Etne C Craes A I N R I W A M O N E E C A P S O E Rthgil .

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NASA Dryden Flight Research CenterAIAA [email protected] 2007 Conference and Exhibit7 - 10 May 2007Doubletree Hotel Sonoma Wine CountryRohnert Park, CaliforniaJohn J. BurkenReconfigurable Control Design with Neural NetworkAugmentation for a Modified F-15 Aircraft

Presentation Outlineλ Purposeλ Backgroundλ Design Methods Used for Paper Background on Model Reference Adaptive Control (MRAC) Background on Robust Servomechanism LQR Radial Basis Function Neural Networksλ Control Failure Survivability Resultsλ Results / Time Historiesλ Conclusions Remarks Lessons LearnedReconfiguration

Goals & Objectives Flight evaluation of neural net software. Increased survivability in the presence of failures or aircraft damage. Increase your boundary of a flyable airplane. Increase your chances to see another day. General/ Problem Statement {The Big Picture} Land a damaged airplane or, return to a safe ejection site. Or continue with mission MotivationReconfiguration Flight Control Systems3

λλλSolution to Adaptive & Robust control issues. Merge adaptive augmentation into a robust baseline controller.Why Robust Control (Such as Robust LQR servo design) Handles unmodeled dynamics. Has good flight experience.Why Adaptive Control. Handles uncertainties and unpredicted parameter deviations.General Background / ConceptsControl Reconfiguration

Two Types of Adaptive controllers1. Direct Adaptive2. Indirect AdaptiveThe Direct Adaptive Controller Works on the Errors. Needs a Reference Model to Generate P err (P cmd-Psensor) The Neural Network “Directly” Adapts to P err. Does not need to know the source of error. No Aero Parameter Estimation Needed No need for persistently exciting signalsThe Indirect Adaptive Works on Identifying the source of Error. Does Not Need a Reference Model. Needs to Identify the Aerodynamics that have changed! (PID) PID is Time Consuming and may not be correct. Needs persistently exciting inputs. General Statements on Adaptive Controller

λλλ ΘPlant (G)Adaptive Law (NN)Controller(H)uymy errorPlant: Actual Plant parameters (G) are unknown.Reference Model: Ideal response (ym) to cmd r (Use a Stable Reference Model).Adaptation Law: Is used to adjust controller (H): can be NNs.rReference Model:Closed Loop SysModel Reference Adaptive Control (MRAC)

& ë I ' A B#rank i n p!% ' C D"The system is controllable and there exist acontrol lawu kx k c x c& # & A0 #& x # & B #x ! ! x ! ' B D!U'BCA %x c !" % cc "% c "% c "Suppose the following condition is satisfiedThe open loop augmented system isx c A c x c Bc (r ' y) If this statement is true thereexist a closed-loop systemthat is stable.Note :ℵ LQR Servo LQR PIℵJammed or failed surface is treatedas a disturbance to the system.ℑ Approach is simple to implement.whe re x ( R n , u ( R m , y ( R pY Cx Du Fww the disturbance (failed surface)The dynamic controller isX Ax Bu Ew Consider a MIMO systemServomechanism Design Methodology

λλλλRemarks:Control LawFor any such control law, asymptotic tracking andu kx k c x cdisturbance rejection are achieved; that is, the errore r !y" 0goes to zero.If the augmented system is controllable, the controllaw can be conveniently found by applying thelinear quadratic regulator (LQR) approach to the The augmented system isaugmented system.& # & A0 #& x # & B #x! After setting up the augmentation we now need to ! ! !U %x c !" %' Bc C A c " %x c " %' BcD"solve for the gain (k, kc) Just use LQR. This setup allows for a LQR tracker solution.Servomechanism Design Methodology (cont.)

λλλu (t ) ! R !1 B ' Px(t ) Kx (t )And the optimal control is given by:0 A ' P PA Q ! PBR !1 B ' PThe algebraic Riccati equation0J ! ( x ' Qx u ' Ru )dtTOptimize the following cost function.Optimal linear-quadratic-regulator (LQR) problem.Servomechanism Design Methodology (cont.)

& x'r' % 2() ( x) e2Activation function#!!"–Neural Networks are Universal Approximators.–Minimizes a H2 norm.–They permit a nonlinear parameterization of uncertainty.–Why Radial Basis Functions (RBF):–RBFs will de-activate when signal is outside “neighborhood”.Why Neural Networks?

λk 1f ( x) NN ( x) ! wk " k ( x) bKThe output of a RBF network with K neurons: ! k (x) is the response of the kth hidden neuron forinput vector x. wk is the connecting weight of the output neuron.RBF Network Outputs

x2x1b!means activation function!!!!1w4w2w3w1w0Σfjfj w0 bw1x1w2x2w3 x3w 4 x1 x21 Hidden layer with 4 Neurons and 2 InputsNeurons

Aerodynamic Failures or uncertainties (A Matrix problems / lostaero surfaces, bent wings) Or Not well known aero terms due to modelling errors.Control Failures (B Matrix problems / jammed control surfaces) Right stab jammed at 8. deg from trim 2 groups of failures are “common” among aircraft mishaps/crashes.FailuresInvestigated

λλλTime History of Surface Failure ( B matrix)Failure Right Stabilator Jammed. At time 10 seconds / 8 deg from trim. At time 30 seconds Failure goes away (crew fixed the failure).Neural Networks Neural Networks turned off for the first run. Neural Networks turned on for second run. Without Dead Zones.Control Reconfiguration Results

Robust Model Reference AdaptiveControl Design

Pilot InputsFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doubletsPitchstickRollstickRudderpedal

Long Axis DataF-15 Longitudinal ParametersFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Lat/Dir Axis DataF-15 Lat/DirParametersFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Neural Network SignalsFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Surface PositionsFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

λλλTime History of Surface Failure ( B matrix)Failure Right Stabilator Jammed. At time 10 seconds / 8 deg from trim. At time 30 seconds Failure goes away (crew fixed the failure).Neural Networks Neural Networks turned off for the first run. Neural Networks turned on for second run. With Dead Zones & 20% decrease in learning rates.Control Reconfiguration Results

Pilot InputsNN withDead-Zones &Slower LearningFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doubletsPitchstickRollstickRudderpedal

Long Axis DataF-15 Longitudinal ParametersNN withDead-Zones &Slower LearningFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Lat/Dir Axis DataF-15 Lat/Dir ParametersNN withDead-Zones &Slower LearningFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Neural Network SignalsNN withDead-Zones &Slower LearningFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

Surface PositionsNN withDead-Zones &Slower LearningFailure Right Stab 8. deg at 10 seconds with & without NNFailure goes away at 30 seconds / Pilot Input is Roll doublets

λλλ Used Radial Basis Function Neural NetworksReference Model was a “healthy” aircraft. The crew could fix the problems and you don’t want the adaptive system to gounstable.Lesson learned: Test the removal of the failure with Neural Networks active to ensure goodperformance.Results: LQR Servomechanism behaved well with a failure. Using the Neural Networks improved the tracking compared to not using theneural networks. Method presented: Robust LQR Servomechanism design with Model Reference Adaptive ControlConclusions & RemarksControl Reconfiguration Conclusions