control of manufacturing process - dspace@mit: … · control of manufacturing process ... 2/5/04...

Control of Manufacturing Control of Manufacturing ProcessProcessSubject 2.830

Spring 2004Spring 2004

Lecture #2 Lecture #2 “Process Modeling for Control”“Process Modeling for Control”

February 5, 2004February 5, 2004

2/5/04 2.830 Lecture #2 2

Key TopicsKey Topics•• Process Taxonomy for ControlProcess Taxonomy for Control

–– Classifying the Universe of ProcessesClassifying the Universe of Processes

•• Control versus VariationControl versus Variation–– The Good, Bad and UglyThe Good, Bad and Ugly

•• Process Model for ControlProcess Model for Control–– Equipment & Material DistinctionsEquipment & Material Distinctions–– Process Parameters: States & PropertiesProcess Parameters: States & Properties

2/5/04 2.830 Lecture #2 3

Recall the ModelRecall the Model

Equipment MaterialE(t ) Geometry &

Properties

What Controls the Geometry Change?

2/5/04 2.830 Lecture #2 4

What Controls the What Controls the Geometry Change?Geometry Change?

•• Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange•• Examples:Examples:

–– Location of Max. Shear Stress in TurningLocation of Max. Shear Stress in Turning–– Heat Transfer at the Mold Surface in Injection MoldingHeat Transfer at the Mold Surface in Injection Molding–– Displacement Field in Sheet StampingDisplacement Field in Sheet Stamping–– Reaction Rate Reaction Rate -- Time Product on Substrate Surface in Time Product on Substrate Surface in

LPCVDLPCVD–– Location of Laser Bean in Laser TrimmingLocation of Laser Bean in Laser Trimming

2/5/04 2.830 Lecture #2 5

Two Extremes of Interactions Two Extremes of Interactions Area of E(t) << Total Area: Serial Process

Area of E(t) ~ Total Area: Parallel Process

v(t)

y(t)K(s)

2/5/04 2.830 Lecture #2 6

What Determines Part What Determines Part Geometry Change?Geometry Change?

•• For Lumped case:For Lumped case:–– time time -- trajectory of the port locationtrajectory of the port location

•• e.g. tool pathse.g. tool paths

•• For Distributed Case: For Distributed Case: –– Shape of the energy distributionShape of the energy distribution

•• patternspatterns•• moldsmolds•• masksmasks

2/5/04 2.830 Lecture #2 7

ExamplesExamples

•• Serial (Lumped) ProcessesSerial (Lumped) Processes–– MachiningMachining -- Tool PathTool Path–– Laser CuttingLaser Cutting -- Beam pathBeam path–– BendingBending -- Tool DepthTool Depth–– Stereolithography Stereolithography -- Beam PathBeam Path–– Three D PrintingThree D Printing -- Binder PathBinder Path

2/5/04 2.830 Lecture #2 8

ExamplesExamples

•• Parallel (Distributed) ProcessesParallel (Distributed) Processes–– Draw Forming Draw Forming -- Die ShapesDie Shapes–– Injection MoldingInjection Molding -- Mold ShapeMold Shape–– Chemical Etching Chemical Etching -- Mask ShapeMask Shape–– CMPCMP -- Tool ShapeTool Shape–– PlatingPlating -- Substrate ShapeSubstrate Shape

2/5/04 2.830 Lecture #2 9

Toward a Process TaxonomyToward a Process Taxonomy

•• Classify by Change ModeClassify by Change Mode–– Why?Why?

•• Classify by Interaction area Classify by Interaction area (serial/parallel)(serial/parallel)–– So what?So what?

•• Classify by Energy DomainClassify by Energy Domain–– Who cares??

