Annex60.Utilities.Math.Examples

IEA EBC Annex 60

Annex60.Utilities.Math.Examples

Collection of models that illustrate model use and test models

Information

This package contains examples for the use of models that can be found in Annex60.Utilities.Math.

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
$Annex60.Utilities.Math.Examples.Average$ Average	Test model for average function
$Annex60.Utilities.Math.Examples.Bicubic$ Bicubic	Test model for bicubic function
$Annex60.Utilities.Math.Examples.Biquadratic$ Biquadratic	Test model for biquadratic function
$Annex60.Utilities.Math.Examples.BooleanReplicator$ BooleanReplicator	Test model for boolean replicator
$Annex60.Utilities.Math.Examples.IntegerReplicator$ IntegerReplicator	Test model for integer replicator
$Annex60.Utilities.Math.Examples.IntegratorWithReset$ IntegratorWithReset	Test model for integrator with reset
$Annex60.Utilities.Math.Examples.InverseXRegularized$ InverseXRegularized	Test model for inverseXRegularized function
$Annex60.Utilities.Math.Examples.Polynominal$ Polynominal	Test model for ploynominal function
$Annex60.Utilities.Math.Examples.PowerLinearized$ PowerLinearized	Test model for powerLinearized function
$Annex60.Utilities.Math.Examples.QuadraticLinear$ QuadraticLinear	Test model for quadraticLinear function
$Annex60.Utilities.Math.Examples.RegNonZeroPower$ RegNonZeroPower	Test model for regNonZeroPower function
$Annex60.Utilities.Math.Examples.SmoothBlocks$ SmoothBlocks	Test model for smooth min and smooth max functions
$Annex60.Utilities.Math.Examples.SmoothExponential$ SmoothExponential	Test model for smoothExponential function
$Annex60.Utilities.Math.Examples.SmoothHeaviside$ SmoothHeaviside	Test model for smoothHeavisidefunction
$Annex60.Utilities.Math.Examples.SmoothLimit$ SmoothLimit	Test model for smooth limit
$Annex60.Utilities.Math.Examples.SmoothMin$ SmoothMin	Test model for smooth minimum
$Annex60.Utilities.Math.Examples.Splice$ Splice	Test model for splice
$Annex60.Utilities.Math.Examples.VectorFunctions$ VectorFunctions	Test model for functions that take a vector as argument

$Annex60.Utilities.Math.Examples.Average$ Annex60.Utilities.Math.Examples.Average

Test model for average function

$Annex60.Utilities.Math.Examples.Average$

Information

This model tests the implementation of Annex60.Utilities.Math.Average.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Average "Test model for average function" extends Modelica.Icons.Example; Annex60.Utilities.Math.Average average(nin=2); Modelica.Blocks.Sources.Ramp x1(duration=1); Modelica.Blocks.Sources.Ramp x2( height=2, duration=1, offset=2); Modelica.Blocks.Routing.Multiplex2 multiplex2_1; equation connect(x1.y, multiplex2_1.u1[1]); connect(x2.y, multiplex2_1.u2[1]); connect(multiplex2_1.y, average.u); end Average;

$Annex60.Utilities.Math.Examples.Bicubic$ Annex60.Utilities.Math.Examples.Bicubic

Test model for bicubic function

$Annex60.Utilities.Math.Examples.Bicubic$

Information

This model tests the implementation of Annex60.Utilities.Math.Bicubic.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Bicubic "Test model for bicubic function" extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Modelica.Blocks.Sources.Ramp x2( height=2, duration=1, offset=2); Annex60.Utilities.Math.Bicubic bicubic(a={1,2,3,4,5,6,7,8,9,10}); equation connect(x1.y, bicubic.u1); connect(x2.y, bicubic.u2); end Bicubic;

$Annex60.Utilities.Math.Examples.Biquadratic$ Annex60.Utilities.Math.Examples.Biquadratic

Test model for biquadratic function

$Annex60.Utilities.Math.Examples.Biquadratic$

Information

This model tests the implementation of Annex60.Utilities.Math.Biquadratic.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Biquadratic "Test model for biquadratic function" extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Modelica.Blocks.Sources.Ramp x2( height=2, duration=1, offset=2); Annex60.Utilities.Math.Biquadratic biquadratic(a={1,2,3,4,5,6}); equation connect(x1.y, biquadratic.u1); connect(x2.y, biquadratic.u2); end Biquadratic;

