DCAP608_real Time System

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www.lpude.in

DIRECTORATE OF DISTANCE EDUCATION

REAL TIME SYSTEMS


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Copyright 2012, Navneet Kumar Singh and Amrita SinghAll rights reserved.

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Directorate of Distance EducationLovely Professional University

Phagwara


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Directorate of Distance Education

LPU is reaching out to the masses by providing an intellectual learning environment that is academically rich with most

affordable fee structure. Supported by the largest University1 in the country, LPU, the Directorate of Distance Education (DDE) is

bridging the gap between education and the education seekers at a fast pace, through the usage of technology which signicantly

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SYLLABUS

Real Time Systems

Objectives: To enable the students to understand the technicalities of Real Time Systems. Student can identify real time tasks

and their criticalness. Student will learn various real time task scheduling techniques.

S. No. Description

1. Introduction to Real Time Applications: Digital Control, High Levels Control, Signal Processing, Other RealTime Applications.

2. Hard Versus Soft Real-Time System:Jobs and Processors, Release Time, Deadline and Timing constraints,Hard and Soft Timing constraints, Hard real time systems, Soft real time systems.

3. A Reference Model of Real Time System: Processors and Resources, Temporal Parameters of real time model,Precedence constraints and data dependencies.

4. Other Types of dependences, Functional parameters, Resource parameters of jobs and parameters of resources,scheduling hierarchy.

5. Commonly used Approaches to Real Time Scheduling: Clock-Driven approach, Weight Round-RobinApproach, Priority-Driven Approach, Dynamic versus Static system, Effective Release Times and Deadlines.

6. Commonly used Approaches to Real Time Scheduling: Optimality of the EDF and LST Algorithm,Nonoptimility of the EDF and the LST Algorithm, Challenges in validating Timing Constraints in Priority-Driven System, Off-Line versus On Line Scheduling.

7. Clock-Driven Scheduling: Notations and Assumptions, Static, Timer-Driven Scheduler, General Structure ofCyclic Scheduler, Cyclic Scheduling.

8. Clock-Driven Scheduling: Improving the Average Response Time of Aperiodic jobs, Scheduling Sporadic Jobs,Practical Consideration and Generalizations, Algorithm for Constructing Static Schedules, Pros and Cons ofClock Driven Scheduling.

9. Priority Driven Scheduling of Periodic Tasks: Static Assumptions, Fixed Priority versus Dynamic PriorityAlgorithms, Maximum Schedulable Utilization, Optimality of the RM and DM Algorithms, A Schedulability

Test for Fixed-Priority Tasks with Short Response Time.

10. Priority Driven Scheduling of Periodic Tasks: Schedulability Test for Fixed--Priority Tasks with ArbitraryResponse Time, Sufcient Schedulability conditions for the RM and DM Algorithm, Practical Factors


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CONTENTS

Unit 1: Concept of Real Times System 1

Unit 2: Introduction to Real Time Applications 13

Unit 3: Hard Versus Soft Real-Time System 38

Unit 4: A Reference Model of Real-Time Systems 59

Unit 5: Real Time System Dependencies 74

Unit 6: Commonly used Approaches to Real Time Scheduling 88

Unit 7: Commonly used Algorithm to Real Time Scheduling 100

Unit 8: Working of Real-Time Scheduling 113

Unit 9: Concept of Clock-Driven Scheduling 126

Unit 10: Working of Clock-Driven Scheduling 137

Unit 11: Application of Clock-Driven Scheduling 151

Unit 12: Priority-Driven Scheduling of Periodic Tasks 165

Unit 13: Working of Priority Driven Scheduling of Periodic Tasks 181

Unit 14: Advance Priority Driven Scheduling of Periodic Tasks 198


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6 LOVELY PROFESSIONAL UNIVERSITY

Corporate and Business Law


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LOVELY PROFESSIONAL UNIVERSITY 1

NotesUnit 1: Concept of Real Times System

CONTENTS

Objectives

Introduction

1.1 Real Time Systems

1.2 Hard Real Time Systems

1.3 Soft Real Time Systems

1.4 Hard Versus Soft Real Time System

1.5 Summary

1.6 Keywords

1.7 Further Reading

Objectives

After studying this unit, you will be able to:

Understandthestructureandcomponentsofrealtimesystem

Explainhardandsoftrealtimesystem

Describethedifferencesbetweenhardandsoftrealtimesystem

Introduction

Arealtimeapplicationisanapplicationwherethecorrectnessoftheapplicationdependsonthe

timelinesandpredictabilityoftheapplicationaswellastheresultsofcomputations.Toassistthe

realtimeapplicationdesignerinmeetingthesegoals,toolsthatprovidefeaturesthatfacilitate

efcientinterprocesscommunicationandsynchronization,a fast interruptresponse time,

asynchronousinputandoutput(I/O),memorymanagementfunctions,lesynchronization,and

facilitiesforsatisfyingtimingrequirementsetc.Realtimeapplicationsarebecomingincreasingly

importantinourdailylivesandcanbefoundinvariousenvironmentssuchasautomotive

applications,medicalequipmentetc.

RealTimethetermisusedtodescribeanumberofdifferentcomputerfeatures.Forexample,

real-timeoperatingsystemsaresystemsthatrespondtoinputimmediately.Theyareusedfor

suchtasksasnavigation,inwhichthecomputermustreacttoasteadyowofnewinformation

withoutinterruption.Mostgeneral-purposeoperatingsystemsarenotreal-timebecausetheycantakeafewseconds,orevenminutes,toreact.

Realtimecanalsorefertoeventssimulatedbyacomputeratthesamespeedthattheywould

occurinreallife.Ingraphicsanimation,forexample,areal-timeprogramwoulddisplayobjects

movingacrossthescreenatthesamespeedthattheywouldactuallymove.

RealtimeSystem,isasystemwhenitcansupporttheexecutionofapplicationswithtime

constraintson thatexecution.Therecanbe madeaclassication intohardandsoftreal-time

systemsbasedontheirproperties;eachofthemisexplainedwiththespecicexample.

Areal-timesystemisanyinformationprocessingsystemwhichhastorespondtoexternally

generatedinputstimuliwithinaniteandspeciedperiod.


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Real Time Systems


Notes Thecorrectnessdependsnotonlyonthelogicalresultbutalsothetimeitwasdelivered.

Failuretorespondisasbadasthewrongresponse!

Areal-timesystemrespondsina(timely)predictablewaytounpredictableexternalstimuli

arrivals.Inshort,areal-timesystemhastofulllunderextremeloadconditions:

1. Timeliness:meetdeadlines,itisrequiredthattheapplicationhastonishcertaintasks

withinthetimeboundariesithastorespect.

2. Simultaneity or simultaneous processing:morethanoneeventmayhappensimultaneously,

all deadlines should be met.

3. Predictability:thereal-timesystemhastoreacttoallpossibleeventsinapredictableway.

4. Dependability or trustworthiness:itisnecessarythatthereal-timesystemenvironmentcan

relay on it.

Real-time systems are systems with timing constraints

Figure 1.1: Constraints of Real Time System

Event

Maximum response time

Eventandmaximumresponsetime(Constraints),boundsonexecutiontimevariation.

Anexampleofahardrealtimesystemisadigitaly-by-wirecontrolsystemofanaircraft:No

latenessisacceptedunderanycircumstances;otherwisetheaircraftisnotcontrollable.Useless

resultsiflateandnotcontrolthesystemandnotrespondtimely,theresultisaholeintheground.

Catastrophicfailure,whichneedsnoexplanationinthecaseofanaircraftcrash.Costofmissingdeadlineisinnitelyhigh;thelivesofpeopledependonthecorrectworkingofthecontrolsystem

of the aircraft.

Asoftreal-timesystemcanbeavendingmachine,risingcostforlatenessofresults:Asitwill

takelongertotreatacustomerwhentheperformanceofthevendingmachineisdegrading,less

customerspayatthismachinewhichresultsinlessprotsfortheshopowner.Acceptlower

performanceforlateness,itisnotcatastrophicwhendeadlinesarenotmet.Itwilltakelongerto

handle one client with the vending machine.

Other real-time systems examplesarenuclearpowerplantcontrol,industrialmanufacturing

control,medicalmonitoring,weapondeliverysystem,spacenavigationandguidance,

reconnaissancesystems,laboratoryexperimentscontrol,automobileenginescontrol,robotics,

telemetrycontrolsystems,printercontrollers,anti-lockbreaking,burglaralarms.

Anoperatingsystem(OS)is responsibleformanagingthehardwareresourcesofacomputer

andhostingapplicationsthatrunonthecomputer.AnRTOSperformsthesetasks,butisalso

speciallydesignedtorunapplicationswithveryprecisetimingandahighdegreeofreliability.

Thiscanbeespeciallyimportantinmeasurementandautomationsystemswheredowntimeis

costlyoraprogramdelaycouldcauseasafetyhazard.

Tobeconsideredreal-time,anoperatingsystemmusthaveaknownmaximumtimeforeachof

theoperationsthatitperforms(oratleastbeabletoguaranteethatmaximummostofthetime).

SomeoftheseoperationsincludeOScallsandinterrupthandling.Operatingsystemsthatcan

absolutelyguaranteeamaximumtimefortheseoperationsarereferredtoashardreal-time,

whileoperatingsystemsthatcanonlyguaranteeamaximummostofthetimearereferredtoas

softreal-time.Tofullygrasptheseconcepts,itishelpfultoconsideranexample.


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Unit 1: Concept of Real Times System


NotesImaginethatyouaredesigninganairbagsystemforanewmodelofcar.Inthiscase,asmallerror

intiming(causingtheairbagtodeploytooearlyortoolate)couldbecatastrophicandcauseinjury.

Therefore,ahardreal-timesystemisneeded.Ontheotherhand,ifyouweretodesignamobile

phonethatreceivedstreamingvideo,itmaybeoktoloseasmallamountofdataoccasionally

eventhoughonaverageitisimportanttokeepupwiththevideostream.Forthisapplication,asoftreal-timeoperatingsystemmaysufce.

Themainpointisthat,ifprogramedcorrectly,anRTOScanguaranteethataprogramwillrun

withveryconsistenttiming.Real-timeoperatingsystemsdothisbyprovidingprogramerswith

ahighdegreeofcontroloverhowtasksareprioritized,andtypicallyalsoallowcheckingtomake

surethatimportantdeadlinesaremet.

AnOSthatcanabsolutelyguaranteeamaximumtimefortheoperationsitperformsisreferred

toashardreal-time.Incontrast,anOSthatcanusuallyperformoperationsinacertaintimeis

referred to as soft real-time.

Self Assessment

Choose the correct answer:

1. The correctness of the applicationdependsonthe.andpredictabilityofthe

application.

(a) timelines (b) deadline

(c) bothaandb (d) noneofthese

2. Realtimetermisusedtodescribeanumberofdifferentcomputerfeatures.

(a) True (b) False

3. Operatingsystemisresponsibleformanagingthehardwareresourcesofacomputerand

.thatrunonthecomputer.

(a) hardwarecomponent (b) hostingapplications

(c) bothaandb (d) noneofthese

4. Asystemisareal-timesystemwhenitcansupportthe.with time constraints on

thatexecution.

