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

19

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

20

+-

+-

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

21

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

26

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