AOE 5204Vehicle Dynamics & Control

Fall 2006Professor Chris HallRandolph 214cdhall@vt.eduhttp://www.aoe.vt.edu/~cdhall

AOE 5204Vehicle 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/weekMidterm I 25% 6th week

first midterm exam will be closed-notes

Midterm II 25% 11th weeksecond midterm exam will be open-notes

Final Exam 25% Finals weekfinal 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:

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

• The governing physical principle is Newton’s 2nd Law:

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

~f = m~awhere~f is the net applied force,m is the vehicle mass, and~a is the acceleration

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 Guidanceand 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:

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

• The governing physical principle is Euler’s Law:

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

~g = ddt

~hwhere~g is the net applied torque, and~h is the angular momentum

Roll, Pitch and Yaw

Roll, Pitch and YawRoll Axis

Pitch Axis

Yaw Axis

Roll

Yaw

Pitch

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 Guidanceand Control of Ocean Vehicles, Wiley, 1994

Fundamental Thoughts (4)• The two governing physical principles

are more alike than appears at first glance:

• Another way to state the 2nd Law is:)~f = d

dt~p

~g = ddt

~h

Newtons 2nd Law~f = m~awhere~f is net applied force,m is vehicle mass, and~a is acceleration

Eulers Law~g = d

dt~h

where~g is net applied torque, and~h is angular momentum

~f = m ddt~v

~f = ddt (m~v)

~f = ddt~p

where~p is linear momentum

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