Model { Name "NonLinearEquations" Version 3.00 SimParamPage "Solver" SampleTimeColors off InvariantConstants off WideVectorLines off ShowLineWidths off ShowPortDataTypes off StartTime "0.0" StopTime "10.0" SolverMode "Auto" Solver "ode45" RelTol "1e-3" AbsTol "auto" Refine "1" MaxStep "auto" InitialStep "auto" FixedStep "auto" MaxOrder 5 OutputOption "RefineOutputTimes" OutputTimes "[]" LoadExternalInput off ExternalInput "[t, u]" SaveTime on TimeSaveName "tout" SaveState off StateSaveName "xout" SaveOutput on OutputSaveName "yout" LoadInitialState off InitialState "xInitial" SaveFinalState off FinalStateName "xFinal" SaveFormat "Matrix" LimitMaxRows off MaxRows "1000" Decimation "1" AlgebraicLoopMsg "warning" MinStepSizeMsg "warning" UnconnectedInputMsg "warning" UnconnectedOutputMsg "warning" UnconnectedLineMsg "warning" InheritedTsInSrcMsg "warning" IntegerOverflowMsg "warning" UnnecessaryDatatypeConvMsg "none" Int32ToFloatConvMsg "warning" SignalLabelMismatchMsg "none" ConsistencyChecking "off" ZeroCross on SimulationMode "normal" BlockDataTips on BlockParametersDataTip on BlockAttributesDataTip off BlockPortWidthsDataTip off BlockDescriptionStringDataTip off BlockMaskParametersDataTip off ToolBar on StatusBar on BrowserShowLibraryLinks off BrowserLookUnderMasks off OptimizeBlockIOStorage on BufferReuse on BooleanDataType off RTWSystemTargetFile "grt.tlc" RTWInlineParameters off RTWRetainRTWFile off RTWTemplateMakefile "grt_default_tmf" RTWMakeCommand "make_rtw" RTWGenerateCodeOnly off ExtModeMexFile "ext_comm" ExtModeBatchMode off ExtModeTrigType "manual" ExtModeTrigMode "oneshot" ExtModeTrigPort "1" ExtModeTrigElement "any" ExtModeTrigDuration 1000 ExtModeTrigHoldOff 0 ExtModeTrigDelay 0 ExtModeTrigDirection "rising" ExtModeTrigLevel 0 ExtModeArchiveMode "off" ExtModeAutoIncOneShot off ExtModeIncDirWhenArm off ExtModeAddSuffixToVar off ExtModeWriteAllDataToWs off ExtModeArmWhenConnect off Created "Sun Mar 18 20:22:41 2001" UpdateHistory "UpdateHistoryNever" ModifiedByFormat "%" ModifiedDateFormat "%" LastModifiedDate "Sun Mar 18 22:41:01 2001" ModelVersionFormat "1.%" ConfigurationManager "none" BlockDefaults { Orientation "right" ForegroundColor "black" BackgroundColor "white" DropShadow off NamePlacement "normal" FontName "Helvetica" FontSize 10 FontWeight "normal" FontAngle "normal" ShowName on } AnnotationDefaults { HorizontalAlignment "center" VerticalAlignment "middle" ForegroundColor "black" BackgroundColor "white" DropShadow off FontName "Helvetica" FontSize 10 FontWeight "normal" FontAngle "normal" } LineDefaults { FontName "Helvetica" FontSize 9 FontWeight "normal" FontAngle "normal" } System { Name "NonLinearEquations" Location [4, 84, 780, 582] Open on ModelBrowserVisibility off ModelBrowserWidth 200 ScreenColor "automatic" PaperOrientation "landscape" PaperPositionMode "auto" PaperType "usletter" PaperUnits "inches" ZoomFactor "100" AutoZoom off ReportName "simulink-default.rpt" Block { BlockType Constant Name "3/2" Position [120, 205, 150, 235] Orientation "left" Value "3/2" } Block { BlockType Math Name "Ca 3/2" Ports [2, 1, 0, 0, 0] Position [70, 176, 100, 209] Orientation "left" Operator "pow" OutputSignalType "auto" } Block { BlockType Display Name "Ca at t" Ports [1, 0, 0, 0, 0] Position [550, 60, 640, 90] Format "short" Decimation "1" Floating off SampleTime "-1" } Block { BlockType Constant Name "Cao" Position [140, 20, 170, 50] ShowName off Value "Cao" } Block { BlockType Display Name "Cb at t" Ports [1, 0, 0, 0, 0] Position [530, 265, 620, 295] Format "short" Decimation "1" Floating off SampleTime "-1" } Block { BlockType Math Name "Cb2" Ports [1, 1, 0, 0, 0] Position [220, 