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Ball and plate system

Ball and plate system. Making an unstable system stable. J. Gorasia and D. Greeley. Goals. Making an unstable system stable Make system capable of rejecting noise Decent transient response. The Plant. Proportional Angular Displacement Approximation. Transfer Function.

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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?

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