(a) analogsignal (b) digitalsignals

(c) bothaandb (d) executionofapplications.

5. Areal-timesystemmayanyinformationprocessingsystem.

(a) True (b) False

1.1 Real Time Systems

Anysystemwhereatimelyresponsebythecomputertoexternalstimuliinvitalisarealtime

system.

Example:ACAR-AND-DRIVEEXAMPLE

Ifweconsiderafamiliarproblemofhumancontroldrivingacar.

Thedriveristhereal-timecontroller,thecaristhecontrolledprocess,andtheothercars

togetherwiththeroadconditionsmakeuptheoperatingenvironment.

Wehavetwotypesofrealtimesystem:

1. Soft real time system.


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Real Time Systems


Notes 2. Hard real time system.

1. Hard real time system: The requirement that all hard timing constraints must be validated

invariablyplacesmanyrestrictionsonthedesignandimplementationofhardreal-time

applicationsaswellasthearchitecturesofhardwareandsystemsoftwareusedtosupportthem.

2. Soft real time system: A system in which jobs have soft deadlines is a soft-real system.

Thedeveloperofarealtimesystemissurelyrequiredtoproverigorouslythatthesystem

surelymeetsitsrealtimeperformanceobjective.

Example:Onlinetransactionsystem,telephoneswitchesaswellaselectronicgames.

Issues of Real Time System

Arealtimecomputermustbemuchmorereliablethanitsindividualhardwareandsoftware

component.Itmustbecapableofworkinginharshenvironments.

For example:Taketaskscheduling.Realtimecomputersystemsdifferfromtheirgeneral-purpose

counterpartsintwoimportantways.Firstlytheyaremuchmorespecicintheirapplications,

andsecond,theconsequencesoftheirfailureallmoredrastic.

Architecture Issues:

(a) Processor architecture:Forreasonsofeconomy,off-the-shelfprocessorsarepreferred,real

timedesignsseldomdesigntheirownprocessor,forthisreason,wedonottreatprocessor

architectural.

(b) Network architecture:Tomakesystemsreliableprovidesufcientprocessingcapacity,

mostrealtimesystemsaremultipleprocessormachine.

(c) Architecture for clock synchronization: In order to facilitate the interaction between the

multipleunitsofarealtimesystem,theclocksofthisunitmustbesynchronizedandtightly.

(d) Fault-tolerance and reliability evaluation:Peoplecandiewhenrealtimesystemfails.Such

systems must therefore be legally fault-tolerant.

Operating System Issues

(a) Task assignment and scheduling: The scheduling of tasks ensures that real time deadlines

aremet.Itiscentraltothemissionofareal-timeoperatingsystem.

(b) Communication protocols:Itisimportanttohaveinterredprocessorcommunicationthat

haspredictabledelaysandiscontrollable.

(c) Failure management and recovery:Whenaprocessororsoftwaremodulefails,thesystem

must limit such failure and recover from it.

(d) Clock synchronization algorithm:Wementionedhardwaresynchronizationarchitecturebuiltoutofphaselockedlocks.

Other Issues

(a) Programming languages: Real times engineers need much greater control our timing and

usedtointerfacetospecialpurposedevice.

(b) Data bases:Therearemanyrealtimedata-baseapplications,suchasthe stockmarket,

airline,reservationsandarticial,intelligence.

(c) Performance measures:Commonlyusedperformancemeasuressuchasconventional

reliabilityandthroughputareuselessforrealtimesystems.


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NotesTypes of Task Classes of Real Time System

Therearevetypesoftaskclasses:

1. Periodic task:Therearemanytasksinrealtimesystemsthataredonerepetitively.For

exampleonemaywishtomonitorthespeedaltitudeandattitudeofanaircraftevery100ms.Thissensorinformationwillbeusedbyperiodictasksthatcontrolandcontrolsurfacesof

theaircraft(e.g.,theailerons,elevator,andrudderandenginethrusts),inordertomaintain

stabilityandotherdesiredcharacteristics.Theperiodicityofthesetasksisknowntothe

designer,andmanytaskscanbepre-scheduled.

2. A periodic task:Therearemanyothertasksthatareaperiodic,thatoccuronlyoccasionally.

Forinstance,whenthepilotwishestoexecuteaturnalargenumbersubtasks.Associated

withthatactionareselfoffaperiodictaskscannotbepredicatedandsufcientcompleting

powermustbeheldinreservetoexecutetheminatimelyfashion.Periodictaskswith

boundedimperativaltimearecalledsporadictasks.

3. Critical tasks:Criticaltasksarethatwhosetimelyexecutioniscritical;ifdeadlinesaremissed

catastrophesoccur.Exampleincludeslifesupportsystemsandtheactabilitycontrolofair

craft.Criticaltasksareoftenexecutedatahigherfrequencythanisabsolutelynecessary.

4. Non critical tasks:Noncriticaltasksarerealtimestasks,thenameimpliesnotcriticalto

theapplication.Howevertheydodealwithtimevaryingdataandhencetheyuselessif

notcompletedwithinadeadline,thegoalinschedulingthesetasksisthesetomaximize

thepercentageofjobssuccessfullyexecutedwithintheirdeadlines.

Theanti-lockbrakesonacarareasimpleexampleofareal-timecomputing

system the real-time constraint in this system is the time in which the brakes

mustbereleasedtopreventthewheelfromlocking.

Structure of a Real System

Thestateofthecontrolledprocessandoftheoperatingenvironment(e.g.,pressure,temperature,

speedandattitude)isacquiredbysensors,whichprovideinputtothecontroller,therealtime

computer.Thereisaxedsetofapplicationtasksorjobs,thejoblist.

Thesoftwareforthesetasksispreloadedintothecomputer.Ifthecomputerhasamainmemory,

then the entire software is loaded into that.

Figure 1.2: Structure of Real Time System

ControlledSensors Job list Clock

Trigger

generator

ExecutionActuators

Display Operator

process

Trigger generator

TheTriggergeneratorisarepresentationatthemechanismusedtotriggertheexecution

ofindividualjobs.Itisnotreallyaseparatehardwareunit,typicallyitispartoftheexecutive

softwaremanyofthejobsareperiodici.e.theyexecuteregularly.Thescheduleforthesejobscan

beobtainedofineandloadedasalookuptabletousebythescheduler.


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Real Time Systems


Notes

Areal-timedeadlinemustbemet,regardlessofsystemload.

1.2 Hard Real Time Systems

A hardreal-timesystemguaranteesthatcriticaltaskscompleteontime.Thisgoalrequiresthatall

delays in the system be bounded from the retrieval of the stored data to the time that it takes the

operatingsystemtonishanyrequestmadeofitotherwisethesystemwillbecrashondeadline

point(afterdelayingthispointthesystemwillcrash)asshowningure1.2.

Realtimeapplicationscanbeclassiedaseitherhardorsoftrealtime.Hardrealtimeapplications

requirearesponsetoeventswithinapredeterminedamountoftimefortheapplicationtofunction

properly.Ifahardrealtimeapplicationfailstomeetspecieddeadlines,theapplicationfails.

While many hard realtimeapplications requirehigh-speedresponses,the granularityofthe

timingisnotthecentralissueinahardrealtimeapplication.

Anexampleofa hardrealtimeapplicationis amissileguidancecontrolsystemwherealate

responsetoaneededcorrectionleadstodisaster.

Figure 1.3: Deadline Point in Hard Real Time System

Cost

Triggeringevent

Deadline

Time

Ahardreal-timesystem(alsoknownasanimmediatereal-timesystem)ishardwareorsoftware

thatmustoperatewithintheconnesofastringentdeadline.Theapplicationmaybeconsidered

tohavefailedifitdoesnotcompleteitsfunctionwithintheallottedtimespan.Examplesofhard

real-timesystemsincludecomponentsofpacemakers,anti-lockbrakesandaircraftcontrolsystems.

Anoverruninresponsetimeleadstopotentiallossoflifeand/orbignancialdamage.

Manyofthesesystemsareconsideredtobesafetycritical.

Sometimestheyareonlymissioningoncritical,withthemissionbeingveryexpensive.

Ingeneralthereisacostfunctionassociatedwiththesystem.

Ahardreal-timesystemisonewhosesequencingtimelinessfactors(therealsomaybenon-

timelinessfactors)areoptimalityisthebinarycasethatmeetingallharddeadlinesisoptimalandotherwiseissuboptimal(insomesystem-,application-,orsituation-specicway)predictability

ofoptimalityisdeterministic.

Thesearetheonlyhardreal-timesequencingtimelinessfactors,andahardreal-timesystemhas

only these timeliness factors in its sequencing criterion. In the sequencing timeliness criterion

2-dimensionalspaceof optimalityand predictabilityof optimality,hardreal-timeis atthe

maximumoptimality/maximumpredictabilitycornerpoint;thetwofactorsarenottradedoff.

Thisdenitioncorrespondstotheconsensuswithinthereal-timecomputingresearchcommunity

thathardreal-timemeansallharddeadlinesarealwaysmet.(Thereal-timecomputingpractitioner

(user,vendor)communityhasnoconsensusonthemeaningsofhardreal-timeandsoftreal-

time,theyusethesetermsinmanydifferentill-denedways.)


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NotesHardreal-timesystemstypicallyariseasfollows:

1. Eitheralltheexecutionentitieshavingharddeadlinesaregatheredtogethertoformahard

real-timesystem(usuallyafrontendsubsystematthedevicelevel)pairedwithasoft

real-time,or(usually)non-real-time,backendsystem(forhumaninterface,database,etc.),because:

Thesoft/non-real-timesystemisagivenandcannotsupportharddeadlines.

Orthesystemdesigners/implementersdonotknowhowtoaccommodatemixedtime

constraints in a single system.

2. Orallthetimeconstraintsarearticiallyforcedtobeharddeadlinesbecausethesystem,

oritsdesigners/implementers/users,cannotdealwithanyotherkindoftimeconstraints.

Partitioningacomputingsystemintoa hardreal-timefrontendanda non-real-timeback

endcanbeanaturalandeffectiveapproachinsomecases.Butinmanyothercasesitlimitsthe

effectivenessoffrontendcomputing,byrestrictingittoharddeadlinesandthehardreal-time

sequencingtimelinesfactors,orofbackendcomputingbypreventingitfromemployingtime-constraint driven resource management.

1.3 Soft Real Time Systems

A soft real-time system isonethatisnotthehardreal-timespecialcase,andisthusthegeneralcase.

Thesequencingtimelinessoptimalityfactormaybeanythingexamplesoffactorsusedverywidely

(outsidethetraditionalreal-timecomputingcommunity)areminimizethenumberofmissed

deadlines,andminimizetotaltardiness.Thepredictabilityofoptimalityisnon-deterministic,

andisoftenmodelledstochastically.Verycommonexamples(outsidethetraditionalreal-time

computingcommunity)ofsequencingtimelinesscriteriaintermsofbothfactorsareminimize

theexpectednumberofmisseddeadlines,andminimizethemeantotaltardiness.

Deadlineoverrunsaretolerable,butnotdesired.

Therearenocatastrophicconsequencesofmissingoneormoredeadlines.

Thereisacostassociatedtooverrunning,butthiscostmaybeabstract.

OftenconnectedtoQuality-of-Service(QoS).

