Trabalho 2 - Identificação de Sistemas

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2 - Identifica��o de Sistemas/aula04_IdentSist_01_sfun.mexw64
2 - Identifica��o de Sistemas/data_A_01.mat
2 - Identifica��o de Sistemas/data_A_02.mat
2 - Identifica��o de Sistemas/data_A_03.mat
2 - Identifica��o de Sistemas/data_B_01.mat
2 - Identifica��o de Sistemas/data_B_02.mat
2 - Identifica��o de Sistemas/data_B_03.mat
2 - Identifica��o de Sistemas/data_B_04.mat
2 - Identifica��o de Sistemas/data_C_01.mat
2 - Identifica��o de Sistemas/data_C_02.mat
2 - Identifica��o de Sistemas/data_C_03.mat
2 - Identifica��o de Sistemas/IdentificacaoSistemas.m
%% CARREGAR DADOS
load('data_A_01');
load('data_A_02');
load('data_A_03');
load('data_B_01');
load('data_B_02');
load('data_B_04');
load('data_C_01');
load('data_C_02');
load('data_C_03');
figure(1)
plot(data_A_01(:,1),'k');
hold on
plot(data_A_01(:,2),'r');
figure(2)
plot(data_B_01(:,1),'k');
hold on
plot(data_B_01(:,2),'r');
figure(3)
plot(data_C_01(:,1),'k');
hold on
plot(data_C_01(:,2),'r');
%% SISTEMA A
yA01 = data_A_01(:,2);
uA01 = data_A_01(:,1);
yA02 = data_A_02(:,2);
uA02 = data_A_02(:,1);
yA03 = data_A_03(:,2);
uA03 = data_A_03(:,1);
dadosA01 = [yA01(1:end-1) uA01(1:end-1)];
saidaA01 = [yA01(2:end)];
dadosA02 = [yA02(1:end-1) uA02(1:end-1)];
saidaA02 = [yA02(2:end)];
dadosA03 = [yA03(1:end-1) uA03(1:end-1)];
saidaA03 = [yA03(2:end)];
matrizA01 = inv((dadosA01')*(dadosA01))*(dadosA01')*saidaA01
matrizA02 = inv((dadosA02')*(dadosA02))*(dadosA02')*saidaA02
matrizA03 = inv((dadosA03')*(dadosA03))*(dadosA03')*saidaA03
z = 0;
for k = 1 : length(uA02)
 z(k+1) = matrizA02(1)*z(k) + matrizA02(2)*uA02(k) ;
end
stairs(z)
hold all
stairs(yA02)
numDA = [matrizA01(2)]
denDA = [1 -matrizA01(1)]
TA = 0.01;
GdA = tf(numDA, denDA, TA)
CA = d2c(GdA)
[nCA,dCA] = tfdata(CA,'v')
% rltool(CA)
numcontA = 25*[0.17 1]
dencontA = [1 0]
%% SISTEMA B
yB01 = data_B_01(:,2);
uB01 = data_B_01(:,1);
yB02 = data_B_02(:,2);
uB02 = data_B_02(:,1);
yB04 = data_B_04(:,2);
uB04 = data_B_04(:,1);
dadosB01 = [yB01(2:end-1) yB01(1:end-2) uB01(1:end-2)];
saidaB01 = [yB01(3:end)];
dadosB02 = [yB02(2:end-1) yB02(1:end-2) uB02(1:end-2)];
saidaB02 = [yB02(3:end)];
dadosB04 = [yB04(2:end-1) yB04(1:end-2) uB04(1:end-2)];
saidaB04 = [yB04(3:end)];
matrizB01 = inv((dadosB01')*(dadosB01))*(dadosB01')*saidaB01
matrizB02 = inv((dadosB02')*(dadosB02))*(dadosB02')*saidaB02
matrizB04 = inv((dadosB04')*(dadosB04))*(dadosB04')*saidaB04
z = [0 0];
for k = 1 : length(uB02)
 z(k+2) = matrizB04(1)*z(k+1) + matrizB04(2)*z(k) + matrizB04(3)*uB02(k) ;
end
stairs(z)
hold all
stairs(yB02)
numB = [matrizB04(3)]
denB = [1 -matrizB04(1) -matrizB04(2)]
TB = 0.01;
GdB = tf(numB, denB, TB)
CB = d2c(GdB)
[nCB,dCB] = tfdata(CB,'v')
% rltool(CB)
numcontB = 2.2*[0.077^2 0.13 1]
dencontB = [0.056 1 0]
%% SISTEMA C