195, 250, 225] Orientation "left" Operator "magnitude^2" OutputSignalType "auto" } Block { BlockType Display Name "Cc at t" Ports [1, 0, 0, 0, 0] Position [585, 395, 675, 425] Format "short" Decimation "1" Floating off SampleTime "-1" } Block { BlockType Math Name "Cc2" Ports [1, 1, 0, 0, 0] Position [275, 340, 305, 370] Orientation "left" Operator "magnitude^2" OutputSignalType "auto" } Block { BlockType Display Name "Cd at t" Ports [1, 0, 0, 0, 0] Position [610, 485, 700, 515] Format "short" Decimation "1" Floating off SampleTime "-1" } Block { BlockType Reference Name "Solve Ca" Ports [1, 1, 0, 0, 0] Position [340, 60, 420, 90] SourceBlock "simulink3/Math/Algebraic Constraint" SourceType "Algebraic Constraint" z0 "0" } Block { BlockType Reference Name "Solve Cb" Ports [1, 1, 0, 0, 0] Position [345, 265, 425, 295] SourceBlock "simulink3/Math/Algebraic Constraint" SourceType "Algebraic Constraint" z0 "0" } Block { BlockType Reference Name "Solve Cc" Ports [1, 1, 0, 0, 0] Position [425, 395, 505, 425] SourceBlock "simulink3/Math/Algebraic Constraint" SourceType "Algebraic Constraint" z0 "0" } Block { BlockType Reference Name "Solve Cd" Ports [1, 1, 0, 0, 0] Position [465, 485, 545, 515] SourceBlock "simulink3/Math/Algebraic Constraint" SourceType "Algebraic Constraint" z0 "0" } Block { BlockType Sum Name "Sum" Ports [3, 1, 0, 0, 0] Position [195, 15, 220, 135] ShowName off IconShape "rectangular" Inputs "++-" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum1" Ports [2, 1, 0, 0, 0] Position [280, 234, 300, 321] ShowName off IconShape "rectangular" Inputs "-+" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum2" Ports [2, 1, 0, 0, 0] Position [340, 364, 360, 451] ShowName off IconShape "rectangular" Inputs "-+" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum3" Ports [2, 1, 0, 0, 0] Position [400, 474, 415, 521] ShowName off IconShape "rectangular" Inputs "-+" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum4" Ports [3, 1, 0, 0, 0] Position [13, 70, 72, 100] Orientation "up" NamePlacement "alternate" ShowName off IconShape "rectangular" Inputs "+|--" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum5" Ports [2, 1, 0, 0, 0] Position [159, 280, 206, 310] Orientation "down" NamePlacement "alternate" ShowName off IconShape "rectangular" Inputs "+-" SaturateOnIntegerOverflow on } Block { BlockType Sum Name "Sum6" Ports [3, 1, 0, 0, 0] Position [176, 390, 224, 420] Orientation "down" NamePlacement "alternate" ShowName off IconShape "rectangular" Inputs "+-+" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k1" Position [109, 130, 131, 155] Orientation "up" NamePlacement "alternate" Gain "k1" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k10" Position [315, 495, 345, 525] ShowName off Gain "t" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k2" Position [35, 145, 65, 175] Orientation "up" NamePlacement "alternate" ShowName off Gain "k2" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k3" Position [220, 340, 250, 370] Orientation "left" ShowName off Gain "k3" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k5" Position [105, 50, 135, 80] ShowName off Gain "t" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k6" Position [155, 195, 185, 225] Orientation "down" NamePlacement "alternate" ShowName off Gain "2*k1" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k7" Position [180, 230, 210, 260] Orientation "down" NamePlacement "alternate" ShowName off Gain "k4" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k8" Position [220, 305, 250, 335] ShowName off Gain "t" SaturateOnIntegerOverflow on } Block { BlockType Gain Name "k9" Position [270, 415, 300, 