Figure 1.4: Deadline Point in Soft Real Time System

Example costfunction

Triggeringevent

CostDeadline

Time

Asoftrealtimesystemwhereacriticalreal-timetaskgetspriorityoverothertasksandretains

thatpriorityuntilitcompletes.Softrealtimeapplicationsdonotfailifadeadlineismissed.Somesoftrealtimeapplicationscanprocesslargeamountsofdataorrequireaveryfastresponsetime,butthekeyissueiswhetherornotmeetingtimingconstraintsisaconditionforsuccess.Anexampleofasoftrealtimeapplicationisanairlinereservationsystemwhereanoccasionaldelayistolerable,butunwanted.

Softreal-timeistheentirespaceexceptforthehardreal-timecornerpoint.Asystemcanbeconsidered to be a hard real-time one to the degree that it has hard deadlines and a sequencing

timeliness factor that includes always meeting all the hard deadlines.


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Notes Somesoftreal-timesystemsarenon-stochasticallynon-deterministic.Theyhavepropertiesthatare

soasynchronous-inthesenseofintermittent,irregular,eitherinterdependentorcompetitivethat

stochasticmodelsofpredictabilityforthemareeitherunknownorcomputationallyintractable.

Reasoningaboutthesequencetimelinessofsuchsystemsistypicallyperformedusingsimulation

modelsorextensional(rule-based)andothermodelsfromeldssuchasarticialintelligence,

decisiontheory,etc.

Preparealistofvelatestrealtimeoperatingsystem.

Hardreal-timesystemsmusthaveatleastsomeactionswithharddeadlines.Buttheconverseis

not true soft real-time systems may have actions with hard deadlines. Those systems are soft real-

timebecausetheydonotemploythehardreal-timesequencingtimelinesscriterion,theyemploy

softreal-timeonessuchasminimizetheexpectednumberofmisseddeadlines,regardlessof

whether the deadlines are hard or soft.

Itis clearthatin thetechnicalsense definedhere(as opposedto popularmiss usageby

practitioners),softreal-timesystemsareconsiderablymoredifculttocreatethanarehardreal-

time ones.

Hardreal-timeandsoftreal-timeapplyonlytoasystem,becausetheir

denitionsarebasedonsequencing.Inthissense,asystemisanyresource

management facility that includes sequencing.

1.4 Hard Versus Soft Real Time System

Ahardreal-timesystemguaranteesthatcriticaltaskscompleteontime.Thisgoalrequiresthat

all delays in the system be bounded from the retrieval of the stored data to the time that it takestheoperatingsystemtonishanyrequestmadeofit.

Acriticaltaskobtainsapriorityoverothertasksandmaintainingthatpriorityuntilthecompletion

ofthetask.Thisisperformedbyasoftrealtimesystem.Thesystemkerneldelaysneedtobe

bounded as in the case of hard real time system.

Hardrealtimetasksmustcompletetheirprocessingbyaparticulardeadline.Normally

somethingbadwillhappenifthedeadlineismissed.

Softrealtimetaskshaveapreferredcompletiontime.Normallymissingthedeadlineisnotfatal.

Drawadiagramforsoftwarerealtimesystemintheairticketing.

Table1.1showsthemajordifferencesbetweenhardandsoftreal-timesystems.Theresponsetime

requirements of hard real-time systems are in the order of milliseconds or less and can result in

acatastropheifnotmet.Incontrast,theresponsetimerequirementsofsoftreal-timesystems

arehigherandnotverystringent.Inasoftreal-timesystem,adegradedoperationinararely

occurringpeakloadcanbetolerated.Ahardreal-timesystemmustremainsynchronouswith

the state of the environment in all cases. On the other hand soft real-time systems will slow down

theirresponsetimeiftheloadisveryhigh.Hardreal-timesystemsareoftensafetycritical.Hard

real-timesystemshavesmalldatalesandreal-timedatabases.Temporalaccuracyisoftenthe

concernhere.Softreal-timesystemsforexample,on-linereservationsystemshavelargerdatabases

andrequirelong-termintegrityofreal-timesystems.Ifanerroroccursinasoftreal-timesystem,


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Notes

thecomputationisrolledbacktoapreviouslyestablishedcheckpointtoinitiatearecoveryaction.

Inhardreal-timesystems,roll-back/recoveryisoflimiteduse.

A real-time system is one whose correctness is based on both the correctness

oftheoutputsandtheirtimeliness.

Inahardreal-timesystem,thepeak-loadperformancemustbepredictable

andshouldnotviolatethepredeneddeadlines.

Table 1.1: Differences Between Hard and Soft Real-time Systems

Characteristic Hard real-time Soft real-time

Response Time Hard-required Soft-desired

Peak-load performance Predictable Degraded

Control of pace EnvironmentComputer

Safety OftencriticalNon-critical

Size of data les Small/medium Large

Redundacy type Active Checkpoint-recovery

Data integrity Short-term Long-term

Error detection Autonomous Userassisted

Correct Development of Real-time Embedded Systems

in UML

OMEGAwilldevelopamethodologyandtoolsforthedevelopmentofreal-timeandembeddedsystemsusingUML,basedonacleansemanticsofthedifferent

architecturalviewpointsandtheirrelations.Theaimoftheprojectistoincreasethe

efciencyandcompetitivenessoftheEuropeansoftwareindustrybyprovidingtoolsimproving

thequalityofsoftwarewhilereducingtheexpenseofthevalidationphase.TheOMEGA

approachtosoftwarequalityistouseUMLforthedescriptionofauniquereferencemodel,

fromwhicharederivedsemanticallyrelatedmodelsforfunctional,validation,performance

analysis,aswellasimplementations;allevolutionsarereportedinthereferencemodelfor

trackingofitsinuence.Asemanticallysoundcomponentbaseddevelopmentplaysan

importantrole,whichmakessurethatinterfacesaresufcienttoguaranteetherequirements.

Objectives

OMEGAaimsatthedenitionofadevelopmentmethodologyinUMLforembeddedand

real-timesystemsbasedonformaltechniquesandusedtoimprovecommerciallyavailableUMLtools.ForthispurposewewillIdentifyreasonableandeffectivesubsetsofUMLfor

real-time,aswellasnecessaryextensions.Provideformalfoundations,methodsandtools

forcompositionalvericationofreal-timesystemswithinUML.Constructadevelopment

methodologybasedontheUMLmodellingandspecicationcapabilitiesandtheverication

methodsandtoolsdevelopedintheproject.Applyindustrialcasestudiesforevaluatingthe

proposedmethodologyandvericationtools.Workdescription:

Toachieveouraim,wewilldevelopresultsinthefollowinginterdependentdirections:

1. Modelling and Specication Language: WeselectasmallsubsetofUMLnotations

thatallowthedesignofreactiveandreal-timesystems.Ifneeded,wealsopropose

smallextensions.Theresultinglanguagecontainsnotationstomodelthesystemunder

development includingboth functional andnon-functionalaspects,and specifythe

requirements to be met by the system. Contd...


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Notes 2. Verification and Synthesis:Wewilladaptandextendexistingformalverification

technologiestoUML,identifythenewneedsinvericationtechniquesraisedbythe

powerfulstructuringfeaturesofUMLanddevelopcompositionalvericationmethods,

allowingderivingpropertiesofsystemsfrompropertiesofcomponents.Thetechniques

areconnectedtotwoindustrialCASEtools,leadingtotwovericationtool-sets.Wewill

also developtoolsthatin certaincasesdirectlysynthesizesystemssatisfyingrequired

properties.

3. Development Methodology:Wewilldevelopamethodology,providingguidelinesabout

theuseandthecombinationofthedifferentnotations.Inparticular,themethodologywill

bebasedonrenementandpropertypreservationrules,relatingthedifferentabstraction

levels.

4. Technology Transfer:Wewillshowhowthedevelopedresults-theory,methodsand

tools-canbeappliedtoreal-timesystemsdevelopmentbyusingappropriateextensions

ofcommerciallyavailabletools.Ourapproachwillbeevaluatedandadaptedonthebasis

of four industrial case studies.

Milestones

1. DenitionofaUMLkernelmodel(KM):aminimalsubsetofUMLforthedevelopment

ofreal-timeandembeddedsystems;

2. SemanticfoundationsoftheKM;

3. Adaptionofexistingmodel-checkingtechniquestotheKMforcomponentverication;

4. Twointegratedtool-setsfor system verication based oncompositionalmethodsand

synthesis;

5. Adevelopmentmethodologybasedonsemanticpreservingnotionsofrenement;

Questions:

1. ExplaintheobjectivesofdevelopmentmethodologyinUMLforembeddedandreal-time

systems.

2. Discussinbriefreal-timeembeddedsystemsinUML.

Self Assessment


6. Hardreal-timesystemishardwareorsoftwarethatmustoperatewithintheconnesofa

stringent timeline.

(a) True (b) False

7. Operatingsystemmusthaveaknownmaximumtimeforeachoftheoperationsthatit

performs.

(a) True (b) False

8. Ahardreal-timesystemnotguaranteedthatcriticaltaskscompleteontime.

(a) True (b) False

9. Predictabilityistheconditionof.hastoreacttoallpossibleeventsinapredictable

way.

(a) typeofsoftrealtimesystem (b) typeofsoftrealtimesystem

(c) real-timesystem (d) noneofthese

10. Simultaneityorsimultaneousprocessingmorethanoneeventmayhappensimultaneously,

all deadlines should be met.

(a) True (b) False


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Notes1.5 Summary

Realtimetermisusedtodescribeanumberofdifferentcomputerfeaturesitrefertoevents

simulatedbyacomputeratthesamespeedthattheywouldoccurinreallife.

Arealtimeapplicationisanapplicationwherethecorrectnessoftheapplicationdepends

onthetimelinesandpredictabilityoftheapplicationaswellastheresultsofcomputations.

Areal-timesystemisanyinformationprocessingsystemwhichhastorespondtoexternally

generatedinputstimuliwithinaniteandspeciedperiod.

Ahard real-time system isone whosesequencingtimeliness factorsare optimality is

thebinarycasethatmeetingallharddeadlinesisoptimalandotherwiseissuboptimal

predictabilityofoptimalityisdeterministic.

Ahardreal-timesystemknownasanimmediatereal-timesystem.

1.6 Keywords

Deadline point:Thisisapointinrealtimesystemafterdelayingthispointthesystemwillcrash.

Dependability or trustworthiness: It is necessary condition that the real-time system environment

can rely on it.

Hard real-time system:Itishardwareorsoftwarethatmustoperatewithintheconnesofa

stringent deadline.

Immediate real-time system:Itishardwareorsoftwarethatmustoperatewithintheconnesof

a stringent deadline.

Predictability: Itis theconditionofreal-time system has toreact toallpossible events ina

predictableway.

Real time:Thetermisusedtodescribeanumberofdifferentcomputerfeatures.Forexample,

real-timeoperatingsystemsaresystemsthatrespondtoinputimmediately.

Real time system:Itisareal-timesystemwhenitcansupporttheexecutionofapplicationswith

timeconstraintsonthatexecution.

Simultaneity or simultaneous processing:Thisismorethanoneeventmayhappensimultaneously,

all deadlines should be met this is a condition of real time system.