yC01 = data_C_01(:,2);
uC01 = data_C_01(:,1);
yC02 = data_C_02(:,2);
uC02 = data_C_02(:,1);
yC03 = data_C_03(:,2);
uC03 = data_C_03(:,1);
dadosC01 = [yC01(3:end-1) yC01(2:end-2) yC01(1:end-3) uC01(1:end-3)];
saidaC01 = [yC01(4:end)];
dadosC02 = [yC02(3:end-1) yC02(2:end-2) yC02(1:end-3) uC02(1:end-3)];
saidaC02 = [yC02(4:end)];
dadosC03 = [yC03(3:end-1) yC03(2:end-2) yC03(1:end-3) uC03(1:end-3)];
saidaC03 = [yC03(4:end)];
matrizC01 = inv((dadosC01')*(dadosC01))*(dadosC01')*saidaC01
matrizC02 = inv((dadosC02')*(dadosC02))*(dadosC02')*saidaC02
matrizC03 = inv((dadosC03')*(dadosC03))*(dadosC03')*saidaC03
z = [0 0 0] ;
for k = 1 : length(uC02)
 z(k+3) = matrizC03(1)*z(k+2) + matrizC03(2)*z(k+1) + matrizC03(3)*z(k) + matrizC03(4)*uC02(k) ;
end
stairs(z)
hold all
stairs(yC02)
numC = [matrizC03(4)]
denC = [1 -matrizC03(1) -matrizC03(2) -matrizC03(3)]
TC = 0.01;
GdC = tf(numC, denC, TC)
CC = d2c(GdC)
[nCC,dCC] = tfdata(CC,'v')
% rltool(CC)
numcontC = 0.09*[0.12^2 0.12 1]
dencontC = [0.11^2 0.11 1 0]
2 - Identifica��o de Sistemas/IdentificacaoSistemas.mdl.r2011b
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2 - Identifica��o de Sistemas/Identifica��o - Parte 1.pdf
Engenharia de Controle e Automac¸a˜o - PUCRS
Identificac¸a˜o de Sistemas
1 Definic¸a˜o do Problema
O primeiro passo na maioria dos projetos de sistemas de controle e´ a aquisic¸a˜o
do modelo da planta (processo) ser controlada.
Este processo se chama “Identificac¸a˜o de Sistemas” e sera´ abordado no
presente laborato´rio. O objetivo e´ encontrar os coeficientes θi, i = 1, 2, 3...,
de uma func¸a˜o de transfereˆncia discreta a partir dos dados de entrada e sa´ıda
da planta. Por exemplo, suponha que seja necessa´rio identificar uma planta
de segunda ordem, enta˜o devemos encontrar θi para i = 1, 2, 3, 4 e 5:
G(z) =
Y (z)
U(z)
=
θ3z
2 + θ4z + θ5
z2 − θ1z − θ2
Depois podemos encontrar o equivalente cont´ınuo do sistema acima e
projetar um controlador usando os me´todos cla´ssicos aprendidos na cadeira
de projetos de sistemas de controle.
2 Mı´nimos Quadrados
Multiplicando a equac¸a˜o (1) pelos seus denominadores e lembrando que z−1
representa um atraso de transporte, obtemos a seguinte expressa˜o:
y(k)− θ1y(k − 1)− θ2y(k − 2) = θ3u(k) + θ4u(k − 1) + θ5u(k − 2)
Resolvendo para a sa´ıda do sistema:
y(k) = θ1y(k − 1) + θ2y(k − 2) + θ3u(k) + θ4u(k − 1) + θ5u(k − 2)
Que pode ser descrita na seguinte forma matricial:
y(k) = [y(k − 1) y(k − 2) u(k) u(k − 1) u(k − 2)]


θ1
θ2
θ1
θ4
θ5


(1)
Prof. Aure´lio Salton To´picos Especiais II - ECA
Engenharia de Controle e Automac¸a˜o - PUCRS
Pore´m, se possu´ımos uma se´rie de N medic¸o˜es ao inve´s de apenas uma,
a equac¸a˜o deve ser representada na seguinte forma matricial:


y(2)
y(3)
y(4)
...
y(N)


=


y(1) y(0) u(2) u(1) u(0)
y(2) y(1) u(3) u(2) u(1)
y(3) y(2) u(4) u(3) u(2)
...
