Buildings.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 Buildings.Utilities.Math.

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

Package Content

Name	Description
Average	Test model for average function
BesselJ0	Test model for besselJ0 function
BesselJ1	Test model for besselJ1 function
BesselY0	Test model for besselY0 function
BesselY1	Test model for besselY1 function
Bicubic	Test model for bicubic function
Binomial	Test model for binomial function
Biquadratic	Test model for biquadratic function
BooleanReplicator	Test model for boolean replicator
ExponentialIntegralE1	Test model for exponentialIntegralE1 function
Factorial	Test model for factorial function
FallingFactorial	Test model for falling factorial function
IntegerReplicator	Test model for integer replicator
IntegratorWithReset	Test model for integrator with reset
Interpolate	Example model of the Interpolate block
InverseXRegularized	Test model for inverseXRegularized function
Polynomial	Test model for ploynominal function
PowerLinearized	Test model for powerLinearized function
QuadraticLinear	Test model for quadraticLinear function
RegNonZeroPower	Test model for regNonZeroPower function
SmoothBlocks	Test model for smooth min and smooth max functions
SmoothExponential	Test model for smoothExponential function
SmoothHeaviside	Test model for smoothHeavisidefunction
SmoothLimit	Test model for smooth limit
SmoothMin	Test model for smooth minimum
Splice	Test model for splice
VectorFunctions	Test model for functions that take a vector as argument

Buildings.Utilities.Math.Examples.Average

Test model for average function

$Buildings.Utilities.Math.Examples.Average$

Information

This model tests the implementation of Buildings.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; Buildings.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;

Buildings.Utilities.Math.Examples.BesselJ0

Test model for besselJ0 function

$Buildings.Utilities.Math.Examples.BesselJ0$

Information

This model tests the implementation of Buildings.Utilities.Math.BesselJ0.

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

Modelica definition

model BesselJ0 "Test model for besselJ0 function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x(duration=30, height=30) "Real signal"; Buildings.Utilities.Math.BesselJ0 J0 "Bessel function J0"; equation connect(x.y, J0.u); end BesselJ0;

Buildings.Utilities.Math.Examples.BesselJ1

Test model for besselJ1 function

$Buildings.Utilities.Math.Examples.BesselJ1$

Information

This model tests the implementation of Buildings.Utilities.Math.BesselJ1.

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

Modelica definition

model BesselJ1 "Test model for besselJ1 function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x(duration=30, height=30) "Real signal"; Buildings.Utilities.Math.BesselJ1 J1 "Bessel function J1"; equation connect(x.y, J1.u); end BesselJ1;

Buildings.Utilities.Math.Examples.BesselY0

Test model for besselY0 function

$Buildings.Utilities.Math.Examples.BesselY0$

Information

This model tests the implementation of Buildings.Utilities.Math.BesselY0.

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

Modelica definition

model BesselY0 "Test model for besselY0 function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x(duration=30, height=30) "Real signal"; Buildings.Utilities.Math.BesselY0 Y0 "Bessel function Y0"; equation connect(x.y, Y0.u); end BesselY0;

Buildings.Utilities.Math.Examples.BesselY1

Test model for besselY1 function

$Buildings.Utilities.Math.Examples.BesselY1$

Information

This model tests the implementation of Buildings.Utilities.Math.BesselY1.

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

Modelica definition

model BesselY1 "Test model for besselY1 function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x(duration=30, height=30) "Real signal"; Buildings.Utilities.Math.BesselY1 Y1 "Bessel function Y1"; equation connect(x.y, Y1.u); end BesselY1;

Buildings.Utilities.Math.Examples.Bicubic

Test model for bicubic function

$Buildings.Utilities.Math.Examples.Bicubic$

Information

This model tests the implementation of Buildings.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); Buildings.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;

Buildings.Utilities.Math.Examples.Binomial

Test model for binomial function

$Buildings.Utilities.Math.Examples.Binomial$

Information

This model tests the implementation of Buildings.Utilities.Math.Binomial.

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

Modelica definition

model Binomial "Test model for binomial function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp k( startTime=0.5, height=10.4, duration=10.4) "Real signal"; Modelica.Blocks.Math.RealToInteger rea2Int "Convert to rounded integer"; Buildings.Utilities.Math.Binomial bin "Binomial coefficient"; Modelica.Blocks.Sources.IntegerConstant n(k=15) "Size of set"; equation connect(k.y, rea2Int.u); connect(rea2Int.y, bin.k); connect(n.y, bin.n); end Binomial;

Buildings.Utilities.Math.Examples.Biquadratic

Test model for biquadratic function

$Buildings.Utilities.Math.Examples.Biquadratic$

Information

This model tests the implementation of Buildings.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); Buildings.Utilities.Math.Biquadratic biquadratic(a={1,2,3,4,5,6}); equation connect(x1.y, biquadratic.u1); connect(x2.y, biquadratic.u2); end Biquadratic;

Buildings.Utilities.Math.Examples.BooleanReplicator

Test model for boolean replicator

$Buildings.Utilities.Math.Examples.BooleanReplicator$

Information

This model tests the implementation of Buildings.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"; Buildings.Utilities.Math.BooleanReplicator booRep(nout= 4) "Replicates boolean values"; equation connect(booTab.y, booRep.u); end BooleanReplicator;

Buildings.Utilities.Math.Examples.ExponentialIntegralE1

Test model for exponentialIntegralE1 function

$Buildings.Utilities.Math.Examples.ExponentialIntegralE1$

Information

This model tests the implementation of Buildings.Utilities.Math.ExponentialIntegralE1.

