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?