...
...
...
...
y(N − 1) y(N − 2) u(N) u(N − 1) u(N − 2)




θ1
θ2
θ1
θ4
θ5


(2)
Ou seja,
y = Ψθ
Para encontrar os valores desejados basta isolar θ na equac¸a˜o:
θ = (ΨTΨ)−1ΨTy
sendo que o termo •T representa a transposta.
3 Tarefas
Baixe os arquivos referentes ao laborato´rio. Sa˜o treˆs arquivos contendo cada
um uma func¸a˜o de transfereˆncia.
• Atrave´s dos dados de entrada e sa´ıda dos processos, estime um modelo
para cada um dos sistemas.
• Encontre um sistema cont´ınuo equivalente e compare com a sa´ıda real.
• Simule cada um dos sistemas dentro do blocoMatlab Function (na bibli-
oteca User-Defined Functions no Simulink). Compare a sua simulac¸a˜o
com a sa´ıda real do sistema.
• Apresente o trabalho para o professor ate´ a data estipulada em aula.
Boa sorte.
Refereˆncias
[1] Aguirre, L.A. Introduc¸a˜o A` Identificac¸a˜o de Sistemas, 2a Edic¸a˜o. Edi-
tora UFMG, 2007.
[2] Ljung, L. System Identification: Theory for the User (2nd Edition)
Wiley Encyclopedia of Electrical and Electronics Engineering, 1987.
Prof. Aure´lio Salton To´picos Especiais II - ECA
2 - Identifica��o de Sistemas/Identifica��o - Parte 2.pdf
Engenharia de Controle e Automac¸a˜o - PUCRS
Controle
1 Definic¸a˜o do Problema
Uma vez que possu´ımos o modelo dos sistemas que queremos controlar, po-
demos fazer um controle mais elaborado como, por exemplo, LGR, alocac¸a˜o
de po´los, controle por modelo de refereˆncia, etc. Este trabalho se resume em
projetar um controlador para os sistemas que foram estimados no laborato´rio
passado. Para tanto utilize a func¸a˜o rltool no Matlab.
2 Tarefas
• Projete um controlador para o sistema de 1a ordem tal que ele estabilize
em menos de 0.1 segundos e sua entrada na˜o ultrapasse a marca de 4
unidades; (3.0 pontos)
• Projete um controlador para o sistema de 2a ordem tal que ele estabilize
sem sobre sinal em menos de um segundo;(4.0 pontos)
• Projete um controlador para o sistema de 3a ordem tal que ele apresente
erro zero em regime sem sobre-sinal;(4.0 pontos)
• Apresente o trabalho para o professor ate´ a data estipulada em aula.
Boa sorte.
Refereˆncias
[1] Engenharia de Sistemas de Controle - 5a Edic¸a˜o Norman S. Nise, Editora
LTC (Grupo GEN), 2009.