$Annex60.Utilities.Math.Examples.BooleanReplicator$ Annex60.Utilities.Math.Examples.BooleanReplicator

Test model for boolean replicator

$Annex60.Utilities.Math.Examples.BooleanReplicator$

Information

This model tests the implementation of Annex60.Utilities.Math.BooleanReplicator.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model BooleanReplicator "Test model for boolean replicator" extends Modelica.Icons.Example; Modelica.Blocks.Sources.BooleanTable booTab(table={100,200,400,500}) "Boolean input signal"; Annex60.Utilities.Math.BooleanReplicator booRep(nout= 4) "Replicates boolean values"; equation connect(booTab.y, booRep.u); end BooleanReplicator;

$Annex60.Utilities.Math.Examples.IntegerReplicator$ Annex60.Utilities.Math.Examples.IntegerReplicator

Test model for integer replicator

$Annex60.Utilities.Math.Examples.IntegerReplicator$

Information

This model tests the implementation of Annex60.Utilities.Math.IntegerReplicator.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model IntegerReplicator "Test model for integer replicator" extends Modelica.Icons.Example; Modelica.Blocks.Sources.IntegerTable intTab(table=[0,1;1, 4;1.5, 5;2, 6]) "Integer input signal"; Annex60.Utilities.Math.IntegerReplicator intRep(nout= 2) "Replicates integer values"; equation connect(intTab.y, intRep.u); end IntegerReplicator;

$Annex60.Utilities.Math.Examples.IntegratorWithReset$ Annex60.Utilities.Math.Examples.IntegratorWithReset

Test model for integrator with reset

$Annex60.Utilities.Math.Examples.IntegratorWithReset$

Information

This model tests the implementation of Annex60.Utilities.Math.IntegratorWithReset with and without reset, and with different start values and reset values.

The integrator intWitRes1 is triggered by a sample trigger which becomes true at t=0, while intWitRes2 is triggered by a boolean pulse with is true at t=0. Hence, intWitRes1 starts with y(0)=y_reset while intWitRes2 starts with y(0)=y_start.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model IntegratorWithReset "Test model for integrator with reset" extends Modelica.Icons.Example; Modelica.Blocks.Sources.Constant cons(k=10) "Constant as source term"; Annex60.Utilities.Math.IntegratorWithReset intWitRes1( y_start=5, reset=Annex60.Types.Reset.Parameter, k=0.5, y_reset=2) "Integrator with reset"; Annex60.Utilities.Math.IntegratorWithReset intWitRes2( y_reset=10, y_start=-5, reset=Annex60.Types.Reset.Input, k=0.5) "Integrator with reset and y_reset = 2"; Modelica.Blocks.Sources.BooleanPulse booleanPulse(width=50, period=0.2) "Boolean pulse"; Annex60.Utilities.Math.IntegratorWithReset intNoReset( reset=Annex60.Types.Reset.Disabled, k=0.5, y_start=1) "Integrator without reset"; Modelica.Blocks.Sources.SampleTrigger sampleTrigger(period=0.2) "Sample trigger"; Modelica.Blocks.Sources.Ramp ramp( height=-1, duration=1, offset=-2) "Ramp as a source term"; Annex60.Utilities.Math.IntegratorWithReset intDef "Integrator with default values"; equation connect(cons.y, intWitRes1.u); connect(intNoReset.u, cons.y); connect(cons.y, intWitRes2.u); connect(sampleTrigger.y, intWitRes1.trigger); connect(booleanPulse.y, intWitRes2.trigger); connect(ramp.y, intWitRes2.y_reset_in); connect(cons.y, intDef.u); end IntegratorWithReset;

$Annex60.Utilities.Math.Examples.InverseXRegularized$ Annex60.Utilities.Math.Examples.InverseXRegularized

Test model for inverseXRegularized function

$Annex60.Utilities.Math.Examples.InverseXRegularized$

Information

This model tests the implementation of Annex60.Utilities.Math.InverseXRegularized.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model InverseXRegularized "Test model for inverseXRegularized function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1, height=2, offset=-1); Annex60.Utilities.Math.InverseXRegularized inverseXRegularized(delta=0.1); equation connect(x1.y, inverseXRegularized.u); end InverseXRegularized;

