laser deflection system: disturbance correction

Laser Deflection System:Laser Deflection System:Disturbance CorrectionDisturbance Correction

Final Presentation Final Presentation

Team 5Team 5

April 23, 2003April 23, 2003

By: Tyler FermanBy: Tyler FermanMatt DiLeoMatt DiLeoJack DamerjiJack Damerji

Laser Laser Disturbance Disturbance CorrectionCorrection

Goals: Goals: movie - movingpantilt.mpegmovie - movingpantilt.mpeg Correct for a measurable input disturbance.Correct for a measurable input disturbance. Redirect laser to target according to Redirect laser to target according to

measured disturbance of input trajectory.measured disturbance of input trajectory. ObjectivesObjectives

Develop accurate controller in order to keep Develop accurate controller in order to keep a laser communication link.a laser communication link.

Develop system to measure input trajectory Develop system to measure input trajectory disturbance.disturbance.

Original SpecificationsOriginal Specifications Input: Laser PenInput: Laser Pen

Range of motion: 53Range of motion: 53o o

Location: 5’’ x 6’’ x 0”Location: 5’’ x 6’’ x 0” Assume user input of 0.1 sec to travel across Assume user input of 0.1 sec to travel across

mirrormirror Controller:Controller:

5” mirror mounted on center of each axis5” mirror mounted on center of each axis Range of motion: 35Range of motion: 35o o

Settling time: ~0.1s Settling time: ~0.1s Overshoot: < 1% Overshoot: < 1%

Output: Point on screenOutput: Point on screen 36” away36” away

Original design ConstraintsOriginal design Constraints First pan-tilt modified to hold a laser pen.First pan-tilt modified to hold a laser pen.

cheap and accuratecheap and accurate Narrows input to 2 DOFNarrows input to 2 DOF

Second pan-tilt modified to carry a Second pan-tilt modified to carry a mirror.mirror.

ChallengesChallenges Accurately calculating input Accurately calculating input PositioningPositioning Calculation of desired mirror anglesCalculation of desired mirror angles Developing fast and accurate controllerDeveloping fast and accurate controller

Project construction and Project construction and functional testsfunctional tests

Construction: Construction: movie - showcase.mpegmovie - showcase.mpeg Input Pan-TiltInput Pan-Tilt Controller Pan-TiltController Pan-Tilt Mounting both system on one plate Mounting both system on one plate

Friction measurementsFriction measurements Tilt:Tilt:

Average Viscous Friction: .002Average Viscous Friction: .002Coulomb Friction = 0.18Coulomb Friction = 0.18

Pan:Pan:Average Viscous Friction: .0005Average Viscous Friction: .0005Coulomb Friction = 0.08Coulomb Friction = 0.08

Controller DesignController Design Linearizing SystemLinearizing System Finding a PID compensatorFinding a PID compensator Simulating the compensator on Simulating the compensator on

nonlinear systemnonlinear system

Controller DesignController Design PanPan

TiltTilt

Step Response Pan SideStep Response Pan Side

Step Response Tilt SideStep Response Tilt Side

Actual Performance Results 1

Hit rate: 100%Avg pan err: 0.0029Avg tilt err: 0.0029

movie - target.mpegmovie - target.mpeg


Hit rate: 99.6%Avg pan err: 0.0045Avg tilt err: 0.49



movie - crazyfreq.mpegmovie - crazyfreq.mpeg

Sinusoidal Response Pan Sinusoidal Response Pan side side

Sinusoidal Response Tilt Sinusoidal Response Tilt side side

Comparison of Comparison of PerformancePerformance

SpecificationSpecification Actual Actual PerformancePerformance

I/P Range of I/P Range of motionmotion

5353oo = 0.925 rad = 0.925 rad Pan: 54Pan: 54oo = 0.94 rad = 0.94 radTilt: 40Tilt: 40oo = 0.70 rad = 0.70 rad

Controller range of Controller range of motionmotion

3535o o = 0.61 rad= 0.61 rad Pan: 26.4Pan: 26.4oo = 0.46 rad = 0.46 radTilt: 40.8Tilt: 40.8oo = 0.71 rad = 0.71 rad

SpeedSpeed 6 rad/s 6 rad/s ~ 3rad/s~ 3rad/s

Error Error 1 cm1 cm 1 in 1 in

Settling timeSettling time < 0.1s< 0.1s Pan[+,-]: [0.28s, 0.36s]Pan[+,-]: [0.28s, 0.36s]Tilt[+,-]: [0.58s, 0.52s] Tilt[+,-]: [0.58s, 0.52s]

Percent OvershootPercent Overshoot < 1%< 1% Pan[+,-]: [0%, 1.5%]Pan[+,-]: [0%, 1.5%]Tilt[+,-]: [0%, 0%] Tilt[+,-]: [0%, 0%]

Steady State ErrorSteady State Error < 0.1< 0.1oo Pan[+,-]: [-0.46, 0.006 ]Pan[+,-]: [-0.46, 0.006 ]Tilt[+,-]: [0.34, 0.57] Tilt[+,-]: [0.34, 0.57]

System ImprovementSystem ImprovementMax Disturbance without controllerMax Disturbance without controller 1313in on average from each sidein on average from each side

VSVS

Max Disturbance with controllerMax Disturbance with controller11in from each sidein from each side

Movie: closeup.mpegMovie: closeup.mpeg

Success and challengesSuccess and challenges Success: Success: movie - mirrorview.mpegmovie - mirrorview.mpeg

Robust ControllerRobust Controller Accurate calculation for desired angles Accurate calculation for desired angles

using math modelusing math model 1300% improvement of disturbance 1300% improvement of disturbance

rejectionrejection Quick interaction between input pan-tilt Quick interaction between input pan-tilt

and controller pan-tilt and controller pan-tilt

Success and challengesSuccess and challenges Challenges:Challenges:

Discrepancy between system model Discrepancy between system model simulation and physical systemsimulation and physical system

Initialization of input and mirror anglesInitialization of input and mirror angles Quantization Effects:Quantization Effects:

Steady-state errorSteady-state error Oscillation due to derivative control Oscillation due to derivative control

Design controller for random input Design controller for random input (different speeds/frequencies)(different speeds/frequencies)

RecommendationsRecommendations Adaptive controller to allow control Adaptive controller to allow control

for random inputfor random input Calibration systemCalibration system Use Kalman filter to reduce Use Kalman filter to reduce

quantization effectsquantization effects Recalculate mass matrix, inertia Recalculate mass matrix, inertia

matrix and friction calculationmatrix and friction calculation

QuestionsQuestions

laser deflection system: disturbance correction

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