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Page 1: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

LUND UNIVERSITY

Page 2: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

LUND UNIVERSITY

Electronic Stability Program (ESP) Electronic Stability Program (ESP) is a new safety system which guides is a new safety system which guides cars through wet or icy bends with cars through wet or icy bends with more safety….more safety….The key is a yaw-rate sensor, which The key is a yaw-rate sensor, which detects vehicle movement around its detects vehicle movement around its vertical axis, and software which vertical axis, and software which recognizes critical driving conditions recognizes critical driving conditions and responds accordingly. and responds accordingly.

Page 3: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Hidden TechnologyThe Hidden Technology

Widely usedWidely usedVery successfulVery successfulSeldom talked aboutSeldom talked about Except when disaster strikesExcept when disaster strikesWhy?Why?

Perhaps easier to talk about devices than ideasPerhaps easier to talk about devices than ideas

Page 4: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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ControlControl The Hidden TechnologyThe Hidden Technology

K. J. ÅströmK. J. Åström

Lund Institute of TechnlogyLund Institute of Technlogy

Lund UniversityLund University

SwedenSweden

Page 5: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

LUND UNIVERSITY

Engineering EducationEngineering EducationFollowed the pattern of emergingFollowed the pattern of emerging

industries in the last century: industries in the last century: Civil Engineering, Mining, Civil Engineering, Mining, Mechanical, Chemical, Electrical.Mechanical, Chemical, Electrical.

New fields such as New fields such as Automatic Control Automatic Control

and Systems and Systems which are not tied to a which are not tied to a

particular industry have appeared in particular industry have appeared in

this century.this century.

Page 6: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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1.1. IntroductionIntroduction

2.2. A Brief HistoryA Brief History

3.3. State of the ArtState of the Art

4.4. The FutureThe Future

5. 5. ConclusionsConclusions

Page 7: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Early use in many fieldsEarly use in many fields Process controlProcess control Vehicle controlVehicle control CommunicationCommunication

Servomechanism TheoryServomechanism Theory Consequences Consequences The Second WaveThe Second Wave Maturity?Maturity?

A Brief HistoryA Brief History

Page 8: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Industrial Process ControlIndustrial Process Control

Windmills MeadWindmills Mead 17871787

Steam EnginesSteam Engines 17881788

GovernorsGovernors 18901890

Water TurbinesWater Turbines 18931893

Tolle’s BookTolle’s Book 19051905

The PID ControllerThe PID Controller 19301930

Page 9: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Wilbur Wright 1901Wilbur Wright 1901

We know how to construct airplanes. We know how to construct airplanes. Men also know how to build engines. Men also know how to build engines.

Inability to balance and steer still confronts Inability to balance and steer still confronts students of the flying problem. When this students of the flying problem. When this one feature has been worked out, the age one feature has been worked out, the age

of flying will have arrived, for all other of flying will have arrived, for all other difficulties are of minor importancedifficulties are of minor importance

Page 10: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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A Quiz!A Quiz!

Robot Piloted Plane makes Robot Piloted Plane makes Safe Crossing of the AtlanticSafe Crossing of the AtlanticNo hands on controls from No hands on controls from

Newfoundland to Oxforshire Newfoundland to Oxforshire Take-Off, Flight and Landing are Take-Off, Flight and Landing are

fully Automatic. fully Automatic.

New York Times 19XXNew York Times 19XX

Page 11: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Wright BrothersThe Wright Brothers 19031903

Sperry’s AutopilotSperry’s Autopilot 19121912

Robert E. LeeRobert E. Lee 19471947

V1 and V2 (A4)V1 and V2 (A4) 19421942

SputnikSputnik 19571957

Apollo Apollo 19691969

Mars PathfinderMars Pathfinder 19971997

Flight ControlFlight Control

Page 12: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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TelecommunicationsTelecommunicationsThe Repeater ProblemThe Repeater Problem

Black’s InventionBlack’s Invention 1928 1928

““Singing” = InstabilitySinging” = Instability

Nyquist’s Theorem 1932Nyquist’s Theorem 1932

Bode’s PaperBode’s Paper 1940 1940Bode: Bode:

Network Analysis Network Analysis and and Feedback Amplifier DesignFeedback Amplifier Design

Page 13: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Feedback AmplifierThe Feedback Amplifier

Telephone Calls Over Long DistancesTelephone Calls Over Long Distances

The Problem: How to Increase Signal Strength?The Problem: How to Increase Signal Strength?