$Annex60.Utilities.Math.Examples.Polynominal$ Annex60.Utilities.Math.Examples.Polynominal

Test model for ploynominal function

$Annex60.Utilities.Math.Examples.Polynominal$

Information

This model tests the implementation of Annex60.Utilities.Math.Polynominal.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Polynominal "Test model for ploynominal function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Annex60.Utilities.Math.Polynominal polynominal(a={1,2}); equation connect(x1.y, polynominal.u); end Polynominal;

$Annex60.Utilities.Math.Examples.PowerLinearized$ Annex60.Utilities.Math.Examples.PowerLinearized

Test model for powerLinearized function

$Annex60.Utilities.Math.Examples.PowerLinearized$

Information

This model tests the implementation of Annex60.Utilities.Math.PowerLinearized.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model PowerLinearized "Test model for powerLinearized function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Annex60.Utilities.Math.PowerLinearized powerLinearized(n=2, x0=0.5); equation connect(x1.y, powerLinearized.u); end PowerLinearized;

$Annex60.Utilities.Math.Examples.QuadraticLinear$ Annex60.Utilities.Math.Examples.QuadraticLinear

Test model for quadraticLinear function

$Annex60.Utilities.Math.Examples.QuadraticLinear$

Information

This model tests the implementation of Annex60.Utilities.Math.QuadraticLinear.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model QuadraticLinear "Test model for quadraticLinear function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Annex60.Utilities.Math.QuadraticLinear quadraticLinear(a={1,2,3,4,5,6}); Modelica.Blocks.Sources.Ramp x2( duration=1, offset=2, height=5); equation connect(x2.y, quadraticLinear.u2); connect(x1.y, quadraticLinear.u1); end QuadraticLinear;

$Annex60.Utilities.Math.Examples.RegNonZeroPower$ Annex60.Utilities.Math.Examples.RegNonZeroPower

Test model for regNonZeroPower function

$Annex60.Utilities.Math.Examples.RegNonZeroPower$

Information

This model tests the implementation of Annex60.Utilities.Math.RegNonZeroPower.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model RegNonZeroPower "Test model for regNonZeroPower function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1); Annex60.Utilities.Math.RegNonZeroPower regNonZeroPower(n=0.5); equation connect(x1.y, regNonZeroPower.u); end RegNonZeroPower;

$Annex60.Utilities.Math.Examples.SmoothBlocks$ Annex60.Utilities.Math.Examples.SmoothBlocks

Test model for smooth min and smooth max functions

$Annex60.Utilities.Math.Examples.SmoothBlocks$

Information

This model tests the implementation of blocks that approximate non-differentiable functions by smooth functions.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SmoothBlocks "Test model for smooth min and smooth max functions" extends Modelica.Icons.Example; SmoothMax smoMax(deltaX=0.5); Modelica.Blocks.Math.Max max; Modelica.Blocks.Sources.Sine sine(freqHz=8); Modelica.Blocks.Sources.Sine sine1(freqHz=1); Diagnostics.AssertEquality assEquMax(threShold=0.08); Annex60.Utilities.Math.SmoothMin smoMin(deltaX=0.5); Modelica.Blocks.Math.Min Min; Diagnostics.AssertEquality assEquMin(threShold=0.08); equation connect(sine.y, smoMax.u1); connect(sine.y, max.u1); connect(sine1.y, smoMax.u2); connect(sine1.y, max.u2); connect(smoMax.y, assEquMax.u1); connect(max.y, assEquMax.u2); connect(sine.y, smoMin.u1); connect(sine.y, Min.u1); connect(sine1.y, smoMin.u2); connect(sine1.y, Min.u2); connect(smoMin.y, assEquMin.u1); connect(Min.y, assEquMin.u2); end SmoothBlocks;

$Annex60.Utilities.Math.Examples.SmoothExponential$ Annex60.Utilities.Math.Examples.SmoothExponential

Test model for smoothExponential function

$Annex60.Utilities.Math.Examples.SmoothExponential$

Information

This model tests the implementation of Annex60.Utilities.Math.SmoothExponential.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SmoothExponential "Test model for smoothExponential function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1, height=2, offset=-1); Annex60.Utilities.Math.SmoothExponential smoothExponential(delta=0.1); equation connect(x1.y, smoothExponential.u); end SmoothExponential;

