Adaptive Flight Control of a Sensor Guided MK82

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

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 2

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 3

The JDAM Weapon Family Affordable, Accurate, Autonomous, Adverse Weather MK-84 (2, 000 lb) BLU-109 (2, 000 lb) *Currently in Developmental Test and Evaluation MK-83, BLU-110 (1, 000 lb) MK-82, BLU-111 (500 lb)* 4

Baseline JDAM Free-Flight Timeline Altitude Roll Over to Pull Down on Target Impact Phase Separation Phase Transfer Alignment Optimal Guidance Phase Time T=0 T=1 sec T=3 sec • Release • Unlock • Start GPS • Start Search Fins Guidance • Start Autopilot T=22 -30 sec (24 sec typ) • First Navigation Update T=1 sec to go • Drive AOA Target Impact to Zero 6

Guidance Law Control of Impact Angle Commands: 30 , 40 , 50 , 60 , 70 Release Target 7

Baseline Control: Feedback Gains Designed Using Optimal Control + Projection Theory Optimal Robust Servomechanism Linear Quadratic Regulator (RSLQR) Model: ARE: CLAW: ~ ~ z • = Az + Bm z R n ~ ~ ATP+PA+Q-PBR-1 BTP = 0 u=-KSFx= -R-1 BTPx Augment Dynamics With Integral Control For Perfect Command Tracking Optimal Projection To Output Feedback Architecture S-Plane X • Preserve Excellent Stability Properties Of State Feedback Using Output Feedback • Eliminates Sensor H/W Required For State Feedback • AUTOGAIN Tunes LQR Parameters • Convergence Criteria Focus On Stability/Actuator Rates • LQR Design Charts Describe Tuning Process X XX 0 XX XX X X • Select Dominant Eigenstructure (Lr, Xr), r<n • Project Gains (Static) K=KSFXr(CXr)-1 0 u=-Ky • Analyze Output Feedback Design • Iterate LQR To Achieve Desired Bandwidth 8

JDAM Greatest Hits Vol 1 Surface Target Buried Target Delay Fuze for Underground Detonation Approved for Public Release 9 Oct 1998 9

JDAM Greatest Hits Vol 2 10

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 11

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 MK 82 aerodynamics to differ from the baseline Adaptive control augmented to the baseline MK 82 autopilot for the MK 82 Laser to compensate for the differences 12

Adaptive Control Transitioned To Advanced 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 Technology Transition Timeline 94 95 96 98 99 97 Intelligent Flight Control System (NASA/Boeing) F-15 ACTIVE • Gen I, flown 1999, 2003 • Gen II, 2002 – 2006 • flight test 4 th Q 2005 • Gen III, 2006 00 01 Adaptive Control For Munitions (AFRL-MN/GST//Boeing) MK-84 Reconfigurable Control For Tailless Fighters (AFRL-VA/Boeing) X-36 Adaptive Flight Control AFOSR Adaptive Control of UCAVs I, II 02 03 04 Boeing IRAD Boeing Collaborates With Prof. N. Hovakimyan at Va. Tech on limited actuation 05 06 Boeing funds MIT (Dr. A. Annaswamy) to initiate research in V&V of adaptive systems MK-82 L-JDAM MK-84 JDAM • Ongoing NASA/Boeing IFCS • Other Transitions 13

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 • Provides robustness to Reference + modeling errors (aero Model uncertainties) Adaptive Control Optimal Guidance Baseline Autopilot + + Airframe 14

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 15

Generalized Plant and Baseline Controller Open-Loop Dynamics system state controller state extended system state moment uncertainties control failures inner-loop commands guidance commands 16

Reference Model and Adaptive Control • Set uncertainties to zero: • Use baseline A/P: • Formulate Closed – Loop System Dynamics Reflects Desired Weapon Dynamics – defines nominal closed-loop dynamics achievable under baseline A/P – forms desired dynamics for adaptive augmentation with uncertainties • Control: 17

Parameter Adaptation • • Theoretical Basis – 2 nd 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) Control Weapon Response Through Reference Model. Uniform Response For Each Weapon – 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) 18

Adaptive Augmentation of RSLQR Optimal Pitch Autopilot Incremental Elevator Command Adaptive Control Turn Rate qcmd AZcmd + - KAZ + Inner Loop + 1/s - KI - da dr AZ KP Cperc de Fin Mixing + 3 Actuators 600 Hz q 3 rd Order Elliptic Filter Lever Arm * s 1 st Order Lag Noise Filter Vehicle Mean AZ Filter IMU 3 rd Order Elliptic Filter 100 Hz 19

Adaptive Augmentation of RSLQR Optimal Roll-Yaw Autopilot Incremental Ail/Rud Commands Adaptive Control Turn Rate rcmd f. Error Aycmd=0 + KPHI + - KAY Cperc + 1/s - - AY 1/s ps Inner Loop + KI + - lead-lag filter dr Fin Mixing 3 Actuators de KP rs Vehicle da 600 Hz Transform to Stability Axes p 4 th Order Elliptic Filter r 4 th Order Elliptic Filter IMU Lever Arm * s 1 st Order Lag Noise Filter 100 Hz + Mean AY Filter 4 th Order Elliptic Filter 20

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 • Histogram of mean aerodynamic perturbation Results show adaptive a/p provides added robustness 21

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 Adaptive a/p Nominal hardware time delays below minimum of chart 22

Oct 04 Flight Data (1 of 2) +30 deg Bank Maneuvers -30 deg AOA Beta Qbar Mach +BETA -BETA 23

Oct 04 Flight Data (2 of 2) -30 deg Delr (deg) Dela (deg) Dele (deg) Roll Maneuver +30 deg +BETA -BETA 24

LJDAM - Jan 05 Fixed Target 25

LJDAM – May 05 Moving Target 26

LJDAM – May 05 Moving Target Remote Controlled Target 27

MK 82 Laser SDD-G 2 28

MK 82 Laser – 40 mph HMV 29

Lessons Learned • X-36 RESTORE Flight Test – Stabilized Unstable Airframe Under Significant Failures – Limited Flight Envelope X-36 • MK-84 JDAM Dynamic Inversion CLAW JDAM • – 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 Flight Results Have Created List of Open Problems 30

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 31

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 32