1. Making an unstable system stable
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 Affine Filter for colors Threshold Find centroid 1 2 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 Substitute s to z using:
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?