$Annex60.Utilities.Math.Examples.SmoothHeaviside$ Annex60.Utilities.Math.Examples.SmoothHeaviside

Test model for smoothHeavisidefunction

$Annex60.Utilities.Math.Examples.SmoothHeaviside$

Information

This model tests the implementation of Annex60.Utilities.Math.SmoothHeaviside.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SmoothHeaviside "Test model for smoothHeavisidefunction " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x1(duration=1, height=2, offset=-1); Annex60.Utilities.Math.SmoothHeaviside smoothHeaviside(delta=0.1); equation connect(x1.y, smoothHeaviside.u); end SmoothHeaviside;

$Annex60.Utilities.Math.Examples.SmoothLimit$ Annex60.Utilities.Math.Examples.SmoothLimit

Test model for smooth limit

$Annex60.Utilities.Math.Examples.SmoothLimit$

Information

This model tests the implementation of Annex60.Utilities.Math.SmoothLimit.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SmoothLimit "Test model for smooth limit" extends Modelica.Icons.Example; Modelica.Blocks.Sources.Sine sine(freqHz=8); Annex60.Utilities.Math.SmoothLimit smoLim( deltaX=0.001, upper=0.5, lower=0) "Smooth limit"; equation connect(sine.y, smoLim.u); end SmoothLimit;

$Annex60.Utilities.Math.Examples.SmoothMin$ Annex60.Utilities.Math.Examples.SmoothMin

Test model for smooth minimum

$Annex60.Utilities.Math.Examples.SmoothMin$

Information

This model tests the implementation of Annex60.Utilities.Math.SmoothMin.

This model also illustrates that the output can be larger than the minimum of the two input signals. Smaller values for deltaX will reduce this effect. Therefore do not use this function when the minimum output value should be respected.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SmoothMin "Test model for smooth minimum" extends Modelica.Icons.Example; Annex60.Utilities.Math.SmoothMin smoLim[2](deltaX={0.1,0.02}) "Smooth limit"; Modelica.Blocks.Sources.Ramp ramp(height=1, duration=1) "Ramp input"; Modelica.Blocks.Sources.Constant const(k=0.5) "Constant input"; equation connect(ramp.y, smoLim[1].u1); connect(smoLim[2].u1, ramp.y); connect(const.y, smoLim[1].u2); connect(const.y, smoLim[2].u2); end SmoothMin;

$Annex60.Utilities.Math.Examples.Splice$ Annex60.Utilities.Math.Examples.Splice

Test model for splice

$Annex60.Utilities.Math.Examples.Splice$

Information

This model tests the implementation of Annex60.Utilities.Math.Splice

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Splice "Test model for splice" extends Modelica.Icons.Example; Annex60.Utilities.Math.Splice splice(deltax=0.2); Modelica.Blocks.Sources.Sine sine(freqHz=0.5); Modelica.Blocks.Sources.Constant const1(k=-0.5); Modelica.Blocks.Sources.Constant const(k=0.5); equation connect(sine.y, splice.x); connect(const1.y, splice.u2); connect(const.y, splice.u1); end Splice;

$Annex60.Utilities.Math.Examples.VectorFunctions$ Annex60.Utilities.Math.Examples.VectorFunctions

Test model for functions that take a vector as argument

$Annex60.Utilities.Math.Examples.VectorFunctions$

Information

This model tests the implementation of functions that take a vector as an argument.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model VectorFunctions "Test model for functions that take a vector as argument" extends Modelica.Icons.Example; Annex60.Utilities.Math.Min minVec( nin=3); Modelica.Blocks.Sources.Sine sine(freqHz=6); Modelica.Blocks.Sources.Sine sine1( freqHz=8); Modelica.Blocks.Sources.Sine sine2(freqHz=10); Annex60.Utilities.Math.Max maxVec( nin=3); Annex60.Utilities.Math.Average aveVec( nin=3); equation connect(sine.y, minVec.u[1]); connect(sine1.y, minVec.u[2]); connect(sine2.y, minVec.u[3]); connect(sine.y, maxVec.u[1]); connect(sine1.y, maxVec.u[2]); connect(sine2.y, maxVec.u[3]); connect(sine.y, aveVec.u[1]); connect(sine1.y, aveVec.u[2]); connect(sine2.y, aveVec.u[3]); end VectorFunctions;

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