Soft real-time system: It can be a vending machine rising cost for lateness of results as it will

takelongertotreatacustomerwhentheperformanceofthevendingmachineisdegrading,less

customerspayatthismachinewhichresultsinlessprotsfortheshopowner.

Trigger generator:Itisarepresentationatthemechanismusedtotriggertheexecutionofindividualjobs.

Timeliness:Itisaconditionofrealtimesystemthatmeetdeadlinesitisrequiredthattheapplication

hastonishcertaintaskswithinthetimeboundariesithastorespect.

1. Designatimegraphforreal-timesystemswithtimingconstraints.

2. Prepareaprocessdiagramforperiodictask.


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Real Time Systems


Notes 1.7 Review Questions

1. What do you understand by real time?

2. Explaintheimportanceofrealtimesystemandstructureofit.

3. Describetheconceptofrealtimeoperatingsystem.

4. Discussinbriefhardandsoftrealtimesystem.

5. Discussintypesoftaskinrealtimesystem.

6. Differentiatebetweenhardandsoftrealtimesystem.

7. Whatisdeadlinepointinrealtimesystem?

8. Denetimelineinrealtimesystem.

9. Whichtypeofrealtimesystemuseinaircraft?

10. Denetimingconstraints.Andwhatisutilityofitinbothrealtimesystems?

Answers to Self Assessment

1. (a) 2. (a) 3. (b) 4. (d) 5. (a)

6. (b) 7. (a) 8. (b) 9. (c) 10. (a)

1.8 Further Reading

Alan, C. Shaw, RTS and Software,byJohnWileyandSons,NewYork,2001.

http://www.ece.cmu.edu/~koopman/des_s99/real_time/


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NotesUnit 2: Introduction to Real Time Applications

CONTENTS

Objectives

Introduction

2.1 DigitalControl

2.1.1 SampledDataSystems

2.1.2 MoreComplexControl-lawComputations

2.2 High-LevelControls

2.2.1 ExamplesofControlHierarchy

2.2.2 GuidanceandControl

2.2.3 Real-timeCommandandControl

2.3 SignalProcessing

2.3.1 ProcessingBandwidthDemands

2.3.2 Radar System

2.4 OtherReal-timeApplications

2.4.1 Real-timeDatabases

2.4.2 MultimediaApplications

2.5 Summary

2.6 Keywords

2.7 ReviewQuestions

2.8 Further Reading

Objectives

After studying this unit, you will be able to:

Discussaboutthedigitalcontrolsinrealtimesystem

Explainthehigh-levelcontrols

Discussthesignalprocessing

Describetheotherreal-timeapplications

Introduction

Thereal-time(computing)systemestimatesfromthesensorreadingsthecurrentstateofthe

plantandcomputesacontroloutputbasedonthedifferencebetweenthecurrentstateandthe

desiredstate(calledreferenceinput).Wecallthiscomputationthecontrol-lawcomputation

ofthecontroller.Theoutputthusgeneratedactivatestheactuators,whichbringtheplant

closer to the desired state. One or more digital controllers at the lowest level directly control

thephysicalplant.Outputofahigher-levelcontrollerisareferenceinputofoneormore

lower-level controllers.

2.1 Digital Control

Many real-time systems are embedded in sensors and actuators and function as digital controllers.

Figure2.1showssuchasystem.Thetermplantintheblockdiagramreferstoacontrolledsystem,


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Real Time Systems


Notes forexample,anengine,abrake,anaircraft,apatient.Thestateoftheplantismonitoredbysensors

and can be changed by actuators.

2.1.1 Sampled Data Systems

Longbeforedigitalcomputersbecamecost-effectiveandwidelyused,analogue(i.e.,continuous

timeandcontinuous-state)controllerswereinuse,andtheirprincipleswerewellestablished.

Consequently,acommonapproachtodesigningadigitalcontrolleristostartwithananalogue

controller that has the desired behaviour. The analogue version is then transformed into a digital

(i.e.,discrete-timeanddiscrete-state)version.Theresultantcontrollerisasampleddatasystem.It

typicallysamples(i.e.,reads)anddigitizestheanaloguesensorreadingsperiodicallyandcarries

outitscontrol-lawcomputationeveryperiod.Thesequenceofdigitaloutputsthusproducedis

then converted back to an analogue form needed to activate the actuators.

A Simple Example

Asanexample,weconsiderananaloguesingle-input/single-outputPID(Proportional,Integral,

andDerivative)controller.Thissimplekindofcontrolleriscommonlyusedinpractice.The

analoguesensorreadingy(t)givesthemeasuredstateoftheplantattime t.Lete(t)=r(t)y(t)denote the difference between the desired state r(t)andthemeasuredstatey(t)attimet. The

outputu(t)ofthecontrollerconsistsofthreeterms:atermthatisproportionaltoe(t),aterm

thatisproportionaltotheintegralofe(t)andatermthatisproportionaltothederivativeofe(t).

Figure 2.1: A Digital Controller

Reference

input

r(t)

rk

yk

ukD/A

Control-law

computation

Sensor Plant Actuator

y(t) u(t)

Controller

A/D

A/D

Inthesampleddataversion,theinputstothecontrol-lawcomputationarethesampledvalues yk

and rk,fork=0,1,2,...,whichanalogue-to-digitalconvertersproducebysamplinganddigitizing

y(t)andr(t)periodicallyeveryTunits of time. The ek=rkyk is the kthsamplevalueofe(t).There

aremanywaystodiscretizethederivativeandintegralof e(t).Forexample,wecanapproximate

the derivative of e(t)for(k1)T


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Unit 2: Introduction to Real Time Applications


Notesdoanalogue-to-digitalconversiontogety;computecontroloutputu;

outputuanddodigital-to-analogueconversion;

enddo;

Here,weassumethatthesystemprovidesatimer.Oncesetbytheprogram,thetimergenerates

aninterrupteveryTunits of time until its setting is cancelled.

Selection of Sampling Period

The length Tof time between any two consecutive instants at which y(t)andr(t)aresampled

is called the sampling period. The Tis a key design choice. The behaviour of the resultant digital

controllercriticallydependsonthisparameter.Ideallywewantthesampleddataversiontobehave

liketheanalogueversion.Thiscanbedonebymakingthesamplingperiodsmall.However,a

smallsamplingperiodmeansmorefrequentcontrol-lawcomputationandhigherprocessor-time

demand.WewantasamplingperiodTthatachievesagoodcompromise.

Weneedtoconsidertwofactors.Therstistheperceivedresponsivenessoftheoverall,system

(i.e.,theplantandthecontroller).Oftentimes,thesystemisoperatedbyaperson(e.g.,adriver

orapilot).Theoperatormayissueacommandatanytime,sayat t. The consequent change in

thereferenceinputisreadandreactedtobythedigitalcontrolleratthenextsamplinginstant.

This instant can be as late as t + T.Thus,samplingintroducesadelayinthesystemresponse.The

operatorwillfeelthesystemsluggishwhenthedelayexceedsatenthofasecond.Therefore,the

samplingperiodofanymanualinputshouldbeunderthislimit.

Thesecondfactoristhedynamicbehaviouroftheplant.Wewanttokeeptheoscillationinits

responsesmallandthesystemundercontrol.Theplantinthisexampleisthearmofadisk.The

controllerisdesignedtomovethearmtotheselectedtrackeachtimewhenthereferenceinput

changes.Ateachchange,thereferenceinput r(t)isastepfunctionfromtheinitialpositiontothe

nalposition.InFigure2.2,thesepositionsarerepresentedby0and1,respectively,andthetime

originistheinstantwhenthestepinr(t)occurs.ThedashedlinesinFigure2.2(a)

Figure 2.2: Effects of Sampling Period


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Real Time Systems


Notes

givetheoutputu(t)of theanaloguecontrollerandtheobservedpositiony(t)ofthearmasa

functionoftime.Thesolidlinesintheloweranduppergraphsgive,respectively,theanalogue

controlsignalconstructedfromthedigitaloutputsofthecontrollerandtheresultantobserved

positiony(t)ofthearm.Atthesamplingrateshownhere,theanalogueanddigitalversionsare

essentiallythe same.Thesolidlinesin Figure2.2(b)givethebehaviourofthe digitalversion

whenthesamplingperiodisincreasedby2.5times.Theoscillatorymotionofthearmismore

pronouncedbutremainssmallenoughtobeacceptable.However,whenthesamplingperiodis

increasedbyvetimes,asshowninFigure2.2(c),thearmrequireslargerandlargercontroltostayinthedesiredposition;whenthisoccurs,thesystemissaidtohavebecomeunstable.

Ingeneral,thefasteraplantcanandmustrespondtochangesinthereferenceinput,thefaster

theinputtoitsactuatorvaries,andtheshorterthesamplingperiodshouldbe.Wecanmeasure

theresponsivenessoftheoverallsystembyitsrise time R. This term refers to the amount of time

thattheplanttakestoreachsomesmallneighbourhoodaroundthenalstateinresponsetoa

stepchangeinthereferenceinput.IntheexampleinFigure2.2,asmallneighbourhoodofthe

nalstatemeansthevaluesofy(t)thatarewithin5%ofthenalvalue.Hence,therisetimeof

thatsystemisapproximatelyequalto2.5.

A good rule of thumb is the ratio R/T of rise time to sampling period is from 10 to 20 .Inotherwords,

thereare1020samplingperiodswithintherisetime.AsamplingperiodofR/10shouldgivean

acceptablysmoothresponse.However,ashortersamplingperiod(andhenceafastersamplingrate)islikelytoreducetheoscillationinthesystemresponseevenfurther.Forexample,the

samplingperiodusedtoobtainFigure2.2(b)isaroundR/10whilethesamplingperiodusedto

obtainFigure2.2(a)isaroundR/20.

Theaboveruleisalsocommonlystatedintermsofthebandwidth, w,ofthesystem.Thebandwidthoftheoverallsystemisapproximatelyequalto1/2RHz.Sothesamplingrate(i.e.,theinverseof

samplingperiod)recommendedaboveis2040timesthesystembandwidthw. The theoreticallowerlimitofsamplingrateisdictatedby Nyquist sampling theorem. The theorem says that any

time-continuous signal of bandwidth w can be reproduced faithfully from its sampled values if and only ifthe sampling rate is 2w or higher.Weseethattherecommendedsamplingrateforsimplecontrollersissignicantlyhigherthanthislowerbound.Thehighsamplingratemakesitpossibletokeep

thecontrolinputsmallandthecontrol-lawcomputationanddigital-to-analogueconversionofthecontrollersimple.

Multirate Systems

Aplanttypicallyhasmorethanone degreeoffreedom.Itsstateisdenedbymultiplestate

variables(e.g.,therotationspeed,temperature,etc.ofanengineorthetensionandpositionofa

videotape).Therefore,itismonitoredbymultiplesensorsandcontrolledbymultipleactuators.

Wecanthinkofamultivariate(i.e.,multi-input/multi-output)controllerforsuchaplantasa

systemofsingle-outputcontrollers.