Prof. Aure´lio Salton To´picos Especiais II - ECA
2 - Identifica��o de Sistemas/SimulinkIdentificacaoSistemas.mdl
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 $PropName		 "ActiveConfigurationSet"
 $ObjectID		 7
 }
 Object {
 $PropName		 "DataTransfer"
 $ObjectID		 19
 $ClassName		 "Simulink.GlobalDataTransfer"
 DefaultTransitionBetweenSyncTasks "Ensure deterministic transfer (maximum delay)"
 DefaultTransitionBetweenAsyncTasks "Ensure data integrity only"
 DefaultTransitionBetweenContTasks "Ensure deterministic transfer (minimum delay)"
 DefaultExtrapolationMethodBetweenContTasks "None"
 AutoInsertRateTranBlk [0]
 }
 ExplicitPartitioning	 off
 BlockDefaults {
 ForegroundColor	 "black"
 BackgroundColor	 "white"
 DropShadow		 off
 NamePlacement	 "normal"
 FontName		 "Helvetica"
 FontSize		 10
 FontWeight		 "normal"
 FontAngle		 "normal"
 ShowName		 on
 BlockRotation	 0
 BlockMirror		 off
 }
 AnnotationDefaults {
 HorizontalAlignment	 "center"
 VerticalAlignment	 "middle"
 ForegroundColor	 "black"
 BackgroundColor	 "white"
 DropShadow		 off
 FontName		 "Helvetica"
 FontSize		 10
 FontWeight		 "normal"
 FontAngle		 "normal"
 UseDisplayTextAsClickCallback off
 }
 LineDefaults {
 FontName		 "Helvetica"
 FontSize		 9
 FontWeight		 "normal"
 FontAngle		 "normal"
 }
 MaskDefaults {
 SelfModifiable	 "off"
 IconFrame		 "on"
 IconOpaque		 "on"
 RunInitForIconRedraw "off"
 IconRotate		 "none"
 PortRotate		 "default"
 IconUnits		 "autoscale"
 }
 MaskParameterDefaults {
 Evaluate		 "on"
 Tunable		 "on"
 NeverSave		 "off"
 Internal		 "off"
 ReadOnly		 "off"
 Enabled		 "on"
 Visible		 "on"
 ToolTip		 "on"
 }
 BlockParameterDefaults {
 Block {
 BlockType		 Inport
 Port		 "1"
 OutputFunctionCall off
 OutMin		 "[]"
 OutMax		 "[]"
 OutDataTypeStr	 "Inherit: auto"
 LockScale		 off
 BusOutputAsStruct	 off
 PortDimensions	 "-1"
 VarSizeSig	 "Inherit"
 SampleTime	 "-1"
 SignalType	 "auto"
 SamplingMode	 "auto"
 LatchByDelayingOutsideSignal off
 LatchInputForFeedbackSignals off
 Interpolate	 on
 }
 Block {
 BlockType		 Mux
 Inputs		 "4"
 DisplayOption	 "none"
 UseBusObject	 off
 BusObject		 "BusObject"
 NonVirtualBus	 off
 }
 Block {
 BlockType		 Outport
 Port		 "1"
 OutMin		 "[]"
 OutMax		 "[]"
 OutDataTypeStr	 "Inherit: auto"
 LockScale		 off
 BusOutputAsStruct	 off
 PortDimensions	 "-1"
 VarSizeSig	 "Inherit"
 SampleTime	 "-1"
 SignalType	 "auto"
 SamplingMode	 "auto"
 SourceOfInitialOutputValue "Dialog"
 OutputWhenDisabled "held"
 InitialOutput	 "[]"
 }
 Block {
 BlockType		 Scope
 ModelBased	 off
 TickLabels	 "OneTimeTick"
 ZoomMode		 "on"
 Grid		 "on"
 TimeRange		 "auto"
 YMin		 "-5"
 YMax		 "5"
 SaveToWorkspace	 off
SaveName		 "ScopeData"
 DataFormat	 "Array"
 LimitDataPoints	 on
 MaxDataPoints	 "5000"
 Decimation	 "1"
 SampleInput	 off
 SampleTime	 "-1"
 }
 Block {
 BlockType		 Step
 Time		 "1"
 Before		 "0"
 After		 "1"
 SampleTime	 "-1"
 VectorParams1D	 on
 ZeroCross		 on
 }
 Block {
 BlockType		 SubSystem
 ShowPortLabels	 "FromPortIcon"
 Permissions	 "ReadWrite"
 PermitHierarchicalResolution "All"
 TreatAsAtomicUnit	 off
 MinAlgLoopOccurrences off