445] ShowName off Gain "t" SaturateOnIntegerOverflow on } Line { SrcBlock "Cao" SrcPort 1 DstBlock "Sum" DstPort 1 } Line { SrcBlock "Sum" SrcPort 1 DstBlock "Solve Ca" DstPort 1 } Line { Labels [1, 0] SrcBlock "Solve Ca" SrcPort 1 Points [55, 0] Branch { DstBlock "Ca at t" DstPort 1 } Branch { Labels [2, 0] Points [0, 95; -310, 0] Branch { Points [-50, 0] Branch { DstBlock "k1" DstPort 1 } Branch { Points [-5, 0] DstBlock "Ca 3/2" DstPort 1 } } Branch { Points [0, -55] DstBlock "Sum" DstPort 3 } Branch { DstBlock "k6" DstPort 1 } } } Line { SrcBlock "3/2" SrcPort 1 DstBlock "Ca 3/2" DstPort 2 } Line { SrcBlock "k1" SrcPort 1 Points [-55, 0] DstBlock "Sum4" DstPort 3 } Line { SrcBlock "Sum4" SrcPort 1 DstBlock "k5" DstPort 1 } Line { SrcBlock "k5" SrcPort 1 Points [0, 10] DstBlock "Sum" DstPort 2 } Line { SrcBlock "Sum1" SrcPort 1 DstBlock "Solve Cb" DstPort 1 } Line { SrcBlock "k6" SrcPort 1 DstBlock "Sum5" DstPort 1 } Line { Labels [1, 0] SrcBlock "Solve Cb" SrcPort 1 Points [30, 0] Branch { DstBlock "Cb at t" DstPort 1 } Branch { Points [0, -70; -195, 0] Branch { DstBlock "Cb2" DstPort 1 } Branch { DstBlock "Sum1" DstPort 1 } } } Line { SrcBlock "Cb2" SrcPort 1 Points [-20, 0] DstBlock "k7" DstPort 1 } Line { SrcBlock "Sum5" SrcPort 1 Points [0, 5] DstBlock "k8" DstPort 1 } Line { SrcBlock "k8" SrcPort 1 Points [10, 0] DstBlock "Sum1" DstPort 2 } Line { SrcBlock "Sum2" SrcPort 1 DstBlock "Solve Cc" DstPort 1 } Line { SrcBlock "Solve Cc" SrcPort 1 Points [30, 0] Branch { DstBlock "Cc at t" DstPort 1 } Branch { Points [0, -55; -215, 0] Branch { DstBlock "Sum2" DstPort 1 } Branch { DstBlock "Cc2" DstPort 1 } } } Line { SrcBlock "Cc2" SrcPort 1 DstBlock "k3" DstPort 1 } Line { SrcBlock "k3" SrcPort 1 Points [-15, 0] Branch { DstBlock "Sum6" DstPort 2 } Branch { Points [-180, 0] DstBlock "Sum4" DstPort 1 } } Line { SrcBlock "k7" SrcPort 1 Points [0, 0] Branch { DstBlock "Sum5" DstPort 2 } Branch { Points [-85, 0; 0, 65] Branch { Points [105, 0] DstBlock "Sum6" DstPort 3 } Branch { Points [0, 180] DstBlock "k10" DstPort 1 } } } Line { SrcBlock "Sum6" SrcPort 1 Points [0, 5] DstBlock "k9" DstPort 1 } Line { SrcBlock "k9" SrcPort 1 DstBlock "Sum2" DstPort 2 } Line { SrcBlock "Sum3" SrcPort 1 DstBlock "Solve Cd" DstPort 1 } Line { Labels [1, 0] SrcBlock "Solve Cd" SrcPort 1 Points [20, 0] Branch { DstBlock "Cd at t" DstPort 1 } Branch { Points [0, -40; -185, 0] DstBlock "Sum3" DstPort 1 } } Line { SrcBlock "k10" SrcPort 1 DstBlock "Sum3" DstPort 2 } Line { SrcBlock "Ca 3/2" SrcPort 1 Points [-15, 0] DstBlock "k2" DstPort 1 } Line { SrcBlock "k2" SrcPort 1 Points [0, 0] Branch { DstBlock "Sum4" DstPort 2 } Branch { Points [-20, 0; 0, 200; 155, 0] DstBlock "Sum6" DstPort 1 } } Annotation { Position [156, 520] Text "\n\n\n\n" } Annotation { Position [182, 620] Text "Solution to:\nF1 = - Ca + Cao + [-k1 Ca - k2 Ca" "3/2 + k3 Cc2] t = 0\nF2= - Cb + [2 k1 Ca - k4 Cb2] t = 0\nF3 = - Cc + [k2 Ca3" "/2 - k3 Cc2 + k4 Cb2] t = 0\nF4 = - Cd + [k4 Cb2] t = 0 \nWith the following " "conditions:\nk1 = 1; k2 = 0.2; k3 = 0.05; k4 = 0.4; Cao = 1; t = 2\nThese con" "ditions are stored in the file 'simult.mat'\nBefore starting simulation load " "the file \nsimult.mat in the Matlab Workspace" FontSize 12 } Annotation { Position [476, 63] Text "Ca" } Annotation { Position [471, 266] Text "Cb" } Annotation { Position [552, 399] Text "Cc" } Annotation { Position [585, 486] Text "Cd" } Annotation { Position [556, 593] Text "The solution will be: at t = 2\nCa = 0.3189; Cb" " = 0.7839; Cc = 0.5350; Cd = 0.4916" FontSize 12 } Annotation { Position [500, 657] Text "Done on: 18-Mar-2001\nM.Subramanian\nmsubbu@svc" "e.ac.in" FontSize 12 } } }