Modelica.Blocks.Math

Information

This package contains basic mathematical operations, such as summation and multiplication, and basic mathematical functions, such as sqrt and sin, as input/output blocks. All blocks of this library can be either connected with continuous blocks or with sampled-data blocks.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
UnitConversions	Conversion blocks to convert between SI and non-SI unit signals
InverseBlockConstraints	Construct inverse model by requiring that two inputs and two outputs are identical (replaces the previously, unbalanced, TwoInputs and TwoOutputs blocks)
Gain	Output the product of a gain value with the input signal
MatrixGain	Output the product of a gain matrix with the input signal vector
MultiSum	Sum of Reals: y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]
MultiProduct	Product of Reals: y = u[1]*u[2]* ... *u[n]
MultiSwitch	Set Real expression that is associated with the first active input signal
Sum	Output the sum of the elements of the input vector
Feedback	Output difference between commanded and feedback input
Add	Output the sum of the two inputs (this is an obsolet block. Use instead MultiSum)
Add3	Output the sum of the three inputs (this is an obsolet block. Use instead MultiSum)
Product	Output product of the two inputs (this is an obsolet block. Use instead MultiProduct)
Division	Output first input divided by second input
Abs	Output the absolute value of the input
Sign	Output the sign of the input
Sqrt	Output the square root of the input (input >= 0 required)
Sin	Output the sine of the input
Cos	Output the cosine of the input
Tan	Output the tangent of the input
Asin	Output the arc sine of the input
Acos	Output the arc cosine of the input
Atan	Output the arc tangent of the input
Atan2	Output atan(u1/u2) of the inputs u1 and u2
Sinh	Output the hyperbolic sine of the input
Cosh	Output the hyperbolic cosine of the input
Tanh	Output the hyperbolic tangent of the input
Exp	Output the exponential (base e) of the input
Log	Output the natural (base e) logarithm of the input (input > 0 required)
Log10	Output the base 10 logarithm of the input (input > 0 required)
RealToInteger	Convert Real to Integer signal
IntegerToReal	Convert integer to real signals
BooleanToReal	Convert Boolean to Real signal
BooleanToInteger	Convert Boolean to Integer signal
RealToBoolean	Convert Real to Boolean signal
IntegerToBoolean	Convert Integer to Boolean signal
RectangularToPolar	Convert rectangular coordinates to polar coordinates
PolarToRectangular	Convert polar coordinates to rectangular coordinates
Mean	Calculate mean over period 1/f
RectifiedMean	Calculate refctified mean over period 1/f
RootMeanSquare	Calculate root mean square over period 1/f
Harmonic	Calculate harmonic over period 1/f
Max	Pass through the largest signal
Min	Pass through the smallest signal
Edge	Indicates rising edge of boolean signal
BooleanChange	Indicates boolean signal changing
IntegerChange	Indicates integer signal changing

Modelica.Blocks.Math.InverseBlockConstraints

Information

Exchange input and ouput signals of a block, i.e., the previous block inputs become block outputs and the previous block outputs become block inputs. This block is used to construct inverse models. Its usage is demonstrated in example: Modelica.Blocks.Examples.InverseModel.

Note, if a block shall be inverted that has several input and output blocks, then this can be easily achieved by using a vector of InverseBlockConstraints instances:

   InverseBlockConstraint invert[3];  // Block to be inverted has 3 input signals

Connectors

Type	Name	Description
input RealInput	u1	Input signal 1 (u1 = u2)
input RealInput	u2	Input signal 2 (u1 = u2)
output RealOutput	y1	Output signal 1 (y1 = y2)
output RealOutput	y2	Output signal 2 (y2 = y2)

Modelica definition

block InverseBlockConstraints 
  "Construct inverse model by requiring that two inputs and two outputs are identical (replaces the previously, unbalanced, TwoInputs and TwoOutputs blocks)"

  Modelica.Blocks.Interfaces.RealInput u1 "Input signal 1 (u1 = u2)";
  Modelica.Blocks.Interfaces.RealInput u2 "Input signal 2 (u1 = u2)";
  Modelica.Blocks.Interfaces.RealOutput y1 "Output signal 1 (y1 = y2)";
  Modelica.Blocks.Interfaces.RealOutput y2 "Output signal 2 (y2 = y2)";

equation 
  u1 = u2;
  y1 = y2;
end InverseBlockConstraints;

Modelica.Blocks.Math.Gain

Information

This block computes output y as product of gain k with the input u:

    y = k * u;

Parameters

Type	Name	Default	Description
Real	k		Gain value multiplied with input signal [1]

Connectors

Type	Name	Description
input RealInput	u	Input signal connector
output RealOutput	y	Output signal connector

Modelica definition

block Gain "Output the product of a gain value with the input signal"

  parameter Real k(start=1, unit="1") "Gain value multiplied with input signal";
public 
  Interfaces.RealInput u "Input signal connector";
  Interfaces.RealOutput y "Output signal connector";

equation 
  y = k*u;
end Gain;

Modelica.Blocks.Math.MatrixGain

Information

This blocks computes output vector y as product of the gain matrix K with the input signal vector u:

    y = K * u;

Example:

   parameter: K = [0.12 2; 3 1.5]

   results in the following equations:

     | y[1] |     | 0.12  2.00 |   | u[1] |
     |      |  =  |            | * |      |
     | y[2] |     | 3.00  1.50 |   | u[2] |

Extends from Interfaces.MIMO (Multiple Input Multiple Output continuous control block).

