
X-36
JDAM
Flight Results Have Created List of Open Problems
31
Open Problems
• Reference Model Design
• Parameter Tuning Guidelines
• Adaptive Dead-zone and Learning Rates
• Adaptive Structural Mode Suppression
• Gain and Phase Margins for Adaptive Systems
• Retrofit For Legacy Systems
32
Summary
• DOD Requires Robust System Behavior for Autonomous UAV and Weapon System Operation – Need for Adaptive Control
• Flight Quality Computer Hardware Now Capable of Advanced Algorithms
• Industry Actively Maturing Technology