Linear and Reconfigurable Control of Wing Damaged Aircraft

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Linear and Reconfigurable Control of Wing Damaged Aircraft

Pascal Nespeca

Ph.D. Exit Seminar

Jan. 7th 2010

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Outline

• Background Material– Goals– Definition for Spanwise Full Loss (SFL)– Wing Damage History– Opinions on Wing Damage– Novel Wing Damage Hardware

• Technical Material– Rigid Body Model– Control Methods– Conventional Control– Reconfigurable Control– Conclusion– Appendix - Basic Inverse Control Concepts– Appendix - Adaptive Control

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Goals

• Study dynamics and control of wing damaged aircraft• Improve aviation safety by controlling a wing damaged

aircraft

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Wing Damage Definition• Spanwise loss, wing

progressively removed from wingtip

• Damage (Dmg) = 0% is nominal

• Damage (Dmg) = 100% is full loss of one wing

• P17 is C17 modified by Pascal• Wings provide lift• Some wings, some lift• Also there will be rolling

moment• Potential loss of fuel and

hydraulic fluid.

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Wing Damage History• Smaller Aircraft

• Larger Aircraft

• Incidents with full wing damage, dmg = 100%• Landed: Israeli F-15, early 80's, 0 deaths

– Mid-air collision, training maneuvers

• Crashed: F-111, 1969, 2 deaths– Fatigued wing box caused by improper weld– 3 million dollar lawsuit with Selb mfg. for bribing inspectors

• Crashed: Piper PA-32, 2009, 9 deaths– Mid-air collision with helicopter

• Incidents with full wing damage, dmg > 75%• Crashed: NW airlines, Lockheed 188C Electra, 1960, 63 deaths

– “Propeller whirl” fatigued wings

• Crashed: Pan Am Boeing 707, 1963, 81 deaths– Lightning struck wings, ignited fire, right engine explodes

• Crashed: Short 360, 5 Feb. 2006, ? Deaths– 75% wing loss due to mid-air collision

• Landed: sub-scale F-18 model (60%)

– Rockwell Collins, 2008

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Wing Damage History• Smaller Aircraft

• Larger Aircraft• Incidents with partial wing damage, dmg < 25%ish• Landed: DHL A300, 2003, 0 deaths

– Terrorist shot a rocket at wings in Iraq– Wing distorted, hydraulic fluid lost, pilots used Throttle-Only Control (TOC)

• Landed: Saudi Air B-777, 2008, 0 deaths– Landing gear malfunctioned and punctured upper surface of wing

• Crashed: XB-70, 1966, 2 deaths– F-104 clipped wings and tail after getting caught in wake

• Incidents with partial wing damage, dmg < 25%ish• Crashed: F-16D, 1997, 0 deaths

– Mid-air incident, formation flying, 100 pound missile carrier torn off right wing, crew ejected

• Landed: Other F-16C, 1997, 0 deaths– Mid-air incident, formation flying, 100 pound missile carrier embedded in left wing, pilot

landed successfully

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Wing Damage History Conclusions

• If wing damage is small, then survival is more likely– International Civil Aviation Authority (ICAO) does not consider

the following to be substantial damage: damage limited to one engine, bent fairings or cowlings, dents in the skin, small puncture holes in the skin, damage to flaps, damage to wingtips.

– Video

• Serious threats to flight control:– Flow separation at the leading edge of the tail (ex: icing)– An unforeseen loss of torsional stiffness of the wing which

causes roll control reversal will potentially destabilize roll control.– Any structural mode slower than 10 times the control bandwidth

which exhibits an unforeseen frequency shift of 1 Hz can potentially create problems for the control system (NATO AGARD RTO-MP-36).

– Total loss or partial loss of hydraulic fluid represents a significant challenge for control system design.

– A large unforeseen shift in the center of mass, either fore or aft.– A very large sideways shift in the center of mass, possibly due to

an exceptionally asymmetric fuel condition.

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Wing Damage Opinions

0102030405060708090

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RockwellCollins

NASAAmes

ICAO Pascal

% dmg - Transport (Sim)

% dmg - ModifiedTransport (P17 Sim)% moment area - scaledF-18 (Reality)% dmg - HL-10 (Reality)

small

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Novel Wing Damage Hardware Ideas

• If wing damage is very large, then it most likely is a big problem. It may be so big that it is not reasonable to expect recovery due to simple force-moment imbalances.

• The HL-10, HL-20, M2-F2 lifting bodies were designed to fly without any wings.

• To really recover from total wing loss, the aircraft hardware should be designed to fly without one or both wings.

