How to Build Practical

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Paul Pounds DERF 08

• How to Build Practical
• Quadrotor Robot Helicopters

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Why Quad-Rotor UAVs?

• Quad-rotor UAVs have many benefits
• Reliable
• Compact
• Low maintenance
• But
• Limited payload
• Limited flight time
• Fast unstable dynamics
• Most quad-rotors are not practical for real
  civilian applications

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Large Quad-Rotors

• Larger (gt4 kg) Quad-rotors fix these limitations
• More payload and batteries
• Slower rigid body dynamics
• Efficient rotors -gt same footprint as lighter
  craft
• But
• Demanding rotor performance specifications
• Slower rotor acceleration
• Rotors exhibit flapping in horizontal translation
• which lead to
• More difficult attitude control problems

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Fixed-Pitch Rotors

• Small, fixed-pitch rotors
• Similar size and speed to model plane propellers
• Single predetermined blade angle of attack
• Simpler, more reliable - cheap to make and
  maintain
• Compact and unobtrusive

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Rotor Design Guidelines

• Optimise performance with developed design
  theory
• Maximise rotor radius to reduce power requirement
• Maximise rotor speed to increase thrust
• Use ideal blade angle and chord to keep air flow
  optimal across the blades
• Use thin airfoils to slice through air
  efficiently

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The Twist Problem

• But, thin blades designed only for aerodynamic
  performance twist into stall under flight loads
• Airfoil design must compromise aerodynamic
  performance for improved stiffness

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Blade Design Modifications

• Increase blade bulk to improve stiffness
• Round leading edge for decreased stall
  sensitivity
• Move the camber rearwards to reduce twist moment
• Add negative pre-twist, such that the blade will
  deform into the correct shape under flight load

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Rotor and Blade Design

• Completed composite blade

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Drive System Guidelines

• Use brushless DC motors for high efficiency,
  convenience and clean indoor use
• Use lithium polymer batteries for high power
  density and long flight time
• Use electronic speed controllers to regulate
  rotor speed and improve dynamic performance

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Motor Dynamics

• Quadrotors rely entirely on rotor speed changes
  for flight stabilisation
• High-bandwidth drive systems are necessary for
  authorative attitude control
• Small quadrotors have light rotors with fast
  acceleration -gt larger craft require active
  control to improve their dynamic response

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The Slew Problem

• Fast speed changes instantaneously draw very high
  battery current gt internal cell resistance causes
  the voltage to drop
• In extreme cases, the voltage drop will cause the
  ESC to reset and halt the motor mid-flight (bad)
• A slew saturation must be implemented to prevent
  the controller from demanding dangerously large
  instantaneous speed changes
• The control response must still be fast enough to
  stabilise the craft and reject disturbances

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Design for Performance Bounds

• Compensated OL Motor Dynamics Bode Plot

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Attitude Control

• With fast motor response and efficient rotors,
  flight control should be straight-forward
• But flying craft are dynamically unstable
• Unstable systems are hard to control
• Can we design a helicopter to be easy to control?

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Aside What is Flapping?

• Rotors in horizontal translation experience a
  thrust imbalance on advancing and retreating
  blades

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Aside What is Flapping?

• Rotors pivot at the hub, changing the angle of
  the on-coming airflow, causing forces to balance

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Aside What is Flapping?

• The horizontal component of thrust acts against
  the direction of motion and induces a torque
  around the vehicles centre of mass

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Aside Rotor Motion in Pitch

• A pitching quadrotor causes the rotors to move
  vertically with respect to the airflow
• Upwards motion causes the thrust to reduce,
  downwards motion causes the thrust to increase
• Rotor response resists the pitching motion
• .

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Linear System Model

• The longitudinal differential equations produce
  the following transfer function between pitch and
  rotor speed (q/w)
• .

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Root-Locus in h
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Optimising for Sensitivity

• Conceptually, we know that unstable poles are
  more difficult to control for than stable poles
• The Bode Integral shows that the magnitude of the
  sensitivity function across all frequencies is
  proportional to the sum of the unstable poles of
  the open loop plant
• The sensitivity function magnitude for a plant
  should be minimised for good disturbance rejection

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Optimising for Sensitivity

• The bode integral is minimised when the rotors
  are level with the centre of gravity h 0

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Putting It All Together

• Big, fast rotors with thin blades, with pre-twist
  to compensate for aeroelasticity
• Brushless motors and lithium polymer cells
• Feedback control for fast rotor dynamics and
  disturbance rejection that observes slew
  saturation bounds
• Put the centre of gravity coincident with the
  rotor plane

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Questions?