Document
Lessons from
Modeling Flexible
Aircraft for Active
Flutter Suppression
JEFFREY OUELLETTE
NASA ARMSTRONG FLIGHT RESEARCH CENTER
AE ROS PACE CON T ROL AN D G UI DAN CE SYST EMS COMMI T TEE ME E TING #1 2 3
MARCH 2 7 - 2 9, 2 0 1 9
Active F lutter Suppression (AFS)
Reducing structural weight
◦ Standards require flutter to be 115% of maximum airspeed (Vne) ◦ Control system could be used to increase flutter speed without structural weight
Addressing design issues
◦ Predicted flutter speed can drop as design matures ◦ AFS could avoid expensive redesigns
X - 56A Multi - Utility Technology Testbed
◦ Designed for testing active flutter suppression ◦ Flexible wings have unstable flutter modes ◦ AFRL Funded ◦ Lockheed Martin Built ◦ NASA has flown slightly past the flutter speed March 28, 2019 ACGSC 123
Objective
Generate models useful for the design and evaluation of control laws
for active structural control and flutter suppression that are able to
accurately predict body freedom flutter.
For design For evaluation Prediction
• Form of the models • Uncertainty • Physically based models
• State - space models • Piloted simulation • Using information typically
available before flight
• Interpolation between flight
conditions • Predictive accuracy
insufficient/inconsistent
• Full envelope design
• Using flight test results to
determine where we went
wrong
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Challenges with Aeroservoelastic Modeling
• Unstable
Challenging Dynamics
• Closed Loop • High Order • Multiple - input
Model Complexity
• Multiple - output • Difficulty in prediction
Nonlinearities
• Difficulty in interpreting • Turbulence • Limited Knowledge
Uncertainty and Noise
• Variability March 28, 2019 ACGSC 123
Types of models being used
Low Order Equivalent Parameter estimation NDoF model System (LOES) Frequency responses models models • Preflight models • Transfer functions • Lower order • Flight derived • Did some updates • Different from • Flight derived • Non parametric from stiff wing handling qualities (high order) • More physical data LOES parameters • Very high order • Lower order system • Still in development • ~300 states • Do have structural modes • Integrated into piloted simulation • Flight derived • Time domain system ID March 28, 2019 ACGSC 123
Maneuvers Used
Doublet Margin Multisine ID Multisine Modeling Envelope Flight Envelope Density Altitude Fuel Weight, lbs Doublet Margin Multisine ID Multisine Modeling Envelope Flight Envelope Airspeed, KEAS Airspeed, KEAS Use air density in place of altitude Use margin multisines for validation ◦ Small effect for low subsonic conditions ◦ Keeps data independent of tuning ◦ Plenty of test points for comparison Use ID multisines for updating ◦ Compares specific input/outputs of interest ◦ Better excitation for system ID March 28, 2019 ACGSC 123 Model Complexity:
“Curse of dimensionality”
HIGH ORDER MODELS
MIMO SYSTEM
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Aeroelastic models have lots of parameters
• Parameters arranged in a matrix
𝑨 𝑩
𝑪 𝑫
• 22 Outputs • 12 Inputs
• Estimate of parameters for multiple model types
Rigid longitudinal Parameter ID Aeroelastic Full Aeroelastic model models Plant Model States 4 6 155 234 Max parameters 416 504 33,807 62,976 Typical parameters 135 270 10,299 14,958
• System order causes many parameters
• Inputs and outputs also mean a lot of parameters • Physical modeling requires more parameters then identifiable from flight March 28, 2019 ACGSC 123
Preflight Flutter Model Tuning
ZAERO C STAR-CCM+ C p p
Flutter model uses a lifting surface method
◦ Similar to vortex lattice ◦ potential flow without boundary layer or thickness effects ◦ Good for unsteady aerodynamics ◦ Poor for steady coefficients
Refining flutter aerodynamic model
◦ AIC matrices relate local velocity to pressures
Common techniques exist for refining these
matrices
◦ Tuning to match wind tunnel/CFD results ◦ Effectively changing the shape to reflect the boundary later and thickness.
