Control of a Ball Control of a Ball & Plate System& Plate System

Andrew PercyAndrew Percy

Academic Supervisor – James Academic Supervisor – James WelshWelsh

SummarySummary

Introduction to the Ball & Plate Introduction to the Ball & Plate SystemSystem

Background & Project MotivationBackground & Project Motivation System ModelingSystem Modeling Actuator Design & ModelingActuator Design & Modeling Sensor Design & IntegrationSensor Design & Integration Control System DesignControl System Design Remaining Work Remaining Work

The Ball & Plate SystemThe Ball & Plate System

ObjectiveObjective Balance a Ball on a Balance a Ball on a

Moveable PlateMoveable Plate Control Control

CharacteristicsCharacteristics UnstableUnstable Non-LinearNon-Linear

ExamplesExamplesx

y

x

y

Ball

Plate

Project MotivationProject Motivation

ApplicationsApplications Control ResearchControl Research Stabilized PlatformsStabilized Platforms Rolling Contact Rolling Contact

ManipulationManipulation Existing ApparatusExisting Apparatus

Actuator BacklashActuator Backlash Measurement ErrorsMeasurement Errors Rolling with SlippingRolling with Slipping

System ModelSystem Model

A Plate Fixed A Plate Fixed Reference FrameReference Frame

Plate Angular Plate Angular VelocityVelocity

x

x

y''

y'

z'

z''

HR

ry

Ball

Plate

x

O

y

y

x'

x

z

z'

HR

rx

Ball

Plate

y

O

yxxyx

yxxyx

yy

coscossinsincos

cossincossinsin

sin0cos

0

0

0

xy

xz

yz

System ModelSystem Model

Modeling Assumptions Modeling Assumptions The Ball is a Perfect SphereThe Ball is a Perfect Sphere Rolling Without SlippingRolling Without Slipping Neglect Plate Potential EnergyNeglect Plate Potential Energy Small Plate AnglesSmall Plate Angles

Lagrange's EquationLagrange's Equation

nkqdt

d

q kk

,...,2,1,0

LL

System ModelSystem Model

Complete & Coupled Non-Linear Complete & Coupled Non-Linear ModelModel

Decoupled Linear ApproximationDecoupled Linear Approximation

System Transfer FunctionsSystem Transfer Functions

xyxyyxxyyyyxxx rrHRgHRrr 2coscossin53sin7

5 2222

yyxxxxxxyyxyyxxxyy rrrHRHRgrr cos22sin57cos56sin2sin7

5 2

yyx HRgr

5

3

7

5

7

5xxy HRgr

5

7

7

5

7

5

2

2

7

535

s

HRsgr

y

x

2

2

7

557

s

gHRsr

x

y

ActuationActuation

Actuator SelectionActuator Selection Servo MotorServo Motor Stepper MotorStepper Motor Linear SolenoidLinear Solenoid Linear Induction Linear Induction

MotorMotor Magnetic ForceMagnetic Force

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

0 1 2 3 4 5 6 7 8 9 10

Displacement (mm)

Res

ulta

nt F

orce

(N)

0At

400At

800At

1200At

222

310

2

1IN

l

llF

gm

SensorsSensors

Plate AnglePlate Angle PotentiometersPotentiometers Tilt SensorTilt Sensor

Ball PositionBall Position Image ProcessingImage Processing Pressure Sensitive Pressure Sensitive

PlatePlate Sensor GridSensor Grid

Solenoid CurrentSolenoid Current Current Sense Current Sense

ResistorResistor

rx

ry Plate

Ball

Camera Buffer

Sync Separation

Sample & Hold

Micro Controller

+

-

CoilCurrent Sense Out

I

I

Control DesignControl Design

Ball Position ControlBall Position Control State FeedbackState Feedback Cascade ControlCascade Control

Ball Position

Controller

Plate Angle

Controller

Plate Dynami

cs

Ball Dynamic

s

Plate Angle Sensor

Ball Position Sensor

Desired Ball

Position

Actual Ball

Position -

+

-+

Remaining WorkRemaining Work

Continue Development of Solenoid Continue Development of Solenoid ActuatorActuator

Rebuild the Existing Ball & Plate Rebuild the Existing Ball & Plate ApparatusApparatus

Design Sensor Interface & Control CircuitsDesign Sensor Interface & Control Circuits Continue Development of System ModelsContinue Development of System Models Design & Simulation of ControllersDesign & Simulation of Controllers Develop Control SoftwareDevelop Control Software Implement & Test Control SystemImplement & Test Control System