Ball and plate system
description
Transcript of Ball and plate system
Ball and plate systemMaking 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
Small angle approximation
Transfer Function
Lead Compensation
Bode of Compensated and Uncompensated
Kplant = .016 τ=1Kl=100 α=10
Implementation
Sensors
1. Affine2. Filter for
colors3. Threshold4. Find centroid
1 2
3 4
33 frames per secondResolution: 160x120
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
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
Discrete Compensator
Algorithm
Read x position
from camera
Determine error
Shift previous values of
error Shift previous values of control signal
Use discrete transfer function
to determine control signal
Condition control signal to a position
of servo
Verification
•Goals met?•Model accurate?•What are the sources of error?
▫Image tracking▫Saturation▫Discrete angle positions▫Bending of the plate▫Model of servos
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
Questions?