 PropExecContextOutsideSubsystem off
 CheckFcnCallInpInsideContextMsg off
 SystemSampleTime	 "-1"
 RTWSystemCode	 "Auto"
 RTWFcnNameOpts	 "Auto"
 RTWFileNameOpts	 "Auto"
 FunctionInterfaceSpec "void_void"
 FunctionWithSeparateData off
 RTWMemSecFuncInitTerm "Inherit from model"
 RTWMemSecFuncExecute "Inherit from model"
 RTWMemSecDataConstants "Inherit from model"
 RTWMemSecDataInternal "Inherit from model"
 RTWMemSecDataParameters "Inherit from model"
 SimViewingDevice	 off
 DataTypeOverride	 "UseLocalSettings"
 DataTypeOverrideAppliesTo	"AllNumericTypes"
 MinMaxOverflowLogging "UseLocalSettings"
 Opaque		 off
 MaskHideContents	 off
 SFBlockType	 "NONE"
 Variant		 off
 GeneratePreprocessorConditionals off
 ContentPreviewEnabled off
 }
 Block {
 BlockType		 Sum
 IconShape		 "rectangular"
 Inputs		 "++"
 CollapseMode	 "All dimensions"
 CollapseDim	 "1"
 InputSameDT	 on
 AccumDataTypeStr	 "Inherit: Inherit via internal rule"
 OutMin		 "[]"
 OutMax		 "[]"
 OutDataTypeStr	 "Inherit: Same as first input"
 LockScale		 off
 RndMeth		 "Floor"
 SaturateOnIntegerOverflow	on
 SampleTime	 "-1"
 }
 Block {
 BlockType		 TransferFcn
 Numerator		 "[1]"
 Denominator	 "[1 2 1]"
 AbsoluteTolerance	 "auto"
 ContinuousStateAttributes	"''"
 Realization	 "auto"
 }
 }
 System {
 Name		 "IdentificacaoSistemas_Parte2"
 Location		 [-8, -8, 1928, 1048]
 Open		 on
 ModelBrowserVisibility off
 ModelBrowserWidth	 200
 ScreenColor		 "white"
 PaperOrientation	 "landscape"
 PaperPositionMode	 "auto"
 PaperType		 "A4"
 PaperUnits		 "centimeters"
 TiledPaperMargins	 [0.500000, 0.500000, 0.500000, 0.500000]
 TiledPageScale	 1
 ShowPageBoundaries	 off
 ZoomFactor		 "80"
 ReportName		 "simulink-default.rpt"
 SIDHighWatermark	 "100"
 Block {
 BlockType		 SubSystem
 Name		 "1a ordem"
 SID		 "1"
 Ports		 [1, 1]
 Position		 [270, 161, 330, 189]
 ZOrder		 -1
 BackgroundColor	 "orange"
 RequestExecContextInheritance off
 Object {
	$PropName		"MaskObject"
	$ObjectID		20
	$ClassName		"Simulink.Mask"
	Description		"Digite sua senha de acesso"
	Initialization		"a=10;\nb=5;\nNUM = a;\nDEN = [1 b];\nseed2=20012;\npower2=0.00001;\nT = 0.01;"
	Object {
	 $PropName		 "Parameters"
	 $ObjectID		 21
	 $ClassName		 "Simulink.MaskParameter"
	 Type			 "edit"
	 Name			 ""
	 Prompt		 "Senha:"
	 Value			 "0"
	}
 }
 System {
	Name			"1a ordem"
	Location		[166, 301, 497, 608]
	Open			off
	ModelBrowserVisibility	off
	ModelBrowserWidth	200
	ScreenColor		"white"
	PaperOrientation	"landscape"
	PaperPositionMode	"auto"
	PaperType		"A4"
	PaperUnits		"centimeters"
	TiledPaperMargins	[0.500000, 0.500000, 0.500000, 0.500000]
	TiledPageScale		1
	ShowPageBoundaries	off
	ZoomFactor		"100"
	Block {
	 BlockType		 Inport
	 Name			 "In1"
	 SID			 "2"
	 Position		 [25, 38, 55, 52]
	 ZOrder		 -1
	 IconDisplay		 "Port number"
	}
	Block {
	 BlockType		 Reference
	 Name			 "Band-Limited\nWhite Noise"
	 SID			 "3"
	 Ports			 [0, 1]
	 Position		 [85, 70, 115, 100]
	 ZOrder		 -2
	 NamePlacement		 "alternate"
	 ShowName		 off
	 LibraryVersion	 "1.256"
	 SourceBlock		 "simulink/Sources/Band-Limited\nWhite Noise"
	 SourceType		 "Band-Limited White Noise."