The Solution: The Feedback Amplifier The Solution: The Feedback Amplifier

Patented by Black 1928Patented by Black 1928

Patent Granted 1937Patent Granted 1937

Strong Development of Theory and Design MethodsStrong Development of Theory and Design Methods

Page 14: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Mervin Kelley on Black 1957Mervin Kelley on Black 1957

It is no exageration to say that without It is no exageration to say that without

Black’s invention of the feedback amplifier, Black’s invention of the feedback amplifier,

the present long-distance telephone and the present long-distance telephone and

television networks, which covers our television networks, which covers our

entire country and the transoceanic entire country and the transoceanic

telephone cables would not exist.telephone cables would not exist.

Page 15: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Make a system behave as desired Make a system behave as desired

Keep variables constant Keep variables constant

Stabilize unstable systemStabilize unstable system

Reduce effects of disturbancesReduce effects of disturbances

and component variationsand component variations New freedom for designersNew freedom for designers

The Magic of FeedbackThe Magic of Feedback

Page 16: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Scene of 1940The Scene of 1940

Widespread use of automatic control inWidespread use of automatic control in

many fieldsmany fields Power generation and distributionPower generation and distribution

Process controlProcess control

Autopilots for ships and aircraftsAutopilots for ships and aircrafts

TelecommunicationsTelecommunications

It was not realized that the problems It was not realized that the problems

were the samewere the same

Page 17: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Industrial Process Industrial Process ControlControl

TelecommunicationsTelecommunications

Flight ControlFlight Control

MathematicsMathematics

PrinciplesPrinciplesTheoryTheory

Design Design MethodologyMethodology

ApplicationsApplications

A Discipline EmergesA Discipline Emerges

Page 18: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Black Box ConceptThe Black Box Concept

OutputOutputInputInput

AbstractionAbstraction

Information hidingInformation hiding

Transfer functionsTransfer functions

Page 19: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Servomechanism TheoryServomechanism Theory

FoundationsFoundationsComplex variablesComplex variablesLaplace TransformsLaplace Transforms

System ConceptsSystem ConceptsFeedbackFeedbackFeedforwardFeedforward

Methodology Design Methodology Design Frequency ResponseFrequency ResponseGraphical MethodsGraphical Methods

Analog SimulationAnalog Simulation

ImplementationImplementation

Page 20: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Theory of ServomechanismsTheory of Servomechanisms

Hubert M. James Hubert M. James Professor of Physics Purdue UniversityProfessor of Physics Purdue University

Nathaniel B. Nichols Nathaniel B. Nichols Director of Research Taylor Instrument CompaniesDirector of Research Taylor Instrument Companies

Ralph S. Phillips Ralph S. Phillips Associate Professor of Mathematics University of Southern CaliforniaAssociate Professor of Mathematics University of Southern California

Office of Scientific Research and DevelopmentOffice of Scientific Research and Development

National Defence Research CommitteeNational Defence Research Committee

Page 21: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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ConsequencesConsequences

EducationEducation

ApplicationApplication

IndustrializationIndustrialization

OrganisationOrganisation

JournalsJournals

ConferencesConferences

Page 22: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Second WaveThe Second Wave

Optimal ControlOptimal Control

Nonlinear ControlNonlinear Control

Computer ControlComputer Control

Stochastic ControlStochastic Control

Robust ControlRobust Control

System IdentificationSystem Identification

Adaptive ControlAdaptive Control

CACECACE

Driving ForcesDriving Forces

ApplicationsApplications

MathematicsMathematics

ComputersComputers

A New ParadigmA New Paradigm

State SpaceState Space

Rapid ExpansionRapid Expansion

SubspecialitiesSubspecialities

Page 23: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Optimal ControlOptimal Control

EulerEuler

LagrangeLagrange

PontryaginPontryagin

HamiltonHamilton

JacobiJacobi

BellmanBellman

1707–17831707–1783

1736–18131736–1813

19621962

1805–18651805–1865

1804–18511804–1851

19571957

ATTITUDE AND THRUST CONTROLATTITUDE AND THRUST CONTROL€ € Swivel Outer Four EnginesSwivel Outer Four Engines

€ € Optimum to Desired End ConditionsOptimum to Desired End Conditions

€ € Inertial Updating of Position and VelocityInertial Updating of Position and Velocity