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• Bigger aircraft could be more resistant to small arms fire than small aircraft (although one could just get bigger weapons).

• Complications: fuel in wings, hydraulic fluid leaks, flap and aileron size

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• Asymmetric high lift devices• Telescoping Wing (Makhonine 10 and 123) • Mega/Giga/Tera aileron for transport aircraft

– Mega aileron = large plain aileron + asymmetric spoiler + taileron – Giga aileron = Mega aileron + asymmetric leading edge flap + asymmetric

externally blown flap– Tera aileron = Giga aileron + all-moveable wing (wingeron)

• Recent Giga-aileron: F-18 Active Aeroelastic Wing (AAW)

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• Crew Transfer: “Executive Decision”, Hollywood movie, 1996

• Risky maneuver • May cause more accidents than it prevents

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Rigid Body Model

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Rigid Body Model for Control

• Flight data for a typical aircraft or helicopters on a typical trajectory shows that linearity is coherent above about 0.01 Hz

• Lightweight aircraft with heavy rotors at low speed will show some strange effects

• Aircraft caught in spins or very fast rolls exhibit non-linearity

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Rigid Body Model for Control• Sources: USAF

DATCOM (DATa COMpendium) / Roskam’s formulae / Strip Theory / Vortex Lattice Code to get stability derivatives

• Pitching the nose up/ down will cause the aircraft to roll at low frequency

• Aerodynamic simplifications are used for rigid body motion and aerodynamics of aircraft, 10-20% error is acceptable for control

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Rigid Body Model for Control• Mild issue: Sum forces and moments at a different location than body-fixed

variables, or use wrong AOA. • Error found in AIAA 2006-6049, Stevens & Lewis 2003, Tim Marchelli’s MS

thesis, I used the quarter chord aerodynamic reference as location O instead of the center of mass. Drawback more numbers more errors

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• Fewer numbers with approximate aerodynamics for small damage near 10-30%

• Easier to use

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• Trim: Forces and moments are balanced.

• Trim calculations for P17 with aircraft empty show that a significant threat is static stability

• Trimmed angle of attack and sideslip angle did not deviate by more than 1 to 2 degrees

• Rudder deflections, elevator deflections were also not significantly large.

• Mega aileron consists of oversized plain aileron, asymmetric flap, differential tail

Possible upset of undamagedaircraft

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Control Methods

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Control Methods

• Initial Methods: – Incomplete knowledge on the topic of

limitations of control and interest with automated design of automatic control systems led my earlier research efforts towards direct adaptive control.

• Revised Methods:– Fixing problems with many recent

adaptive control techniques requires some prior knowledge of plant dynamics. Ex: parameter projection, gain limiting

– Successful application of conventional and reconfigurable controllers to wing damaged aircraft.

Problem:

Solution:

Designer

Designer

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Control Methods

• Automation is continually on the quest to end human involvement in boring, dull and unfulfilling tasks.

• Sometimes, the design of feedback control systems can be boring and dull.

• Designers of automatic control systems may want to automate their own profession. However, this can result in some very poor control designs.

• Generally, some amount of human thought and knowledge of system dynamics should be used into control design regardless of the design technique and application.

User

Designer

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Control Methods• “Following the December 1971 issue of the IEEE

Transactions on Automatic Control, many graduate students (including the reviewer himself) and even experienced researchers in academia started believing that linear quadratic Gaussian (LQG) was the panacea for linear stochastic control problems, ignoring issues of sensitivity to parametric and nonparametric uncertainties that had already been raised by several distinguished scientists…………By the end of the decade of 1970s, it became clear that the sole usage of LQG does not provide solutions to the general class of linear stochastic control problems” – Asok Ray (recent IEEE book review)

• The frequency domain helps the brain• State space and LQG are not bad things to use, it’s

just that one should be checking gain and phase margins or looking at a frequency domain plot like a bode plot or singular value.

Designer

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Conventional Control

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Basic Control Design Concepts

• For a stable system with high frequency delay or unstable zeros:

• Higher Gain Lower stability margins, quick response, better performance

• Lower Gain Higher stability margins, slower response, poorer performance

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Basic Control Design Concepts

• Crossover frequency must be finite

• Do not use infinite gain

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Cross Coupling in MIMO Systems

• Approximate modeling shows that the wing damaged aircraft is triangular.

• Reduce cross coupling by increasing roll gain may cause “roll ratcheting”

• One can also slow down the pitch loop, though this is less effective.

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• Plants which are approximately triangular can become destabilized

• Contrived example, reversal in pairing

• Reversal in pairing poses the potential to possibly destabilize the loops. RGA and Niederlinski index are not known to be reliable indicators of stability or instability for larger systems.

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• The P17 model does not show any indication of dynamic instability even with 70% wing damage.

• No reversal of the RGA occurred because triangularity was well maintained across all frequencies.

•There were simply too many numbers to calculate. Many of which did not change significantly. Model was difficult to use.

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• Simplified model for small wing damage

• Navion study with M-Delta analysis

• Convenient model which only uses 2 numbers

• Half-Physical• 60% actually

did not destabilize

• 80% did destabilize

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10

01

001

sERI

sEMAIsP re

• Big Cross-feed gains for P17

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• Pitch up 6 degrees, bank right 0.6 degrees• Probably not a significant performance

benefit to motivate reconfigurable or iterative identification and control

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Reconfigurable Control

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Reconfigurable Control

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Reconfigurable Control• As soon as you think there is a problem, switch the controller with a

bumpless controller transfer• Times between control switches must be properly managed

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Reconfigurable Design Control Limitations

• Control System Design Limitations– Stabilizability (state controllability and observability)– Functional controllability (invertability)– Achievable tracking requirements come from

hardware limitations (time delays, unstable poles/zeros)

• Fault Detection/Isolation Design Limitations– Perfect fault detection/isolation is not possible– False positives and true negatives will occur– Higher detection rates usually generates higher false

positive rates– Quicker detection usually invites more false positives

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Thinking about Reconfigurable Control with Conditional Probabilities

• Misapplying longitudinallateral crossfeed to undamaged aircraft (EMAI(s) or ERI(s)) would cause strange and unknown handling.

FDIFalse PositiveIn RealityUndamaged aircraft handles like left wing damaged aircraft

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Thinking about Reconfigurable Control with Conditional Probabilities

• There is a known risk with simply increasing the roll gain

• Increase roll gain roll ratcheting

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Thinking About Reconfigurable Design with Conditional Probabilities

• Design 0 – D0 is not reconfigurable• Design 1 – D1 is reconfigurable• Crash – C• Event 0 – E0 is normal flight• Event 1 – E1 is abnormal flight (damage)

• Assumption: D0 and D1 are not responsible for E0 or E1

• It is very important that all of the controllers which are available to the reconfigurable system pose little or no threat to the nominal aircraft.

• 1x10-9 accidents per mission

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Thinking about Reconfigurable Design with Conditional Probabilities

• Unless it is a very frequent fault

• Frequent events/faults deserve more attention than rare ones as long as the controllers for those faults are still benign to the normal aircraft.

• 1x10-9 accidents per mission

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Thinking about Reconfigurable Design without Conditional Probabilities

• Military applications in combat zones might be appropriate, provided that there is actually a net benefit.

• However, military may still be interested in such an aircraft if it perceives a tactical advantage.

• Examples of dangerous aircraft with unique capabilities: Harrier, SR-71 Blackbird, V-22

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Thinking about Reconfigurable Design without Conditional Probabilities

• General public has a strong reaction to aviation accidents due to media coverage.

• It would be ironic if the autopilot intended to improve safety actually caused more accidents.

• The aviation business is very competitive. Reconfigurable control would be an added risk.

• Recent example: AA flight 587 incident question tail design AA retires entire Airbus 300 fleet

• FAA would probably need to make a specific rule relating to reconfigurable control design.

• FAA has a lot of rules it should make, most of them are very basic and have obvious benefits, unlike reconfigurable control.

– Example from NTSB Most Wanted Safety Issues: “Set working hour limits for flight crews, aviation mechanics, and air traffic controllers based on fatigue research, circadian rhythms, and sleep and rest requirements”

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Problems with Time Varying Gain

• Time varying gain is like a minefield.

• If you don’t know where all the mines in the minefield are then it’s not safe to run around in it.

• The minefield must be finite gain limiting

• Walk, don’t run Slow time varying gains behave better than rapid time varying gains.

• Metal Detectors Lur’e system analysis, spectral radius, LMI, Lyapunov stability.

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Switching Control

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Switching Control

• Indicates the potential for instability if the switch occurs near the dutch roll frequency

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Switching Control

• Linear simulation shows instability

• A flight test might not show instability, however there is something weird going on near the dutch roll frequency

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Conclusions• Reconfigurable or switching control may improve safety.• It is not a good idea to fly with one or both wings

missing, unless the aircraft was originally designed for this purpose.

• If the aircraft can land without a re-design, do not re-design. It is better to do a lot of work to justify doing nothing.

• Direct and indirect adaptive control should use gain limiting or parameter projection at least.

• In-flight and automated design of an automatic flight control system is possible, but it would probably make flight less safe instead of making it more safe.

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Appendix A - Basic Inverse Control Concepts

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Basic Inverse Control Concepts

• Inversion or dynamic decoupling design

• Try to reduce cross coupling

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• There are things which are a good idea to invert

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Perfect Modelling

20% increase in elevator 20% reduction in thrust and 0.4 second time delay

Outer loop autoland application

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• The vicious design cycle of the High RGA Plant

• Nothing can reasonably be done to robustly decouple this system

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• A bad idea– Two tank

system– Try to

remove cross coupling

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• RGA vs. Frequency Plots

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• Good books on MIMO feedback control– Control System Design, Graham C. Goodwin

et. al.– Multivariable Feedback Control, Sigurd

Skogestad and Ian Postlethwaite• Graham Goodwin’s book knowledge and

mathematical corrrectness (95% at least)• Sigurd Skogestad’s book excellent

insights into RGA, general breadth and wisdom (however, mathematical half truths regarding the singular value and robust stability are misrepresented in this book)

• John Doyle and Gunter Stein’s 1981 publication in the IEEE is only half true.

• The singular value can only be used to show stability, not instability.

• Graham Goodwin’s book properly represents the singular value.

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Appendix B - Adaptive Control

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History of Adaptive Control• 1959, MIT Rule:

– Pre-cursor to Model Reference Adaptive Control (MRAC), integrates to infinite gain

– Gain limiting sometimes used, possibly inaccurately?– No awareness mechanism for reducing gain other than setting

limit by modeling and design– Never used in flight test (of which I am aware).

• 1955-1967, MH-90 through MH-96:– Used in many flight tests successfully– 1967, one catastrophic incident involving X-15A-3, pilot did not

survive, accident blamed on MH-96 limit cycle, failure rate for X-15A-3 = 1.5% catastrophic failure, Space Shuttle = 2% catastrophic failure

– Gain limiting used, possibly inaccurately?– Had rate limit on gain, which is a good design principle– Awareness mechanism for reducing gain limit cycle, back off– Pilot opinion was favorable.

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History of Adaptive Control• 1960-1964, Pilot Directed Adaptive Control:

– At some early point during the X-15 program, the pilot was allowed to modify feedback gains, there were no accidents with X-15A-1 or X-15A-2

– HL-10 first flight, Bruce Patterson avoids disaster by turning down pitch gain

• Early 1970’s, Adaptive Pilot Filter– Application to space shuttle PIO, reduce pilot gain if pilot inputs

have high frequency content• 1961-1975, Lure System Analysis:

– Theory of gain limiting for time varying gains slowly maturing– Circle Criterion published in a feedback control book, 1975– Mostly used to describe actuator non-linearities

• 1965-1970’s, Significant advances in System Identification:– Maximum Likelihood Estimator awesome– Least Squares Estimator awesome

• 1983-1985, Rhors’ Counterexample:– Charles Rhors shows that direct MRAC integrates to infinite gain

The most important publication in direct adaptive control

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History of Adaptive Control

• 1985-1987, Sigma modification and “e-modification”:– Tricks to avoid excitation problems and to prevent integrating to

infinite gain, time delay can still destabilize these things awful• 1998-Current, Flight testing of direct Model Reference Adaptive

Control (MRAC):– Inconclusive findings of performance benefits PIO sometimes– Few accidents have been reported, gain limiting used for safety?

• 1980’s-current, Real-Time Indirect Adaptive Control:– Real time system ID + normal control synthesis awful– Parameter projection methods, L1 adaptive control less awful

• 2000’s, Iterative Identification and Control:– Windsurfing approach to adaptive control, learning through

mistakes least awful, insight into awfulness• 1980’s-current, Massive Revisions to Adaptive Control:

– Reconfigurable Control / Switching Control / Un-Falsified Adaptive Control

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Iterative Identification and Control

• System Identification and feedback control are somewhat at odds with each other.

• System Identification:– To figure out how something moves, you have to move it around a lot.

This requirement is called Persistence of Excitation (PE).• Control:

– To smoothly reach a set-point and prevent motion from that set-point.• Do not use data for system identification if PE is lost.• Get healthy chunks of data before using a batch system identification

• Get a model before doing control design

• No model no control• Do not try to do both at the

same time

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• “What is in the past is history. What is in the future is a mystery.” – Kung Fu Panda

• System Identification only shows you what has happened in the past.

• Surely, rapidly varying trajectories could create problems. Some aircraft can climb at a rate of 40,000 ft./min.

• Some prior knowledge is needed

Linear and Reconfigurable Control of Wing Damaged Aircraft

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