Sensitivity, resolution

Flexibility, controllability, rate

Who cares?? Rate, resolution

2/5/04 2.830 Lecture #2 10


Dominant Energy Domain

Transformation Methods

Serial Interaction Parallel Interaction


MechanicalThermalChemicalElectrical


2/5/04 2.830 Lecture #2 11








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2/5/04 2.830 Lecture #2 14

Process Taxonomy for ControlProcess Taxonomy for ControlTransformation REMOVAL

Mode SERIAL PARALLEL

Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalCutting Laser Cutting EDM Die Stamping ECM EDMGrinding "Flame" Cutting PhotolithographyBroaching Plasma CuttingPolishingWater Jet

Transformation ADDITION/JOINING


Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical3D Printing Laser E-Beam Welding HIP Sintering LPCVDUltrasonic Sintering Arc Welding PlatingWelding Resistance Welding

Transformation FORMATION


Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalPlasma Spray Stereolithography Inertia Bonding Casting DiffusionDBM Molding Bonding

Transformation DEFORMATION


Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalBending Line Heating DrawingForging(open) Forging(die)Rolling

Process Process Eye ChartEye Chart for Controlfor Control

2/5/04 2.830 Lecture #2 15

Process Taxonomy:Process Taxonomy:RemovalRemoval

Transformation REMOVAL

Mode SERIAL

Energy Source Mechanical Thermal Chemical ElectricalCutting Laser Cutting EDMGrinding "Flame" CuttingBroaching Plasma CuttingPolishingWater Jet

PARALLEL

Mechanical Thermal Chemical ElectricalDie Stamping ECM EDM

Photolithography

2/5/04 2.830 Lecture #2 16

Process Taxonomy:Process Taxonomy:DeformationDeformation

Transformation DEFORMATION

Mode SERIAL

Energy Source Mechanical Thermal Chemical ElectricalBending Line HeatingForging(open)Rolling

PARALLEL

Mechanical Thermal Chemical ElectricalDrawingForging(die)

2/5/04 2.830 Lecture #2 17

Process Taxonomy:Process Taxonomy:AdditionAddition

Transformation ADDITION

Mode SERIAL

Energy Source Mechanical Thermal Chemical Electrical3D Printing Laser E-Beam WeldingUltrasonic Sintering Arc WeldingWelding Resistance Weldin

PARALLEL

Mechanical Thermal Chemical ElectricalHIP Sintering LPCVD

Plating

RAPID

PROTOTYPING

METHODS

2/5/04 2.830 Lecture #2 18

Process Taxonomy:Process Taxonomy:FormationFormation

Transformation FORMATION

Mode SERIAL

Energy Source Mechanical Thermal Chemical ElectricalPlasma Spray StereolithographyDBM

PARALLEL

Mechanical Thermal Chemical ElectricalInertia Bonding Casting RIM

Molding Diffusion Bonding

RAPID

PROTOTYPING

METHOD

2/5/04 2.830 Lecture #2 19

Control vs. VariationControl vs. Variation

•• ControlControl Is Intentional and Is Intentional and DeterministicDeterministic

•• VariationVariation Is Unintentional And/or Is Unintentional And/or RandomRandom

2/5/04 2.830 Lecture #2 20

What Causes What Causes VariationVariationin the Process Output?in the Process Output?

•• Material VariationsMaterial Variations–– Properties, Initial GeometryProperties, Initial Geometry

•• Equipment VariationsEquipment Variations–– NonNon--repeatable, long term wear, deflectionsrepeatable, long term wear, deflections

•• Operator VariationsOperator Variations–– Inconsistent control, excessive “tweaking”Inconsistent control, excessive “tweaking”

•• “Environment” Variations“Environment” Variations–– Temperature and Handling inconsistenciesTemperature and Handling inconsistencies

2/5/04 2.830 Lecture #2 21

Process Model for ControlProcess Model for Control

Equipment MaterialE(t )“controls” Geometry &

Properties

Process Y ≡ Process Ouputs

Y = Φ(α )α ≡ process parameters

What are the α’s?

2/5/04 2.830 Lecture #2 22

What What areare the the Process ParametersProcess Parameters??

