State Flow Tutorial

8/10/2019 State Flow Tutorial

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StateFlow

HandsOn Tutorial

HS/PDEEC20100304

Jos Pinto [email protected]


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Session Outline

Simulink andStateflow

NumericalSimulationofODEs

InitialValueProblem(Handson)

ODEs withresets(Handson)

FiniteStateMachines

FSMs inStateflow (Handson)

DiscreteEventSystems

DESs inStateflow (Handson) HybridAutomata

HybridSystemsinStateflow (Handson)


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Simulink and Stateflow

1.


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Simulink

Canbeusedtomodelandsimulatedynamical

systemsinacomprehensiveandgraphicalway

Modelsaredescribedasblockdiagrams(boxeswith

inputs/outputs)


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Simulink (2)

Modelsarecomposedhierarchicallyallowing:

Modelingofcomplexsystemsinamodularandorganized

way

Differentdetailperspectivesoverthesamemodelat

designandsimulationtime


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Simulink and Stateflow

Simulink includes several builtin

block types (Model Library)

Additionally,extensions tothislibrary can be created by users

and companies (toolboxes)

Stateflow is one such toolbox

Stateflow canbeusedtomodel

thebehaviour ofFSMs


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Numerical Simulation of ODEs

2.


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The Initial Value Problem

Example:

?)(

2)0(

1

tx

x

xx

=

+=&

[Hespanha, J. P. 05]


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ODENumerical SimulationEuler method



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ODESimulationRangeKutta method



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ODESimulation Variablestep methods



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Solving the IVPin Simulink

Simulink has an inbuilt ODEsolver(Integrator)

Different integration methods (including variable step)

Example:

2)0(1 =+= xxx&

(Integrator toolbox accepts initial value)


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ODEs with resets

x1: speed

x2: accelerationg: gravity force

c: ball elasticity constant


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Integrator Block in Simulink

Integratorblockacceptsaresetport

Wheneveraresetistriggered,itsnewvaluewillbe

takenfromtheinitialvalue(x0)port

Stateportholdspreviousvalueofx

Statecan

be

used

to

determine

ifthe

integrator

needstobereset(x)


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ODEs with resetsin Simulink


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ODEs with resetsin Simulink (3)

Simulink ODEsolverdetects zerocrossing behaviour

When aresetis detected,the solvergoes back in

time todeterminewhere the resetoccurred

(zero-crossing detection disabled)

(with zero-crossing detection enabled)


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Finite State Machines (FSMs)

Modelofsystemswhosebehaviorcanbemodeled

asasetofstatesandtransitionsbetweenstates.This

systemsaresometimescalledreactivesystems.

Finitenumberofstates

SystemsmodeledbyFSMs:

Patternrecognition

ATMs

Computationalprocesses

Humanintelligence?

t t

t


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Mathematical Model of FSMs

AFSMis aquintuple(,S,s0,,F),where:

is an inputalphabet (finite set of symbols)

S

is afinite,nonempty,set of states

S0is the initial state,where S0 S

is astatetransition function: :SxS

F

is afinite,(possibly empty)set of finalstates

= []

S = [green, yellow, red]

S0 = green

= [green/ yellow, yellow/ red, red/ green]F= [red]


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Simulation of FSMsStateFlow

Simulink block(toolbox)formodelingFiniteState

Machines

Stateflow chartsreceiveinputsfromSimulink and

provideoutputs(signals,events)

Simulationadvanceswithtime

Hybridstatemachinemodelthatcombinesthe

semanticsofMealyandMoorechartswiththe

extendedStateflow chartsemantics.


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StateFlow States


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StateFlow Transitions


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StateFlow Initial State


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StateFlow Transition Conditions


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StateFlow State Actions

entry: Quando entra no estado, during: enquanto est no estado,exit: quando sai do estado


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StateFlow Transition Actions


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StateFlow FinalStates


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Stateflow integration with Simulink

User definesvariables tobe used inside Stateflow

chart

Variable types areimportant!

Variables may be:

Inputsfrom Simulink

OutputstoSimulink

Local,Constant,

Todefinevariables useModel Explorer(CtrlR)


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Simulink/Stateflow Handson

Create astateflow chart that calculates the factorial

of anumber (uint32),given asinput


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Stateflow Debugger

Usestep toexecutethe FSMstepbystep

Usebrowse data tomonitorvariable changes


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Discrete Event Systems

4.


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Discrete Event Systems

Discreteandqualitativechanges

Statetransitionscausedbyoccurrenceof

asynchronousdiscreteevents

Parallelexecutionofmultiplesystems

Synchronizationbyeventpassing


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DESExample

S1

S2

S1

S3

S2

evA?

evA?

evB? x10

/evB

!

Synchronization through events

Parallel execution

receive?/broadcast!


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Machine composition in Stateflow

Grouped:Inner states arevisible

Subcharted:Creates asubchart

Default behavior:subchart is executed


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Parallel composition in Stateflow


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[even(x)]and[~even(x)]arenowvalidconditions

{actions}arecalledconditionactionsandareevaluatedevenwhendestination(state)isnotvalid

Composition:Graphical functions


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Event passing in Stateflow

UseModel Explorertoadd Event datatypes

Events used both asconditions and actions


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DESin Stateflow Handson

Createastateflow chartthatreceives2inputs

(uint32)andsumsthenumberof1digitsintheir

binaryrepresentation Useeventpassingtocountallthe1digits


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Hybrid Automata

4.


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Hybrid Automata



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Bouncing Ball rerevisited

2=n

q1

}:00,{),,(

}00,{),,(

}:,:{),,(

}{

2221121

121121

221121

1

xcxxxqxxq

qxxqxxq

gxxxqxxqf

qQ

=


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Simulation of Hybrid Automata



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Bouncing Ball in StateFlow


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Bouncing Ball in StateflowSIMPLER

Go toFile>Chart properties

Select Continuous update method


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In Model Exploreryou can now localvariables of

type double ascontinuous variables (update

method)


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Foreach continuous local

variable x

stateflow automatically

definesx_dot

which is derivative of x


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Exercise 1:Thermostat Hybrid System

1. Define the HS formally

2. Simulate Hybrid System


k b d


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Exercise 2:Tank Hybrid System


E i 3 Billi d H b id S


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Exercise 3:Billiard Hybrid System

Ballinsidea10x10box

Ballstartsatunknownposition(x,y)andwith

unknownvelocityvector(vx,vy) Ballbouncesinanyofthe4walls

Constantenergydissipationfactorbetween0and110


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END

References:

http://www.ece.ucsb.edu/~hespanha/ece229/ http://www.mathworks.com/access/helpdesk/help/pdf_doc/stateflow/sf_ug.pdf

Documents

State Flow Tutorial