◦ Downwash correction ◦ Fairly easy to implement ◦ Fairly easy to create problems
Currently only matching steady coefficients
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Issues in flutter model tuning
Correction reflects error in relative change in local CFD Based Correction Factors Final Correction Factors velocity CFD/Wind tunnel includes physics not in potential flow models ◦ Cannot tune to match physics not in the model ◦ Requires replacement of coefficients Coefficients may not be consistent ◦ Matching lift and moment may require unrealistic center of pressure ◦ Mostly an issue in control surfaces ◦ Causes unrealistically large corrections ◦ Can only match a limited number of coefficients Smoothness of corrections ◦ Giesing, Kalman, and Rodden used weighted RMS ◦ Limits total variation ◦ Large changes between neighbors is possible ◦ We have implemented smoothness based on difference between neighboring panels March 28, 2019 ACGSC 123
Direct Tuning with Flight Data
Low order PID results have different model
structure
◦ Lower order means the parameters are biased ◦ Requires an adjustment to parameters
Directly adjusting parameters used in model
generation
◦ No adjustment needed for implementation ◦ Full envelope correction ◦ Also applied to generate LOES models
Frequency Domain
◦ No estimation of states required ◦ No inclusion of control system needed
Output Error
◦ Using only accelerometers and strain gauges ◦ Data directly from flight test instrumentation has more consistent timing March 28, 2019 ACGSC 123
Simplifying the Outputs
Outputs are highly correlated
◦ Each strain gauge contains essentially the same information ◦ Turbulence will cause signal errors to be correlated
Principle component analysis (PCA/POD/KLT)
◦ Combine base on linear relationships ◦ Reducing dimension of the outputs ◦ Combining outputs to average out the noise ◦ Similar to generating modes
Reduced r ank regression
◦ PCA applied to outputs
Tested on generating low order models
◦ Reduces number of parameters fit ◦ Improves speed (~100x) and accuracy of the fitting Accels Strain Gauges March 28, 2019 ACGSC 123
Direct Tuning with Flight Data
Bode Diagram: Wing Flap 4 to Center Forward Accel
Tuning is improving the fit
Additional improvement is still expected
Baseline ◦ Flutter speed is still high Tuned FD LOES ◦ Unable to get full envelope correction ◦ Large corrections
Additional parameters may be needed Magnitude (dB)
◦ Updating 58 parameters ◦ LOES models have ~ 200 parameters ◦ Inertial Parameters ◦ Structural Parameters ◦ Update material properties, rather then frequencies ◦ Mode shapes are fixed Phase (deg) ◦ Output equations are fixed Frequency (Hz) March 28, 2019 ACGSC 123
Nonlinearities
ACTUATORS
TAKE - OFF AND LANDING
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Effect of Actuator Nonlinearities
Medium Magnitude Large Magnitude Magnitude, dB Magnitude, dB Ground Test Ground Test Model Model Flight Test Flight Test Phase, deg Phase, deg Frequency, Hz Frequency, Hz • Actuators do not respond to small commands • Same flight and input (system ID), different magnitudes (x2) • Same low airspeed, similar fuel weight • Smaller magnitude shows more variability, and large error relative to ground test March 28, 2019 ACGSC 123
Take - off Simulation
Rapid decrease in main gear loads with
increased throttle
◦ Not captured in the simulation
Simulation
◦ Change in load is ~40% of change in thrust
Simulation predicted higher rotation
speed
Throttle
◦ Higher rotation speed irritated the pilots
increased
◦ Simulation used in training adjusted ground
Left main gear load, lbf
effect
◦ Not physical ◦ Small detriment to accuracy of landing dynamics Airspeed, KCAS March 28, 2019 ACGSC 123
Take - off Simulation
100 100 Flight Interval 95 95 Flight Mode Sim ulation Flight Interval Flight Mode Sim ulation 66 66 Pitch rate, deg/s Pitch attitude, deg 0 0 Tim e, sec Tim e, sec
Higher rotation speed causes larger pitch up
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Flexibility degrades landing damping
• On touchdown significant energy goes into the wings • Wings are very poorly damped • Reduces effectiveness of landing gear • Rigid body simulation did not reliably predict the response • Out piloted simulation included structural dynamics March 28, 2019 ACGSC 123
