Model Predictive Control of a Parafoil and Payload System

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Model Predictive Control of a Parafoil and
Payload System
By Nathan Slegers Department of Mechanical
Engineering Oregon State University Corvallis,
Oregon 97331
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Topics Covered

• Dynamic Modeling of the Parafoil and Payload
  System
• N. Slegers, M. Costello, Aspects of Control for
  a Parafoil and Payload System, Journal of
  Guidance, Control, and Dynamics, Vol 26, No 6,
  2003.
• N. Slegers, M. Costello, On the Use of Rigging
  Angle and Canopy Tilt for Control of a Parafoil
  and Payload System, AIAA Atmospheric Flight
  Mechanics Conference and Exhibit, Austin, Texas,
  August 2003, AIAA Paper 2003-5609.
• N. Slegers, M. Costello, Comparison of Measured
  and Simulated Motion of a Controllable Parafoil
  and Payload System, AIAA Atmospheric Flight
  Mechanics Conference and Exhibit, Austin, Texas,
  August 2003, AIAA Paper 2003-5611.
• Model Predictive Control
• N. Slegers, M. Costello, Model Predictive
  Control Of A Parafoil And Payload System , AIAA
  Atmospheric Flight Mechanics Conference and
  Exhibit, Providence, RH, August 2004, AIAA Paper
  2004-XXXX.

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Motivation
Deploy System
Download Objective To Payload Through IR Port
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Dynamic Modeling

• Three Models Have Been Created
• 9 DOF With Canopy Modeled As Panels
• Components of the Position Vector
  of the Pivot Point in the Inertial Frame
• Euler Roll, Pitch and Yaw Angles
  of the Payload
• Euler Roll, Pitch and Yaw Angles
  of the Parafoil
• 6 DOF With Canopy and Payload Having Combined
  Aerodynamic Coefficients
• Reduced Order Linear Model Required For Model
  Predictive Control

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9DOF Equations of Motion

• Kinematic Equations

Translation and Rotation Dynamics Equations
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6 DOF Equations of Motion

• Kinematic Equations

Translation and Rotation Dynamics Equations
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Advantage Of Modeling Canopy With Panels

• Control Authority Reverses and Two Modes of
  Control are Demonstrated
• Roll Steering Lift Dominated and Rolls Parafoil
• Skid Steering Drag/Side Force Dominates Yaws
  Parafoil

Turn Rate vs. Curvature (10 deg Right Brake)
Turn Rate vs. Brake Deflection
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Alternative Lateral Control Methods

• Conventionally Lateral Control Is Achieved By
  Deflecting Parafoil Brakes Asymmetrically
• Alters Lift and Drag Magnitudes
• Control Reversal May Be Present At Small Brake
  Deflections
• Alternatively Canopy Tilting Can Achieve Lateral
  Control
• Alters Lift and Drag Direction Not Magnitudes
• Control Reversal Does Not Exist

Canopy Tilt
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Canopy Tilt and Brake Coupling

• Parafoil Canopies Are Highly Flexible Membranes,
  Deflection of Parafoil Brakes Also Tilts the
  Canopy on That Side.

• Coupling Determines Direction of Control Response
• Coupling of 1.4 Degrees of Canopy Tilt From 1
  Inch of Brake Results in Positive Turn Rates
• 1.0 Deg/in Results in Nearly No Response
• 0.5 Deg/in Results in Negative Turn Rates

Brake Deflection and Canopy Tilt Coupling (Deg/in)
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Model Predicted Turn Rates With Canopy Tilt
Correction

• Panel Deflection and Canopy Tilting Control
  Methods Can Be Combined Into the Model
• Two Controls Methods Nearly Cancel Resulting in
  Correct Direction and Magnitude of Response

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Model Predictive Control

• Model Predictive Control Uses A Model To Predict
  The Future Dynamics of A System And Produces An
  Optimal Control Sequence For The Desired Dynamics
• Consider A Linear Discrete Time System Described
  As
• A Cost Function Weighting Tracking Error And
  Control Input Is Formed

