Design of Flight controllers using Quantitative Feedback Theory

1
Design of Flight controllers using Quantitative
Feedback Theory

• By
• Prof. P. S. V. Nataraj
• Systems and Control Engg
• IIT Bombay.

2
Overview

• Introduction to quantitative feedback theory
• QFT design methodology
• Case studies
• Results and conclusion
• Future work

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Introduction to QFT

• Frequency Domain Technique
• Specifically applicable to Plants with large
  Uncertainty
• Feedback Technique which is very effective in
  achieving tracking and disturbance rejection
• Applicable to systems with time delay and
  unstable cases.

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QFT Design Methodology

• Plant templates are generated in QFT design
• Given the plant templates, convert closed loop
  magnitude specifications into magnitude-phase
  constraints on a nominal open loop function.
  These are called QFT bounds.
• A nominal open loop function is then designed to
  simultaneously satisfy its constraints as well as
  to achieve nominal closed loop stability
  Contd.

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QFT Design Methodology Cont.

• The nominal loop has to satisfy composite of all
  stability and tracking bounds
• Loop shaping involves adding poles and zeros
  until the nominal loop lies near its bounds and
  results in closed loop stability.
• Finally, validation of the designed 2 DOF
  controller is carried out both in frequency and
  time domain.

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Case Studies

• Boeing Commercial Aircraft
• AFTI/F16 fighter Aircraft

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Basic Diagram of coordinate axes and forces
acting on an aircraft

• a Angle of attack
• q Pitch rate
• ? Pitch angle
• de Elevator deflection angle
• ge Flight path angle

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Case study 1

• Boeing 707 Commercial Aircraft
• http//www.engin.umich.edu/group/ctm/examples/pi
  tch/Mpitch.html
• Flight conditions
• Steady cruise at constant altitude and velocity
• Pitch angle is independent of speed of aircraft
• SISO transfer Function between pitch angle q and
  elevator deflection angle dc

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Performance Specifications

• Rise time lt 2 sec
• Settling Time lt 10 sec
• Overshoot lt 10
• Steady state Error lt 2

Parameter Uncertainty

• a 1.0935 1.2086
• b 0.1685 0.1862
• c 0.7020 0.7760
• d 0.8750 0.9671

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QFT design

• Controller
• Filter

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Controller design using conventional Methods

• PID technique from Ref. 1
• Kp 2.01
• Ki 2.99
• Kd 4.00

• LQR technique (pole placement design, Ref 1)
• state-cost matrix (Q) CC where C 0 0 1
• weighting factor (p) 50
• performance index matrix (R) 1

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Templates Generated
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Intersection of Bounds
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Loop Shaping
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Filter Design
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Controller Performance
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Case Study 2

• F-16 Fighter Aircraft
• Brian J. Pawlowski, Multivariable Flight for
  control design with parameter uncertainty for the
  AFTI/F-16, Air force Institute of Technology,
  Mar 1989
• SISO case (Longitudinal dynamics)
• Flight conditions
• Speed - 0.6 Mach,
• Altitude 30,000 Feet
• Transfer Function
• q Pitch rate
• de Elevator deflection angle

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Performance Specifications

• Rise time 2.5 sec
• Settling Time lt 5 sec
• Overshoot lt 5
• Steady state Error lt 2

Parameter Uncertainty

• k 111.3780 123.1020
• a 0.0095266 0.0105294
• b 0.522785 0.577815

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QFT design

• Controller
• Filter

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Templates Generated
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Intersection of Bounds
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Loop Shaping
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Filter Design
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Controller Performance
For 27 plants
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Conclusions

• Controller designed by QFT has robust stability
• The controller works well compared to the PID and
  LQR Controllers for Boeing
• QFT technique is successfully applied to two case
  studies, one of which is unstable.

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Future Scope

• Extension of work to different flight conditions
  for AFTI/F-16.
• Attempt to develop a single controller for
  several flight conditions.

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Thank You