•• Equipment Energy “States”Equipment Energy “States”•• Equipment Constitutive “Properties”Equipment Constitutive “Properties”

•• Material Energy “States”Material Energy “States”•• Material Constitutive ”Properties”Material Constitutive ”Properties”

2/5/04 2.830 Lecture #2 23

Energy StatesEnergy States

Energy Domain Energy or Power Variables

Mechanical F, v ; P, Q or F, d ; σ, ε

Electrical V,I

Thermal T, ds/dt (or dq/dt)

Chemical chemical potential, rate

2/5/04 2.830 Lecture #2 24

PropertiesProperties

•• ExtensiveExtensive: : GEOMETRYGEOMETRY•• IntensiveIntensive: Constitutive Properties : Constitutive Properties

–– Modulus of Elasticity, damping, massModulus of Elasticity, damping, mass–– Plastic Flow PropertiesPlastic Flow Properties–– ViscosityViscosity–– Resistance, Inductance, CapacitanceResistance, Inductance, Capacitance–– Chemical ReactivityChemical Reactivity–– Heat Transfer CoefficientHeat Transfer Coefficient

2/5/04 2.830 Lecture #2 25

Topics for TodayTopics for Today•• Causes of VariationCauses of Variation

–– Parameter UncertaintyParameter Uncertainty•• Definition of Control Input to ProcessDefinition of Control Input to Process

–– Accessible, Deterministic ParametersAccessible, Deterministic Parameters•• The Process Variation EquationThe Process Variation Equation•• Process Control HierarchyProcess Control Hierarchy

–– Attacking the Variation EquationAttacking the Variation Equation•• Control Loops in ManufacturingControl Loops in Manufacturing

2/5/04 2.830 Lecture #2 26

Delineation of Process Delineation of Process ParametersParameters

Y = Φ(α )α = (ep ,es ,mp ,ms )

ep = equipment properties

es = equpment statesm p = material properties

ms = material states


Properties

ep, es mp, ms

Y

α

2/5/04 2.830 Lecture #2 27

What Causes Variations?What Causes Variations?If → Y = Φ(α )

Any Change (or uncertainty) in α

α = (ep ,es,m p ,ms)•Which parameters are most certain and least variable?

(The good ones)

•Which parameters are least certain or most variable?

(The bad ones)

2/5/04 2.830 Lecture #2 28

A Rough Scale of “Goodness”A Rough Scale of “Goodness”

ep Machine Structure, Stiffness

e

Constant / known

Variable / unknown

s Positions Forces, temperatures

ms Stresses, Surface Temp., Flowrate, Concentration

mp Stress-strain, Tg, Viscosity, Reactivity, Resistance

Based on What???

2/5/04 2.830 Lecture #2 29

Now Consider a Typical Process:Now Consider a Typical Process:e.g. Machininge.g. Machining

ep Structural GeometryStructural stiffens, damping, and natural frequencies, Tool Geometry

es Tool Velocity, Spindle SpeedCutting ForceTool Temperature and Heat Flux

ms Shear stress at tool interfaceBending Stresses in the workpieceTemperature of chip area

mp Initial Geometry Material hardnessBasic properties: σY, n, r, …

2/5/04 2.830 Lecture #2 30

We Lost the Controls!We Lost the Controls!

Process Y ≡ Process Ouputs

Y = Φ(α )


Properties

•• Where are the control inputs?Where are the control inputs?–– A specific A specific subsetsubset of the parametersof the parameters

2/5/04 2.830 Lecture #2 31

Where are the Control Inputs to a Where are the Control Inputs to a Process?Process?

E(t )

•• Example: the latheExample: the lathe–– The tool positionThe tool position–– The leadscrew positions?The leadscrew positions?–– ??????