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

Modelica definition

model ExponentialIntegralE1 "Test model for exponentialIntegralE1 function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x(duration=30, height=30) "Real signal"; Buildings.Utilities.Math.ExponentialIntegralE1 E1 "Exponential integral E1"; equation connect(x.y, E1.u); end ExponentialIntegralE1;

Buildings.Utilities.Math.Examples.Factorial

Test model for factorial function

$Buildings.Utilities.Math.Examples.Factorial$

Information

This model tests the implementation of Buildings.Utilities.Math.Factorial.

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

Modelica definition

model Factorial "Test model for factorial function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp x( startTime=0.5, height=12.4, duration=12.4) "Real signal"; Buildings.Utilities.Math.Factorial fac "Factorial"; Modelica.Blocks.Math.RealToInteger rea2Int "Conversion to rounded integer"; equation connect(rea2Int.y, fac.u); connect(x.y, rea2Int.u); end Factorial;

Buildings.Utilities.Math.Examples.FallingFactorial

Test model for falling factorial function

$Buildings.Utilities.Math.Examples.FallingFactorial$

Information

This model tests the implementation of Buildings.Utilities.Math.FallingFactorial.

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

Modelica definition

model FallingFactorial "Test model for falling factorial function " extends Modelica.Icons.Example; Modelica.Blocks.Sources.Ramp k( startTime=0.5, height=10.4, duration=10.4) "Real signal"; Modelica.Blocks.Math.RealToInteger rea2Int "Conversion to rounded integer"; Buildings.Utilities.Math.FallingFactorial falFac "Falling factorial"; Modelica.Blocks.Sources.IntegerConstant n(k=13) "Falling factorial power"; equation connect(k.y, rea2Int.u); connect(rea2Int.y, falFac.k); connect(n.y, falFac.n); end FallingFactorial;

Buildings.Utilities.Math.Examples.IntegerReplicator

Test model for integer replicator

$Buildings.Utilities.Math.Examples.IntegerReplicator$

Information

This model tests the implementation of Buildings.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"; Buildings.Utilities.Math.IntegerReplicator intRep(nout= 2) "Replicates integer values"; equation connect(intTab.y, intRep.u); end IntegerReplicator;

Buildings.Utilities.Math.Examples.IntegratorWithReset

Test model for integrator with reset

$Buildings.Utilities.Math.Examples.IntegratorWithReset$

Information

This model tests the implementation of Buildings.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"; Buildings.Utilities.Math.IntegratorWithReset intWitRes1( y_start=5, reset=Buildings.Types.Reset.Parameter, k=0.5, y_reset=2) "Integrator with reset"; Buildings.Utilities.Math.IntegratorWithReset intWitRes2( y_reset=10, y_start=-5, reset=Buildings.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"; Buildings.Utilities.Math.IntegratorWithReset intNoReset( reset=Buildings.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"; Buildings.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;

Buildings.Utilities.Math.Examples.Interpolate

Example model of the Interpolate block

$Buildings.Utilities.Math.Examples.Interpolate$

Information

This example is the same as Buildings.Utilities.Math.Functions.Examples.Interpolate except that the block is used in place of the function.

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

Parameters

Type	Name	Default	Description
Real	table[:, :]	[-50, -0.08709; -25, -0.0615...	Table of mass flow rate in kg/s (second column) as a function of pressure difference in Pa (first column)
Real	xd[:]	table[:, 1]	x-axis support points
Real	yd[size(xd, 1)]	table[:, 2]	y-axis support points
Real	d[size(xd, 1)]	Buildings.Utilities.Math.Fun...	Derivatives at the support points

Modelica definition

model Interpolate "Example model of the Interpolate block" extends Modelica.Icons.Example; parameter Real table[:,:]=[-50,-0.08709; -25,-0.06158; -10,-0.03895; -5,-0.02754; -3,-0.02133; -2,-0.01742; -1,-0.01232; 0,0; 1,0.01232; 2,0.01742; 3,0.02133; 4.5,0.02613; 50,0.02614] "Table of mass flow rate in kg/s (second column) as a function of pressure difference in Pa (first column)"; parameter Real[:] xd=table[:,1] "x-axis support points"; parameter Real[size(xd, 1)] yd=table[:,2] "y-axis support points"; parameter Real[size(xd, 1)] d = Buildings.Utilities.Math.Functions.splineDerivatives( x=xd, y=yd, ensureMonotonicity=true) "Derivatives at the support points"; Buildings.Utilities.Math.Interpolate int( xd=xd, yd=yd, d=d) "Interpolate block"; Modelica.Blocks.Sources.Ramp ramp( duration=500, height=100, offset=-50) "Ramp from -50Pa to +50Pa"; equation connect(ramp.y, int.u); end Interpolate;