	 Cov			 "[power2]"
	 Ts			 "T"
	 seed			 "[seed2]"
	 VectorParams1D	 on
	}
	Block {
	 BlockType		 Sum
	 Name			 "Sum"
	 SID			 "4"
	 Ports			 [2, 1]
	 Position		 [175, 35, 195, 55]
	 ZOrder		 -3
	 ShowName		 off
	 IconShape		 "round"
	 Inputs		 "|++"
	 InputSameDT		 off
	 OutDataTypeStr	 "Inherit: Inherit via internal rule"
	 SaturateOnIntegerOverflow off
	}
	Block {
	 BlockType		 TransferFcn
	 Name			 "Transfer Fcn"
	 SID			 "5"
	 Position		 [90, 27, 150, 63]
	 ZOrder		 -4
	 ShowName		 off
	 Numerator		 "NUM"
	 Denominator		 "DEN"
	}
	Block {
	 BlockType		 Outport
	 Name			 "Out1"
	 SID			 "6"
	 Position		 [220, 38, 250, 52]
	 ZOrder		 -5
	 IconDisplay		 "Port number"
	}
	Line {
	 ZOrder		 1
	 SrcBlock		 "Transfer Fcn"
	 SrcPort		 1
	 DstBlock		 "Sum"
	 DstPort		 1
	}
	Line {
	 ZOrder		 2
	 SrcBlock		 "Band-Limited\nWhite Noise"
	 SrcPort		 1
	 Points		 [65, 0]
	 DstBlock		 "Sum"
	 DstPort		 2
	}
	Line {
	 ZOrder		 3
	 SrcBlock		 "In1"
	 SrcPort		 1
	 DstBlock		 "Transfer Fcn"
	 DstPort		 1
	}
	Line {
	 ZOrder		 4
	 SrcBlock		 "Sum"
	 SrcPort		 1
	 DstBlock		 "Out1"
	 DstPort		 1
	}
 }
 }
 Block {
 BlockType		 SubSystem
 Name		 "1a ordem1"
 SID		 "67"
 Ports		 [1, 1]
 Position		 [270, 236, 330, 264]
 ZOrder		 1
 BackgroundColor	 "orange"
 RequestExecContextInheritance off
 Object {
	$PropName		"MaskObject"
	$ObjectID		22
	$ClassName		"Simulink.Mask"
	Description		"Digite sua senha de acesso"
	Initialization		"a=10;\nb=5;\nNUM = a;\nDEN = [1 b];\nseed2=20012;\npower2=0.00001;\nT = 0.01;"
	Object {
	 $PropName		 "Parameters"
	 $ObjectID		 23
	 $ClassName		 "Simulink.MaskParameter"
	 Type			 "edit"
	 Name			 ""
	 Prompt		 "Senha:"
	 Value			 "0"
	}
 }
 System {
	Name			"1a ordem1"
	Location		[166, 301, 497, 608]
	Open			off
	ModelBrowserVisibility	off
	ModelBrowserWidth	200
	ScreenColor		"white"
	PaperOrientation	"landscape"
	PaperPositionMode	"auto"
	PaperType		"usletter"
	PaperUnits		"inches"
	TiledPaperMargins	[0.500000, 0.500000, 0.500000, 0.500000]
	TiledPageScale		1
	ShowPageBoundaries	off
	ZoomFactor		"100"
	Block {
	 BlockType		 Inport
	 Name			 "In1"
	 SID			 "68"
	 Position		 [25, 38, 55, 52]
	 ZOrder		 -1
	 IconDisplay		 "Port number"
	}
	Block {
	 BlockType		 Reference
	 Name			 "Band-Limited\nWhite Noise"
	 SID			 "69"
	 Ports			 [0, 1]
	 Position		 [85, 70, 115, 100]
	 ZOrder		 -2
	 NamePlacement		 "alternate"
	 ShowName		 off
	 SourceBlock		 "simulink/Sources/Band-Limited\nWhite Noise"
	 SourceType		 "Band-Limited White Noise."
	 Cov			 "[power2]"
	 Ts			 "T"
	 seed			 "[seed2]"
	 VectorParams1D	 on
	}
	Block {
	 BlockType		 Sum
	 Name			 "Sum"
	 SID			 "70"
	 Ports			 [2, 1]
	 Position		 [175, 35, 195, 55]
	 ZOrder		 -3
	 ShowName		 off
	 IconShape		 "round"
	 Inputs		 "|++"
	 InputSameDT		 off
	 OutDataTypeStr	 "Inherit: Inherit via internal rule"
	 SaturateOnIntegerOverflow off
	}
	Block {
	 BlockType		 TransferFcn
	 Name			 "Transfer Fcn"
	 SID			 "71"
	 Position		 [90, 27, 150, 63]
	 ZOrder		 -4
	 ShowName		 off
	 Numerator		 "NUM"
	 Denominator		 "DEN"
	}
	Block {
	 BlockType		 Outport