Equipment Material“controls” Geometry &Properties

2/5/04 2.830 Lecture #2 32

Control Inputs to a ProcessControl Inputs to a Process

•• What are the “best” inputs?What are the “best” inputs?−− αα’s that are’s that are::

•• deterministicdeterministic•• accessibleaccessible•• “fast”“fast”•• “effective”“effective”

–– significant effect on outputsignificant effect on output

E(t )Equipment Material“controls” Geometry &

Properties

2/5/04 2.830 Lecture #2 33

Back to the LatheBack to the Lathe•• Tool PositionTool Position

–– Fast?Fast?–– Accessible?Accessible?–– Effective?Effective?–– Deterministic?Deterministic?

•• What is accessible?What is accessible?

2/5/04 2.830 Lecture #2 34

Back to the LatheBack to the Lathe

•• Tool PositionTool Position–– FastFast yesyes–– AccessibleAccessible nono–– EffectiveEffective yesyes–– DeterministicDeterministic ? ?

•• What is accessible?:What is accessible?:–– Lead Screw RotationLead Screw Rotation–– FastFast yesyes–– AccessibleAccessible yesyes–– EffectiveEffective yesyes–– DeterministicDeterministic yes yes

2/5/04 2.830 Lecture #2 35

BUT!BUT!

•• If the If the tool positiontool position is downstream of the is downstream of the leadscrewleadscrewrotation it is no longer deterministic!rotation it is no longer deterministic!

WHY?

Uncertainties in:leadscrew pitchbearing and nut backlashmachine deflections

loadtemperature

Other Examples?

2/5/04 2.830 Lecture #2 36

DefinitionsDefinitions

•• An An InputInput is a Process Parameter that is:is a Process Parameter that is:–– FastFast–– AccessibleAccessible–– EffectiveEffective–– DeterministicDeterministic

•• A A DisturbanceDisturbance is a Variation in a Process Parameter Caused is a Variation in a Process Parameter Caused By:By:–– uncertainty or randomnessuncertainty or randomness–– inaccessibilityinaccessibility–– forced variationforced variation

2/5/04 2.830 Lecture #2 37

Some QuestionsSome Questions•• What parameters are the best candidates for Inputs?What parameters are the best candidates for Inputs?

•• What parameters have the greatest uncertainty?What parameters have the greatest uncertainty?

•• What process class has highest spatial resolution?What process class has highest spatial resolution?

•• What process class has What process class has highesthighest temporal resolution?temporal resolution?

•• What process class has the What process class has the lowestlowest spatial and temporal spatial and temporal resolution?resolution?

•• Which has the highest precision?Which has the highest precision?

2/5/04 2.830 Lecture #2 38

Some Answers?Some Answers?•• What parameters are the best candidates for Inputs?What parameters are the best candidates for Inputs?

–– Machine StatesMachine States

•• What parameters have the greatest uncertainty?What parameters have the greatest uncertainty?–– Material PropertiesMaterial Properties

•• What process class has highest spatial resolution?What process class has highest spatial resolution?–– Serial ProcessesSerial Processes

•• What process class has What process class has highesthighest temporal resolution?temporal resolution?–– Mechanical ProcessesMechanical Processes

•• What process class has the What process class has the lowestlowest spatial and temporal spatial and temporal resolution?resolution?–– Thermal, Chemical and Electrical all are highly diffusiveThermal, Chemical and Electrical all are highly diffusive

•• Which has the highest precision?Which has the highest precision?

Equipment Material“controls” Geometry &

Properties

2/5/04 2.830 Lecture #2 39

A Model for Process VariationsA Model for Process Variations

Equipment Material

“controls”

Geometry &Properties

•• Recall:Recall:

•• One or more One or more αα’s’s “qualify” as inputs : “qualify” as inputs : uu

•• The first order Variation The first order Variation ∆∆Y gives the “Variation Equation”Y gives the “Variation Equation”

Y = Φ(α )

Y = Φ(α ,u); u = vector of inputs

2/5/04 2.830 Lecture #2 40

The Variation Equation

∆Y = ∂Y∂α

∆α +∂Y∂u

∆u

DisturbanceSensitivity

Disturbances

Control Sensitivity or “Gain”

Control Inputs

2/5/04 2.830 Lecture #2 41

Primary Process Control Goal: Primary Process Control Goal: Minimize Minimize ∆∆YY∆Y → 0How do we make ?