Parameters

Type	Name	Default	Description
Real	K[:, :]	[1, 0; 0, 1]	Gain matrix which is multiplied with the input
Integer	nin	size(K, 2)	Number of inputs
Integer	nout	size(K, 1)	Number of outputs

Connectors

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

Modelica definition

block MatrixGain 
  "Output the product of a gain matrix with the input signal vector"

  parameter Real K[:, :]=[1, 0; 0, 1] 
    "Gain matrix which is multiplied with the input";
  extends Interfaces.MIMO(final nin=size(K, 2), final nout=size(K, 1));
equation 
  y = K*u;
end MatrixGain;

Modelica.Blocks.Math.MultiSum

Information

This blocks computes the scalar Real output "y" as sum of the elements of the Real input signal vector u:

y = k[1]*u[1] + k[2]*u[2] + ... k[N]*u[N];

The input connector is a vector of Real input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.RealNetwork1.

If no connection to the input connector "u" is present, the output is set to zero: y=0.

Extends from Modelica.Blocks.Interfaces.PartialRealMISO (Partial block with a RealVectorInput and a RealOutput signal).

Parameters

Type	Name	Default	Description
Real	k[nu]	fill(1, nu)	Input gains
Advanced
Integer	significantDigits	3	Number of significant digits to be shown in dynamic diagram layer for y

Connectors

Type	Name	Description
input RealVectorInput	u[nu]
output RealOutput	y

Modelica definition

block MultiSum 
  "Sum of Reals: y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]"
   extends Modelica.Blocks.Interfaces.PartialRealMISO;
   parameter Real k[nu] = fill(1,nu) "Input gains";
equation 
  if size(u,1) > 0 then
     y = k*u;
  else
     y = 0;
  end if;

end MultiSum;

Modelica.Blocks.Math.MultiProduct

Information

This blocks computes the scalar Real output "y" as product of the elements of the Real input signal vector u:

y = u[1]*u[2]* ... *u[N];

The input connector is a vector of Real input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.RealNetwork1.

If no connection to the input connector "u" is present, the output is set to zero: y=0.

Extends from Modelica.Blocks.Interfaces.PartialRealMISO (Partial block with a RealVectorInput and a RealOutput signal).

Parameters

Type	Name	Default	Description
Advanced
Integer	significantDigits	3	Number of significant digits to be shown in dynamic diagram layer for y

Connectors

Type	Name	Description
input RealVectorInput	u[nu]
output RealOutput	y

Modelica definition

block MultiProduct "Product of Reals: y = u[1]*u[2]* ... *u[n]"
   extends Modelica.Blocks.Interfaces.PartialRealMISO;
equation 
  if size(u,1) > 0 then
     y = product(u);
  else
     y = 0;
  end if;

end MultiProduct;

Modelica.Blocks.Math.MultiSwitch

Information

This block has a vector of Boolean input signals u[nu] and a vector of (time varying) Real expressions expr[nu]. The output signal y is set to expr[i], if i is the first element in the input vector u that is true. If all input signals are false, y is set to parameter "y_default".

  // Conceptual equation (not valid Modelica)
  i = 'first element of u[:] that is true';
  y = if i==0 then y_default else expr[i];

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.RealNetwork1.

Parameters

Type	Name	Default	Description
Real	expr[nu]	fill(0.0, nu)	y = if u[i] then expr[i] else y_default (time varying)
Real	y_default	0.0	Default value of output y if all u[i] = false
Advanced
Integer	precision	3	Number of significant digits to be shown in dynamic diagram layer for y

Connectors

Type	Name	Description
input BooleanVectorInput	u[nu]	Set y = expr[i], if u[i] = true
output RealOutput	y	Output depending on expression

Modelica definition

block MultiSwitch 
  "Set Real expression that is associated with the first active input signal"

    input Real expr[nu]=fill(0.0, nu) 
    "y = if u[i] then expr[i] else y_default (time varying)";
    parameter Real y_default=0.0 
    "Default value of output y if all u[i] = false";

    parameter Integer nu(min=0) = 0 "Number of input connections";
    parameter Integer precision(min=0) = 3 
    "Number of