Hovercraft Kinematic Modeling

1
Hovercraft Kinematic Modeling

• Lindsey Hines
• Sophomore, Class of 2008
• Faculty Advisor Michael P. Hennessey, Ph.D.
• Center for Applied Mathematics (CAM)
• University of St. Thomas
• August 16, 2005

2
Outline

• Parameter Estimation
• Simulations
• Realism
• Stability
• Conclusions

• The Problem
• Hovercraft
• Developing the State-Space Model

3
The Problem

• Aim to create an accurate mathematical model of
  hovercrafts motion
• Reasons
• to explore an interesting mechanical system
• to achieve correlation between the computer-run
  simulations and real life
• to form a foundation for further applications
• to prepare material for Dr. Hennesseys J-term
  kinematics class

4
Hovercraft

• Lift fan and skirt allow hovercraft to ride on
  cushion of air
• Rear fans provide force necessary for forward
  motion and direction change
• Can be regarded as a 2-D rocket

5
Developing the State-Space Model

• state-space vector
• force input from thrusters
• friction parameters
• inertia parameters
• geometric parameter

6
Equations of Motion
7
Parameter Estimation

• Geometric parameter ( ) simple to determine
• Maximum force ( ) imparted by rear fans
  measured by spring gauge
• Mass ( ) measured by electronic scale
• Determining the translational ( ) and
  rotational ( ) coefficients of viscous
  friction and the moment of inertia ( ) was more
  difficult

8
Viscous Friction Experiment

• Only incorporating viscous friction
• Viscous friction coefficients and
  estimated
• Hovercraft brought to top speed then allowed to
  coast to a stop
• Time to stop measured
• similar to except involves rotational
  motion

vo
9
Moment of Inertia Experiment

• No simple, convenient shape for calculation
  purposes
• Necessary to find moment of inertia experimentally

Two supporting cables
10
Simulations

• Matlab
• Script files
• Simulink
• Open loop
• No active control feed in values and see where
  the hovercraft goes
• Input values ( and ) are parameterized by
  blocks of time where on/off is represented by the
  values of and 0.

11

• Hovercraft Subsystem

12
Simulation Block Diagram
13
Simulink Configuration
14
Is this Realistic?

• Basic maneuvers the test of common sense
• Different initial conditions,
• Left/right turns,
• Straight-line motion
• Obstacle course simulations
• Requires more precision
• Two different courses run in Matlab
• Fan inputs reenacted on remote control by
  blindfolded individual

15
Obstacle Course 1
Finish
Start
16
Obstacle Course 2
Start
Finish
17
Video Clips

• Example of the difficulty directing hovercraft
• Direction and speed
• The ideal run
• Obstacle course 1 human judgment and control

18
Stability

• Linear stability analysis, open loop system
• small
• Marginally stable

Linear model
Six Eigenvalues
19
Conclusions

• Hovercraft can be modeled in Matlab and Simulink
  more accuracy necessary
• Stabilization is possible
• Completing stabilization
• Creating more accurate feedback for closed loop
  sensors

Future Work
20
Questions?