Uncertainty and Noise
T UR BULENCE
LIMI TED KN OWLE DGE (E P I STEMIC)
VARIABILITY (ALEATORIC)
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Turbulence
First flex wing flight (flight 9)
◦ Encountered light to moderate turbulence
Pilot perception
◦ Had simulated similar levels of turbulence ◦ Response was more stressful in flight
Structural dynamics
◦ Added to piloted simulation before flex wing flights ◦ Effects were not added to nose camera motion
Turbulence model
◦ Used standard model from loads and handling qualities ◦ These primarily excite rigid body motion ◦ Higher frequency turbulence caused more structural motion March 28, 2019 ACGSC 123
Limited Knowledge ( Epistemic Uncertainty)
Uncertainty often viewed as a lack of knowledge • More testing could improve knowledge and reduce uncertainty • More testing not always necessary or practical Unrelated parameter uncertainty • Large number of parameters • Caused unrealistically large uncertainty in output • Error in parameters should be related • Down select parameters based on engineering judgement • Missed parameters that are important Mu - analysis was very appealing • Computational cost was excessive • To many parameters to examine • Frequency of parameter occurrence • Mass parameters and air density effect many parameters • LFT format was still useful for Monte Carlo Flight models show what output uncertainty should be • Models were sufficient for controller design, once the uncertainty was known March 28, 2019 ACGSC 123 Pitch rate sensitivity
Variability ( Aleatoric Uncertainty)
Peak nose gear Pitch rate total load sensitivity variation sensitivity Landing Sensitivity Analysis Linear Effect Right Throttle Position Right Throttle Position ◦ Some uncertainty is inherent, and cannot be reduced Linear Effect Main Effect Left Throttle Position Left Throttle Position Main Effect Total Effect Examined sensitivity of the response to parameters Pilot Pitch Com m and Pilot Pitch Com m and Total Effect Fuel Weight Error Fuel Weight Error ◦ To many parameter combinations to consider Roll Angle Roll Angle ◦ Needed to understand interactions between parameters Pitch Rate Pitch Rate 26 8 ◦ For 26 parameters, 2 ≈ 10 possibilities Roll Rate Roll Rate ◦ >2 years for a 1 second simulation Pitch Angle Pitch Angle Sink Rate Sink Rate Monte Carlo/Polynomial chaos expansion Touchdow n Air Speed Touchdow n Air Speed ◦ Generate surrogate model Headw ind Headw ind ◦ Polynomials orthogonal with respect to parameter Crossw ind Crossw ind probability distribution Sea-level tem perature Sea-level tem perature Sea-level pressure Sea-level pressure Used multiple types of sensitivity Nose Dam per Gain Nose Dam per Gain ◦ Linear effect: traditional linear sensitivity Tire Lateral Max Friction Tire Lateral Max Friction ◦ Main effect: direct nonlinear effect Tire Longitudinal Max Friction Tire Longitudinal Max Friction ◦ Total effect: Includes interaction between parameters Tire Rolling Resistence Tire Rolling Resistence Tire Dam ping Tire Dam ping Percent Fuel Weight Percent Fuel Weight 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 March 28, 2019 ACGSC 123
Landing Dynamics
Flight Interval Flight Mode Sim ulation Flight Interval Flight Mode 66 Sim ulation Pitch rate, deg/s Pitch attitude, deg Tim e, sec Tim e, sec
Simulation is capturing initial dynamics
◦ Nonlinearity of ground contact makes comparison difficult Having a piloted simulation allowed for the development of an effective landing technique.
March 28, 2019 ACGSC 123
Landing Monte Carlo
Flight Simulation Flight Interval Flight Mode Sim ulation 66 66 Pitch rate, deg/s Pitch rate, deg/s Tim e, sec Tim e, sec March 28, 2019 ACGSC 123
Landing Monte Carlo
Flight Simulation Flight Interval Flight Mode Sim ulation Pitch attitude, deg Pitch attitude, deg Tim e, sec Tim e, sec March 28, 2019 ACGSC 123
Conclusions
March 28, 2019 ACGSC 123
Conclusions
Have generated models of reasonable accuracy
◦ Used to design control system past flutter ◦ Used to address and validate takeoff and landing issues ◦ Challenges do still remain
Developed tools and methods for ASE challenges
◦ Unstable closed loop system ◦ Complex dynamics ◦ Nonlinear behavior ◦ Uncertainty March 28, 2019 ACGSC 123