Becausedifferentstatevariablesmayhavedifferentdynamics,thesamplingperiodsrequiredto

achievesmoothresponsesfromtheperspectiveofdifferentstatevariablesmaybedifferent.[For

example,becausetherotationspeedsofanenginechangesfasterthanitstemperature,therequired


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NotessamplingrateforRPM(RotationperMinute)controlishigherthanthatforthetemperature

control.]Ofcourse,wecanusethehighestofallrequiredsamplingrates.Thischoicesimplies

thecontrollersoftwaresinceallcontrollawsarecomputedatthesamerepetitionrate.However,

somecontrol-lawcomputationsaredonemorefrequentlythannecessary;someprocessortime

iswasted.Topreventthiswaste,multivariatedigitalcontrollersusuallyusemultipleratesand

are therefore called multirate systems.

Oftentimes,thesamplingperiodsusedinamultiratesystemarerelatedinaharmonicway,that

is,eachlongersamplingperiodisanintegermultipleofeveryshorterperiod.Toexplainthe

control-theoreticalreasonforthischoice,wenotethatsomedegreeofcouplingamongindividual

single-outputcontrollersin asystemis inevitable.Consequently,the samplingperiodsof the

controllerscannotbeselectedindependently.Amethodforthedesignandanalysisofmultirate

systemsisthesuccessiveloopclosuremethod.Accordingtothismethod,thedesignerbeginsby

selectingthesamplingperiodofthecontrollerthatshouldhavethefastestsamplingrateamong

allthecontrollers.Inthisselection,thecontrollerisassumedtobeindependentoftheothersin

thesystem.Afteradigitalversionisdesigned,itisconvertedbackintoananalogueform.The

analoguemodelisthenintegratedwiththeslowerportionoftheplantandistreatedasapart

oftheplant.Thisstepisthenrepeatedforthecontrollerthatshouldhavethefastestsampling

rateamongthecontrollerswhosesamplingperiodsremaintobeselected.Theiterationprocess

continuesuntiltheslowestdigitalcontrollerisdesigned.Eachstepusesthemodelobtainedduring

thepreviousstepastheplant.Whenthechosensamplingperiodsareharmonic,theanalogue

modelsofthedigitalcontrollersusedinthisiterativeprocessareexact.Theonlyapproximation

arisesfromtheassumptionmadeintherststepthatthefastestcontrollerisindependent,and

theerrorduetothisapproximationcanbe-correctedtosomeextentbyincorporatingtheeffectof

theslowercontrollersintheplantmodelandthenrepeatingtheentireiterativedesignprocess.

An Example of Software Control Structures

Asanexample,Figure2.3showsthesoftwarestructureofaightcontroller.Theplantisa

helicopter.Ithasthreevelocitycomponents;together,theyarecalledcollectiveinthegure.It

alsohasthreerotational(angular)velocities,referredtoasroll,pitch,andyaw.Thesystemusesthreesamplingrates:180,90and30Hz.Afterinitialization,thesystemexecutesadoloopatthe

rateofoneiterationevery1/180second;inthegureacyclemeansa1/180-secondcycle,and

thetermcomputationmeansacontrol-lawcomputation.

Specically,atthestartofeach1/180-secondcycle,thecontrollerrstchecksitsownhealthand

reconguresitselfifitdetectsanyfailure.Itthendoeseitheroneofthethreeavionicstasksor

computesoneofthe30-Hzcontrollaws.Wenotethatthepilotscommand(i.e.,keyboardinput)

ischeckedevery1/30second.Atthissamplingrate,thepilotshouldnotperceivetheadditional

delayintroducedby sampling.Themovementofthe aircraftalongeachof thecoordinatesis

monitoredandcontrolledbyaninnerandfasterloopandanouterandslowerloop.Theoutput

producedbytheouterloopisthereferenceinputtotheinnerloop.Eachinnerloopalsousesthe

dataproducedbytheavionicstasks.

Figure 2.3: An Example: Software Control Structure of a Flight Controller

Do the following in each 1/180-second cycle:

Validatesensordataandselectdatasource;inthepresenceoffailures,recongurethesystem.

Dothefollowing30-Hzavionicstasks,eachonceeverysixcycles:

keyboardinputandmodeselection

datanormalizationandcoordinatetransformation

trackingreferenceupdate

Dothefollowing30-Hzcomputations,eachonceeverysixcycles:

controllawsoftheouterpitch-controlloop


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Real Time Systems


Notes controllawsoftheouterroll-controlloop

controllawsoftheouteryaw-andcollective-controlloop

Doeachofthefollowing90-Hzcomputationsonceeverytwocycles,usingoutputsproducedby

30-Hzcomputationsandavionicstasksasinput: controllawsoftheinnerpitch-controlloop

controllawsoftheinnerroll-andcollective-controlloop

Computethecontrollawsoftheinneryaw-controlloop,usingoutputsproducedby90-Hzcontrol

lawcomputationsasinput.

Outputcommands.

Carryoutbuilt-in-test.

Waituntilthebeginningofthenextcycle.

Thismultiratecontrollercontrolsonlyightdynamics.Thecontrolsystemonboardanaircraftis

considerablymorecomplexthanindicatedbythegure.Ittypicallycontainsmanyotherequally

criticalsubsystems(e.g.,airinlet,fuel,hydraulic,brakesandanti-icecontrollers)andmanynotsocriticalsubsystems(e.g.,lightingandenvironmenttemperaturecontrollers).So,inadditiontothe

ightcontrol-lawcomputations,thesystemalsocomputesthecontrollawsofthesesubsystems.

Timing Characteristics

Togeneralize fromthe aboveexample,wecan see that theworkloadgeneratedbyeach

multivariate,multiratedigitalcontrollerconsistsofafewperiodiccontrol-lawcomputations.

Theirperiodsrangefroma fewmillisecondstoa fewseconds.Acontrolsystemmaycontain

numerousdigitalcontrollers,eachofwhichdealswithsomeattributeoftheplant.Togetherthey

demandtensorhundredsofcontrollawsarecomputedperiodically,someofthemcontinuously

andothersonlywhenrequestedbytheoperatororinreactiontosomeevents.Thecontrollaws

ofeachmultiratecontrollermayhaveharmonicperiods.Theytypicallyusethedataproduced

byeachotherasinputsandaresaidtobearategroup.Ontheotherhand,thereisnocontroltheoreticalreasontomakesamplingperiodsofdifferentrategroupsrelatedinaharmonicway.

Eachcontrol-lawcomputationcanbeginshortlyafterthebeginningofeachsamplingperiodwhen

themostrecentsensordatabecomeavailable.(Typically,thetimetakenbyananalogue-to-digital

convertertoproducesampleddataandplacethedatainmemorydoesnotvaryfromperiodto

periodandisverysmallcomparedwiththesamplingperiod.)Itisnaturaltowantthecomputation

completeand,hence,thesensordataprocessedbeforethedatatakeninthenextperiodbecome

available.Thisobjectiveismetwhentheresponsetimeofeachcontrol-lawcomputationnever

exceedsthesamplingperiod.Theresponsetimeofthecomputationcanvaryfromperiodto

period.Insomesystems,itis necessarytokeepthisvariationsmallsothatthedigitalcontrol

outputsproducedbythecontrollerbecomeavailableattimeinstantsmoreregularlyspacedin

time.Inthiscase,wemayimposeatimingjitterrequirementonthecontrol-lawcomputation:

thevariationinitsresponsetimedoesnotexceedsomethreshold.

Real-timecomputationsmaybefailediftheyarenotcompletedbeforetheir

deadline,wheretheirdeadlineisrelativetoanevent.

2.1.2 More Complex Control-law Computations

ThesimplicityofaPIDorsimilardigitalcontrollerfollowsfromthreeassumptions.First,sensor

data give accurate estimates of the state-variable values being monitored and controlled. This

assumptionisnotvalidwhennoiseanddisturbancesinsideoroutsidetheplantpreventaccurate

observationsofitsstate.Second,thesensordatagivethestateoftheplant.Ingeneral,sensors

monitorsomeobservableattributesoftheplant.Thevaluesofthestatevariablesmustbecomputed


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Notesfromthemeasuredvalues(i.e.,digitizedsensorreadings).Third,alltheparametersrepresenting

thedynamicsoftheplantareknown.Thisassumptionisnotvalidforsomeplants.(Anexample

isaexiblerobotarm.Eventheparametersoftypicalmanipulatorsusedinautomatedfactories

arenotknownaccurately.)

Sincetheseassumptionsareoftennotvalid,youoftenseedigitalcontrollersimplementedas

follows.

settimertointerruptperiodicallywithperiodT;

ateachclockinterrupt,do

sampleanddigitizesensorreadingstogetmeasuredvalues;

computecontroloutputfrommeasuredandstate-variablevalues;

convertcontroloutputtoanalogueform;

estimateandupdateplantparameters;

computeandupdatestatevariables;

enddo;

Thelasttwostepsintheloopcanincreasetheprocessortimedemandofthecontrollersignicantly.

Wenowgivetwoexampleswherethestateupdatestepisneeded.

Deadbeat Control

A discrete-time control scheme that has no continuous-time equivalence is deadbeat control. In

responsetoastepchangeinthereferenceinput,adead-beatcontrollerbringstheplanttothe

desiredstatebyexertingontheplantaxednumber(sayn)ofcontrolcommands.Acommand

is generated every Tseconds.(Tisstillcalledasamplingperiod.)Hence,theplantreachesits

desired state in nTsecond.

Inprinciple,thecontrol-lawcomputationofadead-beatcontrollerisalsosimple.Theoutput

producedbythecontrollerduringthekthsamplingperiodisgivenby

uk = ( )r y xi ii

k

i ii

k

+= =

0 0

[ThisexpressioncanalsobewritteninanincrementalformsimilartoEq.(2.1).]Again,theconstants

a and bis are chosen at design time. xiisthevalueofthestatevariableinthesamplingperiod.Duringeachsamplingperiod,thecontrollermustcomputeanestimateofxk from measured values

yi,fori < k.Inotherwords,thestateupdatestepintheabovedoloopisneeded.

Kalman Filter

Kalmanlteringisacommonlyusedmeanstoimprovetheaccuracyofmeasurementsandtoestimatemodelparametersinthepresenceofnoiseanduncertainty.Toillustrate,weconsidera

simplemonitorsystemthattakesameasuredvalueykeverysamplingperiodk in order to estimate

the value xkofastatevariable.Supposethatstartingfromtime0,thevalueofthisstatevariable

is equal to a constant x.Becauseofnoise,themeasuredvalueyk is equal to x + ek,whereek is arandomvariablewhoseaveragevalueis0andstandarddeviationissk.TheKalmanlterstartswith the initial estimate x1 =ylandcomputesanewestimateseachsamplingperiod.Specically,

for k>1,theltercomputestheestimate xk asfollows:

xk = x K y xk k k k + 1 1( ) ...(2.2a)


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Real Time Systems


Notes Inthisexpression,

Kk =P

P

k

k k2+

...(2.2b)

is called the Kalman gain and Pk is the variance of the estimation error x x ; the latter is given by

Pk = E x x K Pk k k[( ) ] ( ) = 2 1 11 ...(2.2c)

ThisvalueoftheKalmangaingivesthebestcompromisebetweentherateatwhich Pk decreases

with kandthesteady-statevariance,thatis,Pk for large k.

