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