AOE 5204 Vehicle Dynamics & Control by rsnRgbG5

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									AOE 5204
Vehicle Dynamics & Control




 Fall 2006
 Professor Chris Hall
 Randolph 214
 cdhall@vt.edu
 http://www.aoe.vt.edu/~cdhall
AOE 5204
Vehicle Dynamics & Control
 Course description:
 This course focuses on the relevant rigid body
 kinematics and dynamics issues common to studying the
 motion of several types of vehicles such as aircraft,
 spacecraft, and ships, and provides a foundation for
 advanced courses and research on the dynamics and
 control of vehicles.       The course includes a review of
 particle motion and its application to aircraft
 performance and satellite orbital mechanics.       Modeling
 of the rotational and translational motion of rigid
 bodies is covered in detail, with emphasis on rigor.
 Special cases are used to illustrate application of the
 general equations of motion. Linearization of the
 equations of motion is demonstrated for stability
 analysis, modal analysis, and control system synthesis,
 with an introduction to classical control system
 concepts.       Sensors and actuators commonly used on
 vehicles are described. Specific examples from
 aircraft, missiles, spacecraft, rockets, ships, and
 submersibles are developed to illustrate applications
 relevant to AOE majors. Pre: AOE 3134, 4140, or
 permission of instructor. (3H, 3C).
      Topics To Be Covered
• Overview (~2 lectures)
• Review of particle motion (~2 lectures)
• Rotational kinematics (~4 lectures)
• Rigid body motion (~4 lectures)
• Linear systems analysis (~6 lectures)
• Applications (~9 lectures)

 Details are included in syllabus
      Assignments and Grading
Homework          25%           ~one/week
Midterm I         25%           6th week
     first midterm exam will be closed-notes
Midterm II        25%           11th week
     second midterm exam will be open-notes
Final Exam        25%           Finals week
     final exam will be open-notes & comprehensive
Homework assignments should be completed in a
professional manner. Typesetting is not required,
but handwritten work should be neat and legible.
                    Overview
• Examples from aircraft, missiles, spacecraft, rockets,
  ships, and submersibles, such as Herbst maneuver,
  target tracking, landmark tracking, launch to orbit,
  capsizing, and gliding. This overview will include
  videos, animations, and examples of successes and
  failures.
• These examples will be used to emphasize that
  translational and rotational motion are coupled, but
  that decoupled analysis is useful. The overview will
  also discuss the importance of control systems in
  these problems, with some discussion of sensors and
  actuators.
               What Vehicles?
• A vehicle is a mechanical system for transporting
  objects in space:
  – oxcarts, chariots, ships, bicycles, motorcycles,
    automobiles, airplanes, spacecraft, submarines, rockets,
    missiles, ….
• In this course, we are primarily interested in
  vehicles whose three-dimensional motion is
  reasonably well-approximated by a combination
  of point-mass and rigid-body models:
  – airplanes, spacecraft, submarines, rockets, missiles, ….
              Key Distinctions
• Land vehicles, such as motorcycles, depend on elastic
  deformation as an important element of vehicle dynamics
• Illustrations from R.S. Sharp, S. Evangelou And D.J.N.
  Limebeer, “Advances in Motorcycle Dynamics,”
  Multibody System Dynamics 12: 251–283, 2004
         Fundamental Thoughts
• The first approximation of the motion of a vehicle is to
  consider the vehicle as a point mass subject to applied
  forces
   – Environmental forces such as gravity and aerodynamic drag
   – Control forces such as propulsive thrust


                                    • The governing physical principle
                                      is Newton’s 2nd Law:
                                         ~   ~
                                         f = ma
                                         wher e
                                         ~ i s t he net appl i ed for ce,
                                         f
                                         m i s t he vehi cl e mass, and
                                         ~ i s t he accel er at i on
                                         a