Inamultivariatesystem,thestatevariablexk is an n-dimensionalvector,wheren is the number of

variableswhosevaluesdenethestateoftheplant.Themeasuredvalueyk is an n-dimensional

vector,ifduringeachsamplingperiod,thereadingsofn sensors are taken. We let A denote the

measurementmatrix;itisan n nmatrixthatrelatesthe n measured variables to the n state

variables.Inotherwords,

yk = Axk + ek

The vector ek gives the additive noise in each of the nmeasuredvalues.Eq.(2.2a)becomesan

n-dimensional vector equation

xk = x K y Axk k k k + 1 1( ) ...(2.3)

Similarly,Kalmangain Kk and variance PkaregivenbythematrixversionofEqs.(2.2b)and

(2.2c).So,thecomputationineachsamplingperiodinvolvesafewmatrixmultiplicationsand

additionsandonematrixinversion.

TheAtanasoffBerryComputer(ABC)wasthefirstelectronicdigital

computingdevice.

Self Assessment


1. Outputofahigher-levelcontrollerisareferenceinputofoneormorelower-levelcontrollers.

(a) True (b) False. 2. Theanalogueversionisthentransformedintoadigital(i.e.,discrete-timeanddiscrete-state)

version. The resultant controller is a..................

(a) panelsystem (b) multiratesystem

(c) sampleddatasystem (d) noneofthese.

3. A discrete-time control scheme that has no continuous-time equivalence is...............

(a) deadbeatcontrol (b) multiratecontrol

(c) sampledcontrol (d) noneofthese.

4. Theresponsetimeofthecomputationcanvaryfromperiodtoperiod.

(a) True (b) False.

5. .isacommonlyusedmeanstoimprove the accuracyofmeasurementsandtoestimatemodelparametersinthepresenceofnoiseanduncertainty.

(a) Deadbeatcontrol (b) Multiratecontrol

(c) Kalmanlter (d) noneofthese.

2.2 High-Level Controls

Controllersinacomplexmonitorandcontrolsystemaretypicallyorganizedhierarchicallywith

fewexceptions,oneormoreofthehigher-levelcontrollersinterfaceswiththetor(s).

2.2.1 Examples of Control Hierarchy

Forexample,apatientcaresystemmayconsistofmicroprocessor-basedcontrollersthatmonitor

andcontrolthepatientsbloodpressure,respiration,glucose,andsoforth.Theremayahigher-


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Noteslevelcontroller(e.g.,inexpertsystem)whichinteractswiththeoperator(anordoctor)andchoosesthedesiredvaluesofthesehealthindicators.Whilethecomputationdonebyeachdigitalcontrollerissimpleandnearlydeterministic,thecomputationofahigh-levelcontrollerislikelytobefarmorecomplexandvariable.Whiletheperiodofalevelcontrol-lawcomputationrangesfrommilliseconds

toseconds,theperiodsofhigh-levelcontrol-lawcomputationsmaybeminutes,evenhours.Figure2.4showsamorecomplexexample:thehierarchyofightcontrol,avionics,andairtrafccontrolsystems.TheAirTrafcControl(ATC)systemisatthehighestlevel.Itregulatestheowofightstoeachdestinationairport.Itdoessobyassigningtoeachaircraftanarrivaltimeateachmeteringx(orwaypoint)enroutetothedestination:Theaircraftissupposedtoarriveatthemeteringxattheassignedarrivaltime.Atanytimewhileinighttheassignedarrivaltimetothenextmeteringxisareferenceinputtotheon-boardightmanagementsystem.Theightmanagementsystemchoosesatime-referencedightpaththatbringstheaircrafttothenextmeteringxattheassignedarrivaltime.Thecruisespeeds,turnradius,descend/ascendrates,andsoforthrequiredtofollowthechosentime-referencedightpatharethereferenceinputstotheightcontrolleratthelowestlevelofthecontrolhierarchy.

Ingeneral,theremaybeseveralhigherlevelsofcontrol.Takeacontrolsystemof robotsthatperformassemblytasksinafactoryforexample.Pathandtrajectoryplannersatthesecondleveldeterminethetrajectorytobefollowedbyeachindustrialrobot.Theseplannerstypicallytakeasaninputtheplangeneratedbyataskplanner,whichchoosesthesequenceofassemblystepstobeperformed.Inaspacerobotcontrolsystem,theremaybeascenarioplanner,whichdetermineshowarepairorrendezvousfunctionshouldbeperformed.Theplangeneratedbythisplannerisaninputofthetaskplanner.

2.2.2 Guidance and Control

Whileadigitalcontrollerdealswithsomedynamicalbehaviourofthephysicalplant,asecondlevel

controllertypicallyperformsguidanceandpathplanningfunctionstoachieveahigher-levelgoal.

Figure 2.4: Air Trafc/Flight Control Hierarchy

Responses Commands

Operator-system

interface

From

sensors

Stateestimator

Air-trafficcontrol

NavigationVirtual plant

Stateestimator

Stateestimator

Flightmanagement

Flightcontrol

Virtual plant

Air data

Physical plant


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Real Time Systems


Notes Inparticular,ittriestondoneofthemostdesirabletrajectoriesamongalltrajectoriesthat

meettheconstraintsofthesystem.Thetrajectoryismostdesirablebecauseitoptimizessome

costfunction(s).Thealgorithm(s)usedforthispurposeis thesolution(s)ofsomeconstrained

optimizationproblem(s).

Asanexample,welookagainataightmanagementsystem.Theconstraintsthatmustbe

satisedbythechosenightpathincludetheonesimposedbythecharacteristicsoftheaircraft,

suchasthemaximumandminimumallowedcruisespeedsanddecent/accentrates,aswellas

constraintsimposedbyexternalfactors,suchasthegroundtrackandaltitudeprolespeciedby

theATCsystemandweatherconditions.Acostfunctionisfuelconsumption:Amostdesirable

ightpathisa mostfuelefcientamongallpathsthatmeetalltheconstraintsandwillbring

theaircrafttothenextmeteringxattheassignedarrivaltime.Thisproblemisknownasthe

constrainedxed-time,minimum-fuelproblem.Whentheightislate,theightmanagement

systemmaytrytobringtheaircrafttothenextmeteringxintheshortesttime.Inthatcase,it

willuseanalgorithmthatsolvesthetime-optimalproblem.

Complexity and Timing Requirements

Theconstrainedoptimizationproblemsthataguidance(orpathplanning)systemmustsolveare

typicallynonlinear.Inprinciple,theseproblemscanbesolvedusingdynamicprogramingand

mathematicalprogramingtechniques.Inpractice,however,optimalalgorithmsarerarelyused

becausemostofthemarenotonlyverycomputingintensivebutalsodonotguaranteetonda

usablesolution.Heuristicalgorithmsusedforguidanceandcontrolpurposestypicallyconsider

oneconstraintatatime,ratherthanalltheconstraintsatthesametime.Theyusuallystartwith

aninitialcondition(e.g.,inthecaseofaightmanagementsystems,theinitialconditionincludes

theinitialposition,speed,andheadingoftheaircraft)andsomeinitialsolutionandadjustthe

valueofonesolutionparameteratatimeuntilasatisfactorysolutionisfound.

Fortunately,aguidancesystemdoesnotneedtocomputeitscontrollawsasfrequentlyasadigital

controller.Often,thiscomputationcanbedoneoff-line.Inthecaseofaightmanagementsystem,

forexample,itneedstocomputeandstoreaclimbspeedscheduleforuseduringtakeoff,an

optimumcruisetrajectoryforuseenroute,andadescenttrajectoryforlanding.Thiscomputation

canbedonebeforetakeoffandhenceisnottime-critical.Whilein-ight,thesystemstillneedsto

computesomecontrollawstomonitorandcontrolthetransitionsbetweendifferentightphases

(i.e.,fromclimbtocruiseandcruisetodescent)aswellasalgorithmsforestimatingandpredicting

timestowaypoints,andsoforth.Thesetime-criticalcomputationstendtobesimplerandmore

deterministicandhaveperiodsinorderofsecondsandminutes.Whenthepre-computedight

planneedstobeupdatedoranewonecomputedin-ight,thesystemhasminutestocompute

andcanacceptsuboptimalsolutionswhenthereisnotime.

Other Capabilities

Thecomplexityofahigher-levelcontrolsystemarisesformanyotherreasonsinadditionto

itscomplicatedcontrolalgorithms.Itofteninterfaceswiththeoperatorandothersystems.To

interactwiththeoperator,itupdatesdisplaysandreactstooperatorcommands.Byothersystems,

wemeanthoseoutsidethecontrolhierarchy.Anexampleisavoice,telemetry,ormultimedia

communication system thatsupports operatorinteractions. Other examplesare radar and

navigationdevices.Thecontrolsystemmayusetheinformationprovidedbythesedevicesand

partiallycontrolthesedevices.

Anavionicorightmanagementsystemhasthesecapabilities.Oneofitsfunctionsistoupdate

thedisplayofradar,ightpath,andair-datainformation.Likekeyboardmonitoring,thedisplay

updatesmustdonenolessfrequentlythanonceevery100millisecondstoachieveasatisfactory

performance.Similarly,itperiodicallyupdatesnavigationdataprovidedbyinertialandradio

navigation aids. An avionics system for a military aircraft also does tracking and ballistic


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Notescomputationsandcoordinatesradarandweaponcontrolsystems,anditdoesthemwithrepetition

periodsofafewtoafewhundredmilliseconds.Theworkloadduetothesefunctionsisdemanding

evenfortodaysfastprocessorsanddatalinks.

2.2.3 Real-time Command and ControlThecontrolleratthehighestlevelof,acontrolhierarchyisacommandandcontrolsystem.An

AirTrafcControl(ATC)systemisanexcellentexample.Figure2.5showsapossiblearchitecture.

TheATCsystemmonitorstheaircraftinitscoverageareaandtheenvironment(e.g.,weather

condition)andgeneratesandpresentstheinformationneededbytheoperators(i.e.,theairtrafc

controllers).OutputsfromtheATCsystemincludetheassignedarrivaltimestometeringxes

forindividualaircraft.Asstatedearlier,theseoutputsarereferenceinputstoon-boardight

managementsystems.Thus,theATCsystemindirectlycontrolstheembeddedcomponentsinlow

levelsofthecontrolhierarchy.Inaddition,theATCsystemprovidesvoiceandtelemetrylinksto

on-boardavionics.Thusitsupportsthecommunicationamongtheoperatorsatbothlevels(i.e.,

thepilotsandairtrafccontrollers).

TheATCsystemgathersinformationonthestateofeachaircraftviaoneormoreactiveradars.Suchradarinterrogateseachaircraftperiodically.

Figure 2.5: An Architecture of Air Trafc Control System

Digital

signalprocessors

Database oftrack recordsand tracks

Communication network

DP DP Surveillanceprocessor

Display processors

Displays

Communicationnetwork

DSP DSP DSP

Sensors

DB DB

Wheninterrogated,anaircraftrespondsbysendingtotheATCsystemitsstatevariables:

identier,position,altitude,heading,andsoon.(InFigure2.5,thesevariablesarereferred


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Real Time Systems


Notes tocollectivelyasatrackrecord,andthecurrenttrajectoryof theaircraftisa track.)TheATC

systemprocessesmessagesfromaircraftandstoresthestateinformationthusobtainedina

database.Thisinformationispickedupandprocessedbydisplayprocessors.Atthesametime,

asurveillancesystemcontinuouslyanalyzesthescenarioandalertstheoperatorswheneverit

detectsanypotentialhazard(e.g.,apossiblecollision).Again,theratesatwhichhumaninterfaces(e.g.,keyboardsanddisplays)operatemustbeatleast10Hz.Theotherresponsetimescanbe

considerablylarger.Forexample,theallowedresponsetimefromradarinputsisonetotwo

seconds,andtheperiodofweatherupdatesisintheorderof10seconds.