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Model Predictive Control

• Estimated States Are Found To Be
• Cost Function Can Be Rewritten As

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Model Predictive Control

• The Optimal Control Sequence Is Found By
  Minimizing The Cost Function With Respect To The
  Control Sequence Resulting In
• Notice That K Is Constant And Is Calculated Ahead
  Of Time. The Sequence Only Requires A Desired
  State And The Current State.
• Only The Next Control Is Found By Using Only The
  First Row Of K.

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Parafoil Linear Model

• MPC Requires A Linear Model
• A Full State Linear Model Can Only Be Produced
  For A Small Range Of Yaw/Heading Angle
• A Reduced State Linear Model Was Created From The
  Nonlinear 6DOF Model
• It Turns Out That Yaw Angle Is The State With The
  Most Significant Control Authority

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Acquiring Desired States

• Optimal Control Sequence Requires Current States
  And Desired Output As A Linear Combination Of The
  States.
• The Desired Path In The X-Y Plane Was Mapped Into
  A Desired Heading Angle Assuming A Constant
  Velocity And No Side Slip

• Intersect Distance
• Used To Define How Quickly To Get On Desired Path
• Small Value Used If Important To Be On Path From
  Pt 1 To Pt 2
• Large Value Used If More Concerned With Only
  Points
• Look Ahead Distance
• Defines When To Increment Desired Path Points

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Full State Measurement

• Model Predictive Control Requires Roll and Yaw
  Angles and Rates Along With Latitude and
  Longitude
• WAAS Enabled GPS Receiver Acquires 3 Inertial
  Positions
• Attitude Is Acquired Through A Three Axis
  Magnetometer, 3 Axis Accelerometer And 3 Axis
  Gyroscope

4 PWM Output Channels
Kalman Select Channels
4 PWM Input Channels
Control Select Channel
Attitude Sensor
Wireless Transeiver
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Parafoil And Payload Test System
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Estimation Of Reduced State Aerodynamic
Coefficients

• Constant Linear Model Aerodynamic Coefficients
  Are Estimated Through A Recursive Weighted Least
  Squares Estimator (Kalman Filter Estimating
  Constants)
• Requires Rate Of Change Of the Roll and Yaw Rate

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Implementation Of Estimation

• A Control Sequence Is Initiated And Continuously
  Cycled
• The Control Sequence Creates A Sinusoidal Roll
  And Yaw Rate So The Numerically Estimated
  Derivatives Are Well Behaved

KALMAN MODE ON
KALMAN MODE OFF
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Estimation Flight Data
Angular Accelerations
Control Sequence
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Comparison Of Model Vs Flight Data
Roll Angle
Roll Rate
Yaw Angle
Yaw Rate
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Tracking A Box With Model Predictive Control
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Tracking Zigzag With Model Predictive Control
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Summary Of Model Predictive Control

• A Reduced State Linear Model Was Developed For
  Use In MPC
• A Mapping From A Desired X-Y Path To A Desired
  Yaw Angle Was Established
• Model Parameters Were Estimated Effectively
  Performance And Steady State Error Is Directly
  Related To Errors In Measured Yaw Angle
• Through An Intersect Distance And Look Ahead
  Distance MPC Can Be Tuned For Different
  Objectives
• MPC is a natural and effective way to
  autonomously control the trajectory of a parafoil
  and payload system

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Dynamic Modeling, Control Aspects and Model
Predictive Control of a Parafoil and Payload
System
By Mark Costello, Associate Professor Nathan
Slegers, Ph.D. Student Department of Mechanical
Engineering Oregon State University Corvallis,
Oregon 97331
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Model Predictive Control of a Parafoil and
Payload System
By Nathan Slegers Department of Mechanical
Engineering Oregon State University Corvallis,
Oregon 97331