                                    • The D&C analyst’s challenge is to
                                      correctly model the forces to
                                      determine, and control, the
                                      vehicle’s motion
     Fundamental Thoughts (2)
• For aircraft, there is no special terminology for
  translational motion or deviations from nominal
  translational motion
• For spacecraft, deviations from nominal motion are
  referred to as in-track, cross-track, and radial motions
• For ships, translational motion components are referred
  to as surge, sway, and heave
   – Illustration from on-line notes
     of T. I. Fossen, author of Guidance
     and Control of Ocean Vehicles,
     Wiley, 1994
      Fundamental Thoughts (3)
• The second approximation of the motion of a vehicle is
  to consider the vehicle as a rigid body subject to applied
  forces and moments
   – Environmental forces and moments such as those due to gravity
     and aerodynamic drag
   – Control forces and moments such as those due to propulsive
     thrust and momentum exchange devices
                                    • The governing physical principle
                                      is Euler’s Law:
                                         ~= d~
                                         g        h
                                               dt
                                         wher e
                                         ~ i s t he net appl i ed t or que, and
                                         g
                                         ~ i s t he angul ar moment um
                                         h


                                    • The D&C analyst’s challenge is to
                                      correctly model the moments
                                      and forces to determine, and
                                      control, the vehicle’s motion
Roll, Pitch and Yaw
                   Roll, Pitch and Yaw
                                            Yaw
                                Yaw Axis                                       Roll Axis

                Pitch

                                                                            Roll
Pitch Axis




             Note: RPY Axes can vary significantly from spacecraft to spacecraft,
             depending on the specifics of a particular spacecraft’s mission.
  Roll, Pitch, and Yaw




Illustration from on-line notes of T. I. Fossen, author of Guidance
and Control of Ocean Vehicles, Wiley, 1994
       Fundamental Thoughts (4)
• The two governing physical principles are
  moresalikewthan appearsEat r first glance:
  N ew t on 2n d L a      u l e s L aw
  ~ = m~
  f       a                         ~= d~
                                    g        h
                                          dt
  wher e                            wher e
  ~ i s net appl i ed for ce,
  f                                 ~ i s net appl i ed t or que, and
                                    g
  m i s vehi cl e mass, and         ~ i s angul ar moment um
                                    h
  ~ i s accel er at i on
  a


• Another way to state the 2~ = dis:
   ~
   f = md~
             dt
   ~ = d ( m~ )
                v
                            nd Law
                            f   )  ~
                                   p
                                                      dt
   f
   ~= d~
   f
         dt
             p
                  v
                                          ~=
                                          g            d    ~
                                                            h
         dt
   wher e                                             dt
   ~ i s l i near moment um
   p
Fundamental Thoughts (5)
             • One of the more
               difficult elements of
               modeling rotational
               motion is the
               connection between the
               orientation of the
               vehicle and the angular
               momentum

             • Rotational kinematics is
               sufficiently important
               that we will discuss it in
               a separate series of
               lectures before
               discussing rigid body
               motion
                    Examples
• The remainder of this lecture and the next
  will provide some examples of vehicle
  dynamics and control problems from the
  literature
  –   Hubble Space Telescope
  –   Shuttle Pilot-Induced Oscillation (PIO)
  –   C-17 Aerial Refueling PIO
  –   YF22 PIO and Crash
  –   USS Bakula Missile Fin Flutter
  –   F-15 Missile Deployment
  –   Atlantis Launch
           Hubble Space Telescope
•   Launched April 1990
•   Mass = 11000 kg
•   Pointing = 0.007 arc seconds
•   Orbit:
    –   Low-Earth Orbit (LEO)
    –   ~580 km altitude, 96 min period
    –   Velocity ~17,000 mph (7.6 km/s)
    –   28.5 inclination
• Attitude sensors:
    – Fine Guidance Sensors, Gyros,
      Star trackers, Sun sensors,
      Magnetometers
• Attitude actuators:
    – Momentum wheels and Magnetic torque bars
• Attitude control is extremely precise, but rotational maneuvers are
  quite slow: about the speed of the minute hand on a clock
                  Videos
• Shuttle Pilot-Induced Oscillation (PIO)
• C-17 Aerial Refueling PIO
• YF22 PIO and Crash
• USS Bakula Missile Fin Flutter
• F-15 Missile Deployment
• Atlantis Launch

								
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