GUIDANCE – SATURNGUIDANCE – SATURN

NAVIGATIONNAVIGATION

SII STAGESII STAGEFive J-2 EnginesFive J-2 Engines

2, 500, 000N Thrust2, 500, 000N Thrust

Page 24: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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CSLCSL1957 The Control Systems Laboratory1957 The Control Systems Laboratory1959 Interdisciplinary, interdepartmental 1959 Interdisciplinary, interdepartmental graduate research center graduate research center1967 New building, physics, control 1967 New building, physics, control

communication, computer communication, computer engineering engineering

1992 This building, 80 faculty, 1992 This building, 80 faculty, 7 departments, 320 grad students7 departments, 320 grad students

Page 25: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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1.1. IntroductionIntroduction

2.2. A Brief HistoryA Brief History

3.3. State of the ArtState of the Art

4.4. The FutureThe Future

5. 5. ConclusionsConclusions

Page 26: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Current StatusCurrent Status

A well established body of ideas, A well established body of ideas,

concepts, theory and design concepts, theory and design

methods.methods.

Wide and growing application areasWide and growing application areas

Still developing rapidlyStill developing rapidly

Page 27: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Perhaps Most ImportantPerhaps Most Important

A good group of very talented A good group of very talented

and creative young researchers.and creative young researchers.

Page 28: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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System TheorySystem Theory

A large body of results with connections A large body of results with connections

to many branches of mathematicsto many branches of mathematics

Compactification badly needed!Compactification badly needed!

LinearLinear

NonlinearNonlinear

StochasticStochastic

DiscreteDiscrete

SampledSampled

DistributedDistributed

Discrete Discrete EEventvent

HybridHybrid

Page 29: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Design MethodologyDesign Methodology

Modeling and IdentificationModeling and Identification

DesignDesign

SimulationSimulation

ImplementationImplementation

Computer Aided Control Computer Aided Control

EngineeringEngineering

Page 30: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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ApplicationsApplications

Energy generationEnergy generation

Energy transmissionEnergy transmission

Process controlProcess control

Discrete manufacturingDiscrete manufacturing

CommunicationCommunication

TransportationTransportation

BuildingsBuildings

EntertainmentEntertainment

InstrumentationInstrumentation

MechatronicsMechatronics

MaterialsMaterials

PhysicsPhysics

BiologyBiology

EconomicsEconomics

Page 31: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 32: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 33: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 34: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 35: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 36: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Page 37: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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CD Player CD Player

TrackingTracking

SearchingSearching

FocusingFocusing DC-motorDC-motor

photo diodesphoto diodesradial armradial arm

Optical Pick-upOptical Pick-upUnitUnit

Page 38: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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PhysicsPhysics

Particle AcceleratorsParticle Accelerators

The 1984 Nobel Prize Van Der MeerThe 1984 Nobel Prize Van Der Meer

Repetetive Control TakanoRepetetive Control Takano

Adaptive OpticsAdaptive Optics

Atomic Force MicroscopeAtomic Force Microscope

Quantum and Molecular SystemsQuantum and Molecular Systems

Page 39: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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EconomicsEconomics

Complex Dynamical Systems With Much Complex Dynamical Systems With Much

Manual Feedback and Complicated CriteriaManual Feedback and Complicated Criteria

H. Simon 1956: Certainty EquivalenceH. Simon 1956: Certainty Equivalence

Program Trading – Relay FeedbackProgram Trading – Relay Feedback

Merton-scholes – Stochastic ControlMerton-scholes – Stochastic Control

Wall Street and the CityWall Street and the City

The Financial CrisisThe Financial Crisis

Page 40: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Feedback is a central feature of life. The process of Feedback is a central feature of life. The process of

feedback governs how we grow, respond to stress feedback governs how we grow, respond to stress

and challenge, and regulate factors such as body and challenge, and regulate factors such as body

temperature, blood pressure, and cholesterol level.temperature, blood pressure, and cholesterol level.

It also makes it possible for us to stand upright. The It also makes it possible for us to stand upright. The

mechanisms operate at every level, from the mechanisms operate at every level, from the

interaction of proteins in cells to the interaction of interaction of proteins in cells to the interaction of

organisms in complex ecologies. organisms in complex ecologies.

BiologyBiology

Page 41: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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It is not the strongest of the species that It is not the strongest of the species that

survive, nor the most intelligent, it is the survive, nor the most intelligent, it is the

one that is most adaptable to change.one that is most adaptable to change.

