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Buildings.Utilities.Math

Library with functions such as for smoothing

Information

This package contains blocks and functions for commonly used mathematical operations. The classes in this package augment the classes Modelica.Blocks.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

NameDescription
Buildings.Utilities.Math.Functions Functions Package with mathematical functions
Buildings.Utilities.Math.Average Average Average of a vector
Buildings.Utilities.Math.Bicubic Bicubic Bicubic function
Buildings.Utilities.Math.Biquadratic Biquadratic Biquadratic function
Buildings.Utilities.Math.BooleanReplicator BooleanReplicator Boolean signal replicator
Buildings.Utilities.Math.IntegerReplicator IntegerReplicator Integer signal replicator
Buildings.Utilities.Math.Max Max Maximum element of a vector
Buildings.Utilities.Math.Min Min Minimum element of a vector
Buildings.Utilities.Math.SmoothHeaviside SmoothHeaviside Once continuously differentiable approximation to the Heaviside function
Buildings.Utilities.Math.SmoothLimit SmoothLimit Once continuously differentiable approximation to the limit function
Buildings.Utilities.Math.SmoothMax SmoothMax Once continuously differentiable approximation to the maximum function
Buildings.Utilities.Math.SmoothMin SmoothMin Once continuously differentiable approximation to the minimum function
Buildings.Utilities.Math.Splice Splice Block for splice function opertation
Buildings.Utilities.Math.Examples Examples Collection of models that illustrate model use and test models

Buildings.Utilities.Math.Average Buildings.Utilities.Math.Average

Average of a vector

Buildings.Utilities.Math.Average

Information

This function outputs the average of the vector.

Extends from Modelica.Blocks.Interfaces.MISO (Multiple Input Single Output continuous control block).

Parameters

TypeNameDefaultDescription
Integernin1Number of inputs

Connectors

TypeNameDescription
input RealInputu[nin]Connector of Real input signals
output RealOutputyConnector of Real output signal

Modelica definition

block Average "Average of a vector"
  extends Modelica.Blocks.Interfaces.MISO;
equation 
 y = sum(u)/nin;
end Average;

Buildings.Utilities.Math.Bicubic Buildings.Utilities.Math.Bicubic

Bicubic function

Buildings.Utilities.Math.Bicubic

Information

This block computes

y = a1 + a2 x1 + a3 x12 + a4 x2 + a5 x22 + a6 x1 x2 + a7 x1^3 + a8 x2^3 + a9 x12 x2 + a10 x1 x22

Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block).

Connectors

TypeNameDescription
input RealInputu1Connector of Real input signal 1
input RealInputu2Connector of Real input signal 2
output RealOutputyConnector of Real output signal

Modelica definition

block Bicubic "Bicubic function"
  extends Modelica.Blocks.Interfaces.SI2SO;
 input Real a[10] "Coefficients";
equation 
  y =  Buildings.Utilities.Math.Functions.bicubic(a=a, x1=u1, x2=u2);
end Bicubic;

Buildings.Utilities.Math.Biquadratic Buildings.Utilities.Math.Biquadratic

Biquadratic function

Buildings.Utilities.Math.Biquadratic

Information

This block computes

y = a1 + a2 x1 + a3 x12 + a4 x2 + a5 x22 + a6 x1 x2

Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

TypeNameDefaultDescription
Reala[6] Coefficients

Connectors

TypeNameDescription
input RealInputu1Connector of Real input signal 1
input RealInputu2Connector of Real input signal 2
output RealOutputyConnector of Real output signal

Modelica definition

block Biquadratic "Biquadratic function"
  extends Modelica.Blocks.Interfaces.SI2SO;
  parameter Real a[6] "Coefficients";
equation 
  y =  Buildings.Utilities.Math.Functions.biquadratic(a=a, x1=u1, x2=u2);
end Biquadratic;

Buildings.Utilities.Math.BooleanReplicator Buildings.Utilities.Math.BooleanReplicator

Boolean signal replicator

Buildings.Utilities.Math.BooleanReplicator

Information

This block replicates the boolean input signal to an array of nout identical output signals.

