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## Ball and plate system

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**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**Bode of Compensated and Uncompensated**Kplant= .016 Kl=100 τ=1 α=10**Sensors**1 2 • Affine • Filter for colors • Threshold • Find centroid 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 • 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**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