∆Y = ∂Y∂α

∆α +∂Y∂u

∆u

•• hold hold uu fixed (fixed (∆∆uu = 0)= 0)–– operator training (SOP’s)operator training (SOP’s)–– good steadygood steady--state machine physicsstate machine physics

•• minimize disturbancesminimize disturbances∆α∆α -->>∆α∆αminmin

This is the goal of Statistical Process Control (SPC) This is the goal of Statistical Process Control (SPC)

2/5/04 2.830 Lecture #2 42

OROR∆Y = ∂Y

∂α∆α +

∂Y∂u

∆u ∆Y → 0

•• hold u fixed (hold u fixed (∆∆uu = 0)= 0)•• minimize the term:minimize the term: the disturbance sensitivitythe disturbance sensitivity

This is the goal of Process Optimization This is the goal of Process Optimization

∂Y∂α

••AssumingAssuming ∂Y∂α

= Φ(α ) αα = operating point= operating point

2/5/04 2.830 Lecture #2 43

OROR∆Y = ∂Y

∂α∆α +

∂Y∂u

∆u ∆Y → 0

•• manipulate manipulate ∆∆uu by measuring by measuring ∆∆Y such thatY such that

∆u∂Y∂u

= −∂Y∂α

∆α

This is the goal of Process Feedback Control This is the goal of Process Feedback Control

••Compensating for (not eliminating) disturbancesCompensating for (not eliminating) disturbances

2/5/04 2.830 Lecture #2 44

Statistical Process Control

∆Y = ∂Y∂α

∆α +∂Y∂u

∆u

Detect and Minimize

2/5/04 2.830 Lecture #2 45

Process Optimization

∆Y = ∂Y∂α

∆α +∂Y∂u

∆u

Empirically Minimize

2/5/04 2.830 Lecture #2 46

Output Feedback Control

∆Y = ∂Y∂α

∆α +∂Y∂u

∆u

Manipulate Actively Such that

∂Y∂u

∆u = −∂Y∂α

∆α

Compensate for Disturbances

2/5/04 2.830 Lecture #2 47

Process Control HierarchyProcess Control Hierarchy

•• Reduce DisturbancesReduce Disturbances–– Good HousekeepingGood Housekeeping–– Standard Operations (SOP’s)Standard Operations (SOP’s)–– Statistical Analysis and Identification of Sources (SPC)Statistical Analysis and Identification of Sources (SPC)–– Feedback Control of MachinesFeedback Control of Machines

•• Reduce Sensitivity (Reduce Sensitivity (increase “Robustnessincrease “Robustness”)”)–– Measure Sensitivities via Designed ExperimentsMeasure Sensitivities via Designed Experiments–– Adjust “free” parameters to minimizeAdjust “free” parameters to minimize

•• Measure output and manipulate inputsMeasure output and manipulate inputs–– Feedback control of Output(s)Feedback control of Output(s)

2/5/04 2.830 Lecture #2 48

Limitations?Limitations?

•• SPC?SPC?•• DOE/PO?DOE/PO?•• FBC?FBC?

2/5/04 2.830 Lecture #2 49

Topics for TodayTopics for Today•• Causes of VariationCauses of Variation

–– Parameter UncertaintyParameter Uncertainty•• Definition of Control Input to ProcessDefinition of Control Input to Process

–– Accessible, Deterministic ParametersAccessible, Deterministic Parameters•• The Process Variation EquationThe Process Variation Equation•• Process Control HierarchyProcess Control Hierarchy

–– Attacking the Variation EquationAttacking the Variation Equation•• Control Loops in ManufacturingControl Loops in Manufacturing

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