Buildings.Utilities.Math

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

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

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

Type	Name	Default	Description
Integer	nin	1	Number of inputs

Connectors

Type	Name	Description
input RealInput	u[nin]	Connector of Real input signals
output RealOutput	y	Connector 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

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

Type	Name	Description
input RealInput	u1	Connector of Real input signal 1
input RealInput	u2	Connector of Real input signal 2
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Real	a[6]		Coefficients

Connectors

Type	Name	Description
input RealInput	u1	Connector of Real input signal 1
input RealInput	u2	Connector of Real input signal 2
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Integer	nout	1	Number of outputs

Connectors

Type	Name	Description
input BooleanInput	u	Connector of boolean input signal
output BooleanOutput	y[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

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

Type	Name	Default	Description
Integer	nout	1	Number of outputs

Connectors

Type	Name	Description
input IntegerInput	u	Connector of integer input signal
output IntegerOutput	y[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

Information

Outputs the minimum of the vector.

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

Parameters

Type	Name	Default	Description
Integer	nin	1	Number of inputs

Connectors

Type	Name	Description
input RealInput	u[nin]	Connector of Real input signals
output RealOutput	y	Connector 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

Information

Outputs the minimum of the vector.

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

Parameters

Type	Name	Default	Description
Integer	nin	1	Number of inputs

Connectors

Type	Name	Description
input RealInput	u[nin]	Connector of Real input signals
output RealOutput	y	Connector 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

Information

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

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

Parameters

Type	Name	Default	Description
Real	delta		Width of transition interval

Connectors

Type	Name	Description
input RealInput	u	Connector of Real input signal
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Real	deltaX		Width of transition interval
Real	upper		Upper limit
Real	lower		Lower limit

Connectors

Type	Name	Description
input RealInput	u	Connector of Real input signal
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Real	deltaX		Width of transition interval

Connectors

Type	Name	Description
input RealInput	u1	Connector of Real input signal 1
input RealInput	u2	Connector of Real input signal 2
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Real	deltaX		Width of transition interval

Connectors

Type	Name	Description
input RealInput	u1	Connector of Real input signal 1
input RealInput	u2	Connector of Real input signal 2
output RealOutput	y	Connector 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

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

Type	Name	Default	Description
Real	deltax		Half width of transition interval

Connectors

Type	Name	Description
input RealInput	x	Independent value
input RealInput	u1	Argument of u > 0 (pos)
input RealInput	u2	Argument of u < 0 (neg)
output RealOutput	y	Smoothed 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;