Adaptive Controls

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Adaptive Controls

• CDS 270 Aircraft Control Project II
• James Martin
• May 27, 2005

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Aircraft Pitch Dynamics

• Control Task
• AOA Tracking
• e (a aref) ? 0
• Baseline Controller w/ Nominal Parameters
• Adaptive Increment for uncertainty and robustness

• a Angle of Attack (rad)
• q Pitch Rate (rad/s)

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Baseline Controller Design

• Gain Scheduling
• Use ? aref as scheduling variable
• Augment system to include integrator
• Use feedback to place poles at (-2, -.5 .5 j)

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Baseline Controller Design

• Modification as in Khalil Section 12.5
• Restore original zeros of transfer function
• Baseline Controller Performance
• Rise time 1.5 sec
• 5 Settling 6.5 sec

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Baseline Controller Design
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Adaptive Control Design

• Model Reference Adaptive Increment
• u ubl uad
• Radial Basis Functions
• Functions Fj(a,q) are Gaussian in 2-dim
• Centers located in 4x4 array over anticipated
  operating region

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Adaptive Control Design

• Choice of Aref
• Attempt to recover pre-disturbance system
  behavior
• ubl was designed for steps of ? 25 deg
• Use nominal linearization at ? 25 degrees for
  Aref

• But we have a problem

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Adaptive Control Design
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Adaptive Control Design

• What Happened?
• Near steady state conditions, ubl acts like a
  pure integrator
• However system is no longer asymptotically
  stable, only UUB
• Solution
• Add uad term to baseline controller dynamics

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Free Design Parameters

• Q diag(1.75, 1.75, 1.75) is chosen to minimize
  ?max(P) / ?min(Q) by brute force computation
• Gx G? GT .1
• Projection Operator constants
• xmax ?max 10
• Tmax 250 ex e? eT
  .1
• Weighted Error Vector
• eW diag(1, .001, .001) e

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Adaptive Control Performance
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Adaptive Control Performance
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Adaptive Control Performance
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Adaptive Control Performance
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Adaptive Control Performance