Extends from Modelica.Blocks.Interfaces.BooleanBlockIcon (Basic graphical layout of Boolean block).

Parameters

TypeNameDefaultDescription
Integernout1Number of outputs

Connectors

TypeNameDescription
input BooleanInputuConnector of boolean input signal
output BooleanOutputy[nout]Connector of boolean output signals

Modelica definition

block BooleanReplicator "Boolean signal replicator"
  extends Modelica.Blocks.Interfaces.BooleanBlockIcon;
  parameter Integer nout=1 "Number of outputs";
  Modelica.Blocks.Interfaces.BooleanInput u "Connector of boolean input signal";
  Modelica.Blocks.Interfaces.BooleanOutput y[nout] 
    "Connector of boolean output signals";
equation 
  y = fill(u, nout);
end BooleanReplicator;

Buildings.Utilities.Math.IntegerReplicator Buildings.Utilities.Math.IntegerReplicator

Integer signal replicator

Buildings.Utilities.Math.IntegerReplicator

Information

This block replicates the integer input signal to an array of nout identical output signals.

Extends from Modelica.Blocks.Interfaces.IntegerBlockIcon (Basic graphical layout of Integer block).

Parameters

TypeNameDefaultDescription
Integernout1Number of outputs

Connectors

TypeNameDescription
input IntegerInputuConnector of integer input signal
output IntegerOutputy[nout]Connector of integer output signals

Modelica definition

block IntegerReplicator "Integer signal replicator"
  extends Modelica.Blocks.Interfaces.IntegerBlockIcon;
  parameter Integer nout=1 "Number of outputs";
  Modelica.Blocks.Interfaces.IntegerInput u "Connector of integer input signal";
  Modelica.Blocks.Interfaces.IntegerOutput y[nout] 
    "Connector of integer output signals";
equation 
  y = fill(u, nout);
end IntegerReplicator;

Buildings.Utilities.Math.Max Buildings.Utilities.Math.Max

Maximum element of a vector

Buildings.Utilities.Math.Max

Information

Outputs the minimum of the vector.

Extends from Modelica.Blocks.Interfaces.MISO (Multiple Input Single Output continuous control block).

Parameters

TypeNameDefaultDescription
Integernin1Number of inputs

Connectors

TypeNameDescription
input RealInputu[nin]Connector of Real input signals
output RealOutputyConnector of Real output signal

Modelica definition

block Max "Maximum element of a vector"
  extends Modelica.Blocks.Interfaces.MISO;
equation 
 y = max(u);
end Max;

Buildings.Utilities.Math.Min Buildings.Utilities.Math.Min

Minimum element of a vector

Buildings.Utilities.Math.Min

Information

Outputs the minimum of the vector.

Extends from Modelica.Blocks.Interfaces.MISO (Multiple Input Single Output continuous control block).

Parameters

TypeNameDefaultDescription
Integernin1Number of inputs

Connectors

TypeNameDescription
input RealInputu[nin]Connector of Real input signals
output RealOutputyConnector of Real output signal

Modelica definition

block Min "Minimum element of a vector"
  extends Modelica.Blocks.Interfaces.MISO;
equation 
 y = min(u);
end Min;

Buildings.Utilities.Math.SmoothHeaviside Buildings.Utilities.Math.SmoothHeaviside

Once continuously differentiable approximation to the Heaviside function

Buildings.Utilities.Math.SmoothHeaviside

Information

Once Lipschitz continuously differentiable approximation to the Heaviside(.,.) function.

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

TypeNameDefaultDescription
Realdelta Width of transition interval

Connectors

TypeNameDescription
input RealInputuConnector of Real input signal
output RealOutputyConnector of Real output signal

Modelica definition

block SmoothHeaviside 
  "Once continuously differentiable approximation to the Heaviside function"
  extends Modelica.Blocks.Interfaces.SISO;
 parameter Real delta "Width of transition interval";
equation 
  y = Buildings.Utilities.Math.Functions.smoothHeaviside(x=u, delta=delta);
end SmoothHeaviside;

Buildings.Utilities.Math.SmoothLimit Buildings.Utilities.Math.SmoothLimit

Once continuously differentiable approximation to the limit function

Buildings.Utilities.Math.SmoothLimit

Information

Once continuously differentiable approximation to the limit(.,.) function. The output is bounded to be in [lower, upper].

