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Hovercraft Kinematic Modeling

. Outline. The ProblemHovercraftDeveloping the State-Space Model. Parameter EstimationSimulationsRealismStabilityConclusions. . The Problem. Aim: to create an accurate mathematical model of hovercraft's motionReasons: to explore an interesting mechanical system to achieve correlation betwe

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Hovercraft Kinematic Modeling

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    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 The Problem Hovercraft Developing the State-Space Model Parameter Estimation Simulations Realism Stability Conclusions

    3. The Problem Aim: to create an accurate mathematical model of hovercraft’s 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. Hennessey’s 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

    9. Moment of Inertia Experiment No simple, convenient shape for calculation purposes Necessary to find moment of inertia experimentally -Hovercraft makes small oscillations -Number of rotations counted over 60 sec This experiment’s usefulness is not limited to toy hovercraft. UMTRI (University of Michigan Transportation Research Institute) uses a similar process to measure the moment of inertia in very large commercial and military vehicles.-Hovercraft makes small oscillations -Number of rotations counted over 60 sec This experiment’s usefulness is not limited to toy hovercraft. UMTRI (University of Michigan Transportation Research Institute) uses a similar process to measure the moment of inertia in very large commercial and military vehicles.

    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

    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

    16. Obstacle Course 2

    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

    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

    20. Questions?

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