Charles DarwinCharles Darwin

Page 42: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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A DilemmaA Dilemma

Automatic control is a collection of Automatic control is a collection of

ideas, concepts and theories with ideas, concepts and theories with

very wide applications areas. How to very wide applications areas. How to

cope with:cope with: Coupling to hardwareCoupling to hardware

Coupling to industries Coupling to industries

Process knowledge Process knowledge

Academic positioningAcademic positioning

Page 43: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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A Soul but No BodyA Soul but No Body Technology transferTechnology transfer

Student attractionStudent attraction

No home courtNo home court

No base industryNo base industry

GeneralityGenerality

Academic positioningAcademic positioning

Page 44: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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1.1. IntroductionIntroduction

2.2. A Brief HistoryA Brief History

3.3. State of the ArtState of the Art

4.4. The FutureThe Future

5. 5. ConclusionsConclusions

Page 45: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Understand Nature vs Man-made SystemsUnderstand Nature vs Man-made Systems

Design and Operation of SystemsDesign and Operation of Systems

Physical Laws vs System PrinciplesPhysical Laws vs System Principles

Equally ChallengingEqually Challenging

Useful for MankindUseful for Mankind

Theoretical Physics vs System TheoryTheoretical Physics vs System Theory

Use of MathematicsUse of Mathematics

Natural and Engineering SciencesNatural and Engineering Sciences

Page 46: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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ModelingModelingReal World Automatic ControlReal World Automatic Control

ProcessesProcesses System TheorySystem Theory

SystemsSystems Control DesignControl Design

ImplementationImplementation

CommissioningCommissioning

OperationOperation

A PerspectiveA Perspective

Page 47: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Stability and ControllabilityStability and Controllability Wright Brothers rejected the dogma that aircraft Wright Brothers rejected the dogma that aircraft

should be inherently stable should be inherently stable

Minorsky 1922: It is an old adage that a stable Minorsky 1922: It is an old adage that a stable

ship is difficult to steership is difficult to steer

Integrated process and control designIntegrated process and control design

The cardinal sin of controlThe cardinal sin of control

Page 48: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Co-Design of Process and ControlCo-Design of Process and Control

Page 49: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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The Mercedes A-classThe Mercedes A-classAutomatic control gives extra freedom to the designerAutomatic control gives extra freedom to the designer

Unstable behavior improved byUnstable behavior improved by

Electronic Stabilization Program (ESP)Electronic Stabilization Program (ESP)

ESPESP

Page 50: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Educational ChallengesEducational Challenges

Theory and applications expanding Theory and applications expanding

How to compactify the knowledge? How to compactify the knowledge?

The engineering aspectThe engineering aspect

The field had changed a lot The field had changed a lot

The introductory courses have notThe introductory courses have not

Is it time for CSL to take an initiative? Is it time for CSL to take an initiative?

Page 51: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Recipe for SuccessRecipe for Success

Good ideas and demanding problems Good ideas and demanding problems

Respect for solid theoryRespect for solid theory

Good engineeringGood engineering

ExamplesExamples

Servomechanisms, Optimal controlServomechanisms, Optimal control

Robust control, Digital controlRobust control, Digital control

Page 52: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Interesting AreasInteresting Areas

CC33

Control, Computing and CommunicationControl, Computing and Communication

A very strong base at CSLA very strong base at CSL

BiologyBiology Many previous attempts will it work this time?Many previous attempts will it work this time?

Long tradition at UIUCLong tradition at UIUC

Page 53: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Computer ControlComputer Control

0123456789

10

1960 1970 1980 1990 2000

Process controlRegularEmbedded

Page 54: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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1.1. IntroductionIntroduction

2.2. A Brief HistoryA Brief History

3.3. State of the ArtState of the Art

4.4. The FutureThe Future

5. 5. ConclusionsConclusions

Page 55: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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ConclusionsConclusions An exciting field An exciting field

Use of feedback often revolutionaryUse of feedback often revolutionary

Rapid growth of applicationsRapid growth of applications

Many unsolved problemsMany unsolved problems

Streamline knowledgeStreamline knowledge

Intellectual drivesIntellectual drives

Education is a key issueEducation is a key issue

Page 56: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Take Care of Both Body and SoulTake Care of Both Body and Soul

Intellectual challenges (the soul)Intellectual challenges (the soul)

Basics that generalizes easilyBasics that generalizes easily

Give the general pictureGive the general picture

Particular attention to introductory coursesParticular attention to introductory courses The engineering aspect (the body)The engineering aspect (the body)

Educate students broadly so that theyEducate students broadly so that they

can take full systems responsibilitycan take full systems responsibility Learn theory and at least one applicationLearn theory and at least one application

Page 57: LUND UNIVERSITY. Electronic Stability Program (ESP) is a new safety system which guides cars through wet or icy bends with more safety…. The key is a

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Thank You for the InvitationThank You for the Invitation

Congratulations!Congratulations!