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Ball and plate system PowerPoint Presentation
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Ball and plate system

Ball and plate system

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Ball and plate system

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  1. Ball and plate system Making an unstable system stable J. Gorasia and D. Greeley

  2. Goals • Making an unstable system stable • Make system capable of rejecting noise • Decent transient response

  3. The Plant Proportional Angular Displacement Approximation

  4. Transfer Function Small angle approximation Transfer Function

  5. Lead Compensation

  6. Bode of Compensated and Uncompensated Kplant= .016 Kl=100 τ=1 α=10

  7. Implementation

  8. Sensors 1 2 • Affine • Filter for colors • Threshold • Find centroid 3 4 Resolution: 160x120 33 frames per second

  9. Motors • Hitec HSR-5995TG • Moves at maximum speed of 0.12 sec/60degrees • Which translates to a maximum frequency of 1.4rad/s of the plate • Torque 417 oz-in

  10. Discretization • Use design by emulation • Do everything in s domain, then digitize • Substitute s to z using: • Solve for largest power of the output • Then perform the inverse z transform

  11. Discrete Compensator

  12. Algorithm Shift previous values of error Determine error Shift previous values of control signal Read x position from camera Condition control signal to a position of servo Use discrete transfer function to determine control signal

  13. Verification • Goals met? • Model accurate? • What are the sources of error? • Image tracking • Saturation • Discrete angle positions • Bending of the plate • Model of servos

  14. Going forward • Use vvvv or FPGA for vision tracking • More angular displacement of plant • Use RTOS or embedded chip for control system • Better plant design

  15. Questions?