Buildings.Utilities.Math.Examples.InverseXRegularized

Test model for inverseXRegularized function

$Buildings.Utilities.Math.Examples.InverseXRegularized$

Information

This model tests the implementation of Buildings.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); Buildings.Utilities.Math.InverseXRegularized inverseXRegularized(delta=0.1); equation connect(x1.y, inverseXRegularized.u); end InverseXRegularized;

Buildings.Utilities.Math.Examples.Polynomial

Test model for ploynominal function

$Buildings.Utilities.Math.Examples.Polynomial$

Information

This model tests the implementation of Buildings.Utilities.Math.Polynomial.

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

Modelica definition

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

Buildings.Utilities.Math.Examples.PowerLinearized

Test model for powerLinearized function

$Buildings.Utilities.Math.Examples.PowerLinearized$

Information

This model tests the implementation of Buildings.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); Buildings.Utilities.Math.PowerLinearized powerLinearized(n=2, x0=0.5); equation connect(x1.y, powerLinearized.u); end PowerLinearized;

Buildings.Utilities.Math.Examples.QuadraticLinear

Test model for quadraticLinear function

$Buildings.Utilities.Math.Examples.QuadraticLinear$

Information

This model tests the implementation of Buildings.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); Buildings.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;

Buildings.Utilities.Math.Examples.RegNonZeroPower

Test model for regNonZeroPower function

$Buildings.Utilities.Math.Examples.RegNonZeroPower$

Information

This model tests the implementation of Buildings.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); Buildings.Utilities.Math.RegNonZeroPower regNonZeroPower(n=0.5); equation connect(x1.y, regNonZeroPower.u); end RegNonZeroPower;

Buildings.Utilities.Math.Examples.SmoothBlocks

Test model for smooth min and smooth max functions

$Buildings.Utilities.Math.Examples.SmoothBlocks$

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(f=8); Modelica.Blocks.Sources.Sine sine1(f=1); Diagnostics.AssertEquality assEquMax(threShold=0.08); Buildings.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;

Buildings.Utilities.Math.Examples.SmoothExponential

Test model for smoothExponential function

$Buildings.Utilities.Math.Examples.SmoothExponential$

Information

This model tests the implementation of Buildings.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); Buildings.Utilities.Math.SmoothExponential smoothExponential(delta=0.1); equation connect(x1.y, smoothExponential.u); end SmoothExponential;

Buildings.Utilities.Math.Examples.SmoothHeaviside

Test model for smoothHeavisidefunction

$Buildings.Utilities.Math.Examples.SmoothHeaviside$

Information

This model tests the implementation of Buildings.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) "Ramp input signal"; Buildings.Utilities.Math.SmoothHeaviside smoothHeaviside(delta=0.1) "Smooth approximation to Heaviside function"; equation connect(x1.y, smoothHeaviside.u); end SmoothHeaviside;

Buildings.Utilities.Math.Examples.SmoothLimit

Test model for smooth limit

$Buildings.Utilities.Math.Examples.SmoothLimit$

Information

This model tests the implementation of Buildings.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(f=8); Buildings.Utilities.Math.SmoothLimit smoLim( deltaX=0.001, upper=0.5, lower=0) "Smooth limit"; equation connect(sine.y, smoLim.u); end SmoothLimit;

Buildings.Utilities.Math.Examples.SmoothMin

Test model for smooth minimum

$Buildings.Utilities.Math.Examples.SmoothMin$

Information

This model tests the implementation of Buildings.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; Buildings.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;

Buildings.Utilities.Math.Examples.Splice

Test model for splice

$Buildings.Utilities.Math.Examples.Splice$

Information

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

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

Modelica definition

model Splice "Test model for splice" extends Modelica.Icons.Example; Buildings.Utilities.Math.Splice splice(deltax=0.2); Modelica.Blocks.Sources.Sine sine(f=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;

Buildings.Utilities.Math.Examples.VectorFunctions

Test model for functions that take a vector as argument

$Buildings.Utilities.Math.Examples.VectorFunctions$

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; Buildings.Utilities.Math.Min minVec( nin=3); Modelica.Blocks.Sources.Sine sine(f=6); Modelica.Blocks.Sources.Sine sine1(f=8); Modelica.Blocks.Sources.Sine sine2(f=10); Buildings.Utilities.Math.Max maxVec( nin=3); Buildings.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;