Fromthisexample,wecanseethatacommandandcontrolsystembearslittleresemblanceto

low-levelcontrollers.Incontrast toa low-levelcontrollerwhoseworkloadiseitherpurelyor

mostlyperiodic,acommandandcontrolsystemalsocomputesandcommunicatesinresponseto

sporadiceventsandoperatorscommands.Furthermore,itmayprocessimageandspeech,query

andupdatedatabases,simulatevariousscenarios,andthelike.Theresourceandprocessingtime

demandsofthesetaskscanbelargeandvaried.Fortunately,mostofthetimingrequirementsof

acommandandcontrolsystemarelessstringent.Whereasalow-levelcontrolsystemtypically

runsononecomputerorafewcomputersconnectedbyasmallnetworkordedicatedlinks,a

command and control system is often a large distributed system containing tens and hundredsofcomputersandmanydifferentkindsofnetworks.Inthisrespect,itresemblesinteractive,on-

linetransactionsystems(e.g.,astockpricequotationsystem)whicharealsosometimescalled

real-time systems.

2.3 Signal Processing

Mostsignalprocessingapplications have some kind of real-time requirements. We focus here

onthosewhoseresponsetimesmustbeunderafewmillisecondstoafewseconds.Examples

aredigitalltering,videoandvoicecompressing/decompression,andradarsignalprocessing.

Signalprocessingisanareaofsystemsengineering,electricalengineeringandappliedmathematics

thatdealswithoperationsonoranalysisofsignals,ineitherdiscreteorcontinuoustime.Signalsofinterestcanincludesound,images,time-varyingmeasurementvaluesandsensordata,for

examplebiologicaldatasuchaselectrocardiograms,controlsystemsignals,telecommunication

transmissionsignals,andmanyothers.Signalsareanalogordigitalelectricalrepresentationsof

time-varyingorspatial-varyingphysicalquantities.Inthecontextofsignalprocessing,arbitrary

binarydatastreamsandon-offsignallingarenotconsideredassignals,butonlyanaloganddigital

signalsthatarerepresentationsofanalogphysicalquantities.

2.3.1 Processing Bandwidth Demands

Typically,a real-timesignalprocessingapplicationcomputesineachsamplingperiodoneor

moreoutputs.Eachoutputx(k)isaweighted sum of ninputsy(i)s:

x(k) = a k i y i

i

n

( , ) ( )

=

1

Inthesimplestcase,theweights,a (k, i)s,areknownandxed.In essence,thiscomputation

transforms the given representationofanobject(e.g.,avoice,animageoraradarsignal)interms

oftheinputs,y(i)s,intoanotherrepresentationintermsoftheoutputs, x(k)s.Differentsetsof

weights,a(k,i)s,givedifferentkindsoftransforms.Thisexpressiontellsusthatthetime-required

toproduceanoutputisO(n).

Theprocessortimedemandofanapplicationalsodependsonthenumberofoutputsitisrequired

toproduceineachsamplingperiod.Atoneextreme,adigitallteringapplication(e.g.,alter

thatsuppressesnoiseandinterferencesinspeechandaudio)producesoneoutputeachsampling

period.ThesamplingratesofsuchapplicationsrangefromafewkHztotensofkHz.Then

ranges from tens to hundreds. Hence,suchanapplicationperforms104to107multiplications

andadditionspersecond.


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NotesSome other signalprocessingapplicationsaremorecomputationallyintensive.Thenumberofoutputsmayalsobeofordern,andthecomplexityofthecomputationisO(n2)ingeneral.Anexampleisimagecompression.Mostimagecompressionmethodshaveatransformstep.Thissteptransformsthespacerepresentationofeachimageintoatransformrepresentation(e.g.,a

hologram).To illustratethecomputationaldemandofa compressionprocess,let usconsideran m mpixel,30framespersecondvideo.Supposethatweweretocompresseachframebyrstcomputingitstransform.Thenumberofinputsisn =m2. The transformation of each frametakes m4multiplicationsandadditions.Ifmis100,thetransformationofthevideotakes3109multiplicationsandadditionspersecond!Onewaytoreducethecomputationaldemandattheexpenseofthecompressionratioistodivideeachimageintosmallersquaresandperformthetransformoneachsquare.ThisindeediswhatthevideocompressionstandardMPEG[IS094])does.Eachimageisdividedintosquaresof88pixels.Inthisway,thenumberofmultiplicationsandadditionsperformedinthetransformstageisreducedto64m2perframe(inthecaseofour

example,to1.92107).Today,thereisabroadspectrumofDigitalSignalProcessors(DSPs)designed specicallyfor signal processingapplications.ComputationallyintensivesignalprocessingapplicationsrunononeormoreDSPs.Inthisway,thecompressionprocesscankeeppacewiththerateatwhichvideoframesarecaptured.

2.3.2 Radar System

Asignalprocessingapplicationistypicallyapartofalargersystem.Asanexample,Figure2.6showsablockdiagramofa(passive)radarsignalprocessingandtrackingsystem.Thesystem

consistsofanInput/Output(I/O)subsystemthatsamplesanddigitizestheechosignalfromtheradarandplacesthesampledvaluesinasharedmemory.Anarrayofdigitalsignalprocessorsprocessesthesesampledvalues.Thedatathusproducedareanalyzedbyoneormoredataprocessors,whichnotonlyinterfacewiththedisplaysystem,butalsogeneratecommandstocontroltheradarandselectparameterstobeusedbysignalprocessorsinthenextcycleofdatacollection and analysis.

Radar Signal Processing

Tosearchforobjectsofinterestinitscoveragearea,theradarscanstheareabypointingitsantenna

inonedirectionatatime.Duringthetimetheantennadwellsinadirection,itrstsendsashortradiofrequencypulse.Itthencollectsandexaminestheechosignalreturningtotheantenna.

Theechosignalconsistssolelyofbackgroundnoiseifthetransmittedpulsedoesnothitanyobject.Ontheotherhand,ifthereisareectiveobject(e.g.,anairplaneorstormcloud)atadistancexmetersfromtheantenna,theechosignalreectedbytheobjectreturnstotheantenna

atapproximately2x/csecondsafterthetransmittedpulse,wherec=3108meterspersecondisthespeedoflight.

Figure 2.6: Radar Signal Processing and Tracking System

Sampled

digitized

data

Signalprocessors

DSP

2561024samples/bin

Trackrecords

Trackrecords

Control

status

Dataprocessor

Signal

processingparameters

Memory

Radar


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Real Time Systems


Notes Theechosignalcollectedatthistimeshouldbestrongerwhenthereisnoreectedsignal.Ifthe

objectismoving,thefrequencyofthereectedsignalisnolongerequaltothatofthetransmitted

pulse.Theamountoffrequencyshift(calledDopplershift)isproportionaltothevelocityofthe

object.Therefore,byexaminingthestrengthandfrequencyspectrumoftheechosignal,thesystem

can determine whetherthereareobjectsinthedirectionpointedatbytheantennaandifthere

areobjects,whattheirpositionsandvelocitiesare.

Specically,thesystemdividesthetimeduringwhichtheantennadwellstocollecttheechosignal

intosmalldisjointintervals,Eachtimeintervalcorrespondstoadistancerange,andthelengthof

the interval is equal to the range resolution divided by c.(Forexample,ifthedistanceresolution

is300meters,thentherangeintervalisonemicrosecondlong.)Thedigitalsampledvaluesof

the,echosignalcollectedduringeachrangeintervalareplacedinabuffer,calledabininFigure

2.6.Thesampledvaluesineachbinaretheinputsusedbyadigitalsignalprocessortoproduce

outputsoftheformgivenbyEq.(2.3).TheseoutputsrepresentadiscreteFouriertransformof

thecorrespondingsegmentoftheechosignal.Basedonthecharacteristicsofthetransform,the

signalprocessordecideswhetherthereisanobjectinthatdistancerange.Ifthereisanobject,it

generates a track record containingthepositionandvelocityoftheobjectandplacestherecord

in the shared memory.

ThetimerequiredforsignalprocessingisdominatedbythetimerequiredtoproducetheFourier

transforms,andthistimeisnearlydeterministic.ThetimecomplexityofFastFourierTransform

(FFT)isO(n log n),where nis thenumberofsampledvaluesineachrangebin.nistypically

intherangefrom128 toa few thousand. So, ittakes roughly103to105multiplicationsand

additionstogenerateaFouriertransform.Supposethattheantennadwellsineachdirectionfor

100millisecondsandtherangeoftheradarisdividedinto1000rangeintervals.Thenthesignal

processingsystemmustdo107to109multiplicationsadditionspersecond.Thisiswellwithin

thecapabilityoftodaysdigitalsignalprocessors.

However,the100-milliseconddwelltimeisaballparkgureformechanicalradarantennas.Thisisordersofmagnitudelargerthanthatforphasearrayradars,suchasthoseusedinmanymilitary

applications.Phasearrayradarcanswitchthedirectionoftheradarbeamelectronically,within

amillisecond,andmayhavemultiplebeamsscanningthecoverageareaandtrackingindividual

objects at the same time. Since the radar can collect data orders of magnitude faster than the rates

statedabove,thesignalprocessingthroughputdemandisalsoconsiderablyhigher.Thisdemand

ispushingtheenvelopeofdigitalsignalprocessingtechnology.

TheSCR-268(forSignalCorpsRadiono.268)wastheUSArmysrstradar

system.

Tracking

Strongnoiseandman-madeinterferences,includingelectroniccountermeasure(i.e.,jamming),canleadthesignalprocessinganddetectionprocesstowrongconclusionsaboutthepresenceof

objects.Atrackrecordonanon-existingobjectiscalledafalsereturn.Anapplicationthatexamines

allthetrackrecordsinordertosortoutfalsereturnsfromrealonesandupdatethetrajectories

of detected objects is called a tracker.Usingthejargonofthesubjectarea,wesaythatthetracker

assignseachmeasuredvalue(i.e.,thetupleofpositionandvelocitycontainedineachofthetrack

recordsgeneratedinascan)toatrajectory.Ifthetrajectoryisanexistingone,themeasuredvalue

assignedtoitgivesthecurrentpositionandvelocityoftheobjectmovingalongthetrajectory.If

thetrajectoryisnew,themeasuredvaluegivesthepositionandvelocityofapossiblenewobject.

IntheexampleinFigure2.6,thetrackerrunsononeormoredataprocessorswhichcommunicate

withthesignalprocessorsvia the shared memory.


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NotesGating

Typically,trackingiscarriedoutintwosteps:gatinganddataassociation.Gatingistheprocess

ofputtingeachmeasuredvalueintooneoftwocategoriesdependingonwhetheritcanorcannot

betentativelyassignedto oneormoreestablishedtrajectories. Thegatingprocesstentativelyassigns a measured value to an established trajectory if it is within a threshold distance G away

fromthepredictedcurrentpositionandvelocityoftheobjectmovingalongthetrajectory.(Below,

wecallthedistancebetweenthemeasuredandpredictedvaluesthedistanceoftheassignment.)