Extends from Modelica.Blocks.Interfaces.SISO (Single Input Single Output continuous control block).

Parameters

TypeNameDefaultDescription
RealdeltaX Width of transition interval
Realupper Upper limit
Reallower Lower limit

Connectors

TypeNameDescription
input RealInputuConnector of Real input signal
output RealOutputyConnector of Real output signal

Modelica definition

block SmoothLimit 
  "Once continuously differentiable approximation to the limit function"
 extends Modelica.Blocks.Interfaces.SISO;
 parameter Real deltaX "Width of transition interval";
 parameter Real upper "Upper limit";
 parameter Real lower "Lower limit";
equation 
  y = Buildings.Utilities.Math.Functions.smoothLimit(u, lower, upper, deltaX);
end SmoothLimit;

Buildings.Utilities.Math.SmoothMax Buildings.Utilities.Math.SmoothMax

Once continuously differentiable approximation to the maximum function

Buildings.Utilities.Math.SmoothMax

Information

Once continuously differentiable approximation to the max(.,.) function.

Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

TypeNameDefaultDescription
RealdeltaX Width of transition interval

Connectors

TypeNameDescription
input RealInputu1Connector of Real input signal 1
input RealInputu2Connector of Real input signal 2
output RealOutputyConnector of Real output signal

Modelica definition

block SmoothMax 
  "Once continuously differentiable approximation to the maximum function"
  extends Modelica.Blocks.Interfaces.SI2SO;
 parameter Real deltaX "Width of transition interval";
equation 
  y =  Buildings.Utilities.Math.Functions.smoothMax(x1=u1, x2=u2, deltaX=deltaX);
end SmoothMax;

Buildings.Utilities.Math.SmoothMin Buildings.Utilities.Math.SmoothMin

Once continuously differentiable approximation to the minimum function

Buildings.Utilities.Math.SmoothMin

Information

Once continuously differentiable approximation to the max(.,.) function.

Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

TypeNameDefaultDescription
RealdeltaX Width of transition interval

Connectors

TypeNameDescription
input RealInputu1Connector of Real input signal 1
input RealInputu2Connector of Real input signal 2
output RealOutputyConnector of Real output signal

Modelica definition

block SmoothMin 
  "Once continuously differentiable approximation to the minimum function"
  extends Modelica.Blocks.Interfaces.SI2SO;
  parameter Real deltaX "Width of transition interval";
equation 
  y = Buildings.Utilities.Math.Functions.smoothMin(x1=u1, x2=u2, deltaX=deltaX);
end SmoothMin;

Buildings.Utilities.Math.Splice Buildings.Utilities.Math.Splice

Block for splice function opertation

Buildings.Utilities.Math.Splice

Information

This block implements Buildings.Utilities.Math.Functions.spliceFunction, which provides a continuously differentiable transition between two arguments.

Extends from Modelica.Blocks.Interfaces.BlockIcon (Basic graphical layout of input/output block).

Parameters

TypeNameDefaultDescription
Realdeltax Half width of transition interval

Connectors

TypeNameDescription
input RealInputxIndependent value
input RealInputu1Argument of u > 0 (pos)
input RealInputu2Argument of u < 0 (neg)
output RealOutputySmoothed value

Modelica definition

block Splice "Block for splice function opertation"
  extends Modelica.Blocks.Interfaces.BlockIcon;

  Modelica.Blocks.Interfaces.RealInput x "Independent value";
  Modelica.Blocks.Interfaces.RealInput u1 "Argument of u > 0 (pos)";
  Modelica.Blocks.Interfaces.RealInput u2 "Argument of u < 0 (neg)";
  Modelica.Blocks.Interfaces.RealOutput y "Smoothed value";
parameter Real deltax "Half width of transition interval";
equation 
  y=Buildings.Utilities.Math.Functions.spliceFunction(
    pos=u1,
    neg= u2,
    x= x,
    deltax= deltax);
end Splice;

Automatically generated Wed Feb 12 08:20:59 2014.