Making an unstable system stable 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 Small angle approximation Transfer Function

Lead Compensation

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

Implementation

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

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 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

Discrete Compensator

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

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?