ThethresholdGiscalledthetrackgate.Itischosensothattheprobabilityofavalidmeasured

valuefallingintheregionboundedbyasphereofradiusGcentredonapredictedvalueisa

desired constant.

Figure2.7illustratesthisprocess.Atthestart,thetrackercomputesthepredictedposition(and

velocity)oftheobjectoneachestablishedtrajectory.Inthisexample,therearetwoestablished

trajectories;L1 and L2Wealsocallthepredictedpositionsoftheobjectsonthesetracks L1 and

L2. The X1,X2 and X3 are the measured values given by three track records. The X1 is assigned

to L1 because it is within distance G from L1. The X3 is assigned to both L1 and L2 for the same

reason.Ontheotherhand,X2isnotassignedtoanyofthetrajectories.Itrepresentseitherafalse

returnoranewobject.Sinceitisnotpossibletodistinguishbetweenthesetwocases,thetracker

hypothesizesthatX2isthepositionofanewobject.Subsequentradardatawillallowthetracker

toeithervalidateor invalidatethishypothesis.Inthe lattercase,the trackerwilldiscardthis

trajectory from further consideration.

Figure 2.7: Gating Process

Data Association

Thetrackingprocesscompletesif,aftergating,everymeasuredvalueisassignedtoatmostone

trajectory and every trajectory is assigned at most one measured value. This is likely to be case

when(1)theradarsignalisstrongandinterferenceislow(andhencefalsereturnsarefew)and

(2)thedensityofobjectsislow.Underadverseconditions,theassignmentproducedbygating

maybeambiguous,thatis,somemeasuredvalueisassignedtomorethanonetrajectoryora

trajectoryisassignedmorethanonemeasuredvalue.Thedataassociationstepisthencarried

outtocompletetheassignmentsandresolveambiguities.

There are many data association algorithms. One of the most intuitive is the nearest neighbour

algorithm.Thisalgorithmworksasfollows:

1. Examinethetentativeassignmentsproducedbythegatingstep.

(a) Foreachtrajectorythatistentativelyassignedasingleuniquemeasuredvalue,assign

themeasuredvaluetothetrajectory.Discardfromfurtherexaminationthetrajectory

andthemeasuredvalue,togetherwithalltentativeassignmentsinvolvingthem.

(b) Foreachmeasuredvaluethatistentativelyassignedtoasingletrajectory,discardthe

tentative assignments of those measured values that are tentatively assigned to this

trajectory if the values are also assigned to some other trajectories.

2. Sort the remaining tentative assignments in order of non-decreasing distance.


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Real Time Systems


Notes 3. Assign themeasuredvaluegivenbythersttentativeassignmentin thelist tothe

correspondingtrajectoryanddiscardthemeasuredvalueandtrajectory.

4. Repeatstep(3)untilthelistoftentativeassignmentsisempty.

IntheexampleinFigure2.7,thetentativeassignmentproducedbythegatingstepisambiguous.Step(1a)doesnoteliminateanytentativeassignment.However,step(1b)ndsthatX1 is assigned

to only L1,whileX3 is assigned to both L1 and L2.Hence,theassignmentofX3 to L1 is discarded

fromfurtherconsideration.Afterstep(1),therestillaretwo,tentativeassignments,X1 to L1 and

X3 to L2.Step(2)leavestheminthisorder,andthesubsequentstepsmaketheseassignments.

The X2initiatesanewtrajectory.Ifduringsubsequentscans,nomeasuredvaluesareassigned

tothenewtrajectory,itwillbediscardedfromfurtherconsideration.

Thenearestneighbouralgorithmattemptstominimizeasimplelocalobjectivefunction:the

distance(betweenthemeasuredandpredictedvalues)ofeachassignment.Dataassociation

algorithms ofhigher time complexityare designed tooptimizesomeglobal, andtherefore

morecomplicated,objectivefunctions,forexample,thesumofdistancesofallassignments

andprobabilityoferrors.Themostcomplexinbothtimeandspaceistheclassofmultiple

hypothesistrackingalgorithms.Oftenitisimpossibletoeliminatesomeassignmentsfromfurther

considerationbylookingatthemeasuredvaluesproducedinonescan.(Anexampleiswhenthe

distancesbetweenmeasuredvaluestotwoormorepredictedvaluesareessentiallyequal.)While

asingle-hypothesistrackingalgorithm(e.g.,thenearestneighbouralgorithm)mustchooseone

assignmentfromequallygoodassignments,amultiple-hypothesistrackingalgorithmkeepsall

ofthem.Inotherwords,atrajectorymaybetemporallybranchedintomultipletrajectories,each

endingatoneofmanyhypothesizedcurrentpositions.Thetrackerthenusesthedataprovided

infuturescanstoeliminatesomeofthebranches.Theuseofthiskindofalgorithmsisconned

towherethetrackedobjectsaredenseandthenumberoffalsereturnsarelarge(e.g.,fortracking

militarytargetsinthepresenceofdecoysandjamming).

Complexity and Timing Requirements

Incontrasttosignalprocessing,theamountsofprocessortimeandmemoryspacerequiredby

thetrackeraredatadependentandcanvarywidely.Whenthereare n established trajectories

and mmeasuredvalues,thetimecomplexityofgatingisO(nm log m).(Thiscanbedonebyrst

sorting the mmeasuredvaluesaccordingtotheirdistancesfromthepredictedvalueforeachof

theestablishedtrajectoriesandthencomparingthedistanceswiththetrackgateG.)Intheworst

case,allm measured values are tentatively assigned to all ntrajectoriesinthegatingstep.The

nearest neighbour algorithm must sort all nmtentativeassignmentsandhencehastimecomplexity

O(nm log nm).Theamountsoftimeandspacerequiredbymultiple-hypothesistrackinggrow

exponentiallywiththemaximumnumberofhypotheses,theexponentbeingthenumberofscans

requiredtoeliminateeachfalsehypothesis.Withoutmodernfastprocessorsandlargememory,

multiplehypothesistrackingwouldnotbefeasible.

Figure2.6showsthattheoperationoftheradariscontrolledbya controllerthatexecutesonthedataprocessor.Inparticular,thecontrollermayalterthesearchstrategyorchangetheradar

operationmode(sayfromsearchingtotrackinganobject)dependingontheresultsfoundby

thetracker.Similarly,thecontrollermayalterthesignalprocessingparameters(e.g.,detection

thresholdandtransformtype)inordertobemoreeffectiveinrejectinginterferencesand

differentiatingobjects.Theresponsivenessanditerationrateofthisfeedbackprocessincreaseas

thetotalresponsetimeofsignalprocessingandtrackingdecreases.Forthisreason,thedevelopers

oftheseapplicationsareprimarilyconcernedwiththeirthroughputsandresponsetimes.

Createastructureusingtheradarsysteminacollegecampus.


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Notes2.4 Other Real-time Applications

Thecharacteristicsandrequirementsoftwomostcommonreal-timeapplications.Theyarereal-

timedatabasesandmultimediaapplications.

Table 2.1: Requirements of Typical Real-Time Databases

Applications Size Ave. Max Abs. Cons. Rel. Cons. Permanence

Airtrafccontrol 20,000 0.50ms 5.00ms 3.00sec. 6.00sec. 12 hours

Aircraft mission 3,000 0.05ms 1.00ms 0.05sec. 0.20sec. 4 hours

Spacecraftcontrol 5,000 0.05ms 1.00ms 0.20sec. 1.00sec. 25 years

Processcontrol 0.80ms 5.00sec 1.00sec. 2.00sec 24 hours

2.4.1 Real-time Databases

Thetermreal-timedatabasesystemsreferstoadiversespectrumofinformationsystems,rangingfromstockpricequotationsystems,totrackrecordsdatabases,toreal-timelesystems.Table2.1

listsseveralexamples.Whatdistinguishesthesedatabasesfromnonreal-timedatabasesisthe

perishablenatureofthedatamaintainedbythem.

Specically,areal-timedatabasecontainsdataobjects,called image objectsthatrepresentreal-

worldobjects.Theattributesofanimageobjectarethoseoftherepresentedreal-worldobject.

Forexample,anairtrafccontroldatabasecontainsimageobjectsthatrepresentaircraftinthe

coveragearea.Theattributesofsuchanimageobjectincludethepositionandheadingof the

aircraft.Thevaluesoftheseattributesareupdatedperiodicallybasedonthemeasuredvaluesof

theactualpositionandheadingprovidedbytheradarsystem.Withoutthisupdate,thestored

positionandheadingwilldeviatemoreandmorefromtheactualpositionandheading.Inthis

sense,thequalityofstoreddatadegrades.Thisiswhywesaythatreal-timedataareperishable.

Incontrast,anunderlyingassumptionofnonreal-timedatabases(e.g.,apayrolldatabase)isthatintheabsenceofupdatesthedatacontainedinthemremaingood(i.e.,thedatabaseremainsin

someconsistentstatesatisfyingallthedataintegrityconstraintsofthedatabase).

Absolute Temporal Consistency

Thetemporalqualityofreal-timedataisoftenquantiedbyparameterssuchasageandtemporal

dispersion.Theageofadataobjectmeasureshowup-to-datetheinformationprovidedbythe

objectis.Therearemanyformaldenitionsofage.Intuitively,theage of an image object at any time

isthelengthoftimesincetheinstantofthelastupdate,thatis,whenitsvalueismadeequalto

thatofthereal-worldobjectitrepresents.Theageofadataobjectwhosevalueiscomputedfrom

the values of other objects is equal to the oldest of the ages of those objects.

Asetofdataobjectsissaidtobeabsolutely(temporally)consistentifthemaximumageofthe

objectsinthesetisnogreaterthanacertainthreshold.ThecolumnlabelledAbs.Cons.inTable

2.1liststhetypicalthresholdvaluesthatdeneabsoluteconsistencyfordifferentapplications.As

anexample,aircraftmissionlistedinthetablereferstothekindofdatabaseusedtosupport

combatmissionsofmilitaryaircraft.Aghterjetandthetargetsittracksmoveatsupersonic

speeds.Hencetheinformationonwheretheyaremustbelessthan50millisecondsold.Onthe

otherhand,anairtrafccontrolsystemmonitorscommercialaircraftatsubsonicspeeds;thisis

whytheabsolutetemporalconsistencythresholdforairtrafccontrolismuchlarger.

Relative Temporal Consistency

A set of data objects is said to be relatively consistentifthemaximumdifferenceinagesoftheobjects

inthesetisnogreaterthantherelativeconsistencythresholdusedbytheapplication.Thecolumn

labelledRel.Cons.inTable2.1givestypicalvaluesofthisthreshold.Forsomeapplications


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Notes theabsoluteageofdatamaynotbeasimportantasthedifferencesintheirages.Anexampleisa

planningsystemthatcorrelatestrafcdensitiesalongahighwaywiththeowratesofvehicles

enteringandexitingthehighway.Thesystemdoesnotrequirethemostup-to-dateowratesat

DCAP608_real Time System

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