F4C High Angle of Attack

1

• F-4C High Angle of Attack
• Control Design
• Dan King, David Lazzara, Mike Park
• The Ungrouped
• 16.333 Project Presentation
• December 7, 2004

Picture Source www.eng.vt.edu/fluids/
msc/gallery/conden/f4bv.htm
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Overview

• High Angle of Attack (AOA) Control Problem
  Description
• Low AOA Control Development
• High AOA Control Development
• Comparison of Low to High AOA Controls
• Real-Time Demonstration

Picture Source www.netti.fi/halle/
planes/usa/f-4.htm
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Nonlinear Model

• F-4C Aerodynamic Model Details
• A Collection of Nonlinear Aircraft Simulations
  in MATLAB
• NASA Technical Memorandum TM-2003-212145
• Aerodynamic Model Empirically fit CL vs. a
• 0 lt a lt 15 , 15 lt a lt 30 and 30 lt a lt 55 deg.
• Valid for 20 deg. sideslip
• Nonlinear EOM provides state vector
  time-derivative
• 4th Order Runge-Kutta time integration scheme
  used
• Linearized model determined by central-differencin
  g the state derivative
• Trim state vector and control input used for the
  linear model, also a function of a

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High AOA Control Problem

• Lift, Drag and Pitching Moment vs. a
• Slope Discontinuities are consequence of
  empirical fit
• Aircraft is statically stable longitudinally
• Trim below 27 AoA

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High AOA Control Problem

• Rolling and Yawing Moment Coeff. vs. ß (and a)
• Above a 20 deg., slope sign changes indicate
  lateral instability

Indication of Limit Cycle Oscillation
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High Alpha Limit Cycle Oscillation

• Low alpha is laterally stable
• open loop lt20 AoA
• Lateral non linearity
• causes open loop limit cycle
• oscillation at 20-22 AoA
• Diverge above 22 AoA

20.5a
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High AOA Control Problem
Picture Source http//membres.lycos.fr/militaryav
iation/F-420Phantom/
Wing Slats Deployed
Figures Sourcehttp//www.aoe.vt.edu/mason/Mason_
f/ConfigAeroHiAlphaNotes.pdff
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Longitudinal Control

• Longitudinal Control (valid at low and high
  alpha)
• Developed an Altitude Controller using the linear
  model
• Found Inner Loop Gains (used satisfactory Thumb
  Print guidelines)
• ? 2.5, ? 0.9
• Altitude FB root-locus required small (Kh
  -0.01) for stability

? Root Locus
Altitude Step Response
h Root Locus
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Low AOA Lateral Stabilization

• Lateral Control (a 5 deg.)
• Classically designed gains for rudder control
  (with washout, Kr-100, t 1), roll control (PD,
  Kf-10, ?1/3) and ? FB (t1 5.5)
• Outer-Loop ? FB fast due to tight inner loops

Rudder w/ Washout Root Locus
f and p PD Root Locus
? Step Response
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Low AOA Controller--Simulink
Altitude
Plant
Heading
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Low AOA Control

• Combined Longitudinal Lateral Controllers
• Flight modes decoupled in the linear model

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High AOA Lateral Stabilization

• Standard Low AOA Controller is incapable of
  stabilizing the lateral Dutch-Roll mode
• Sideslip aileron feedback (lead works best)
• In the end, state space methods were used for
  pole placement (gains scheduled over alpha)

Lead Controller
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High AOA Controller SimulinkClassical
Longitudinal, State Aileron Feedback (Scheduled)
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Simulation Results

• Stability and flying qualities rudder doublets
• Psi tracking task
• High alpha evasion maneuver (Psi tracking of sine
  wave)

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Rudder Doublet - 20 AOA
Low Alpha Controller
Open Loop Response
Bad
Low alpha controller destabilizes system at 20
AOA
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Rudder Doublet - 26 AOA

• High alpha controller stable to 26/27, loses
  trim above 27

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Tracking Psi Command

• Low alpha controller at alpha 5 High alpha
  controller at alpha 26

Ground Track
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Evasion Maneuver

• High AOA controller tracking ? at sin(0.04t)

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Evasion Maneuver

• Low alpha controller maximum ? tracking at
  sin(0.029382t)

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Evasion Maneuver

• Low AOA lateral controller diverges where high
  AOA controller was stable ? tracking at
  sin(0.04 t)

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Evasion Maneuver

• Ground track of ? command at sin(0.04t)

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Conclusions

• Low AOA Constant Longitudinal Controller works up
  to moderate AOA
• Lateral moment sideslip derivative and
  nonlinearities cause open loop limit cycle
  oscillation and divergence
• High AOA Lateral Controller uses Roll-Yaw
  coupling to stabilize sideslip
• Elevator effectiveness and engine thrust limit
  altitude control at High AOA
• Heading tracking at High AOA limited by elevator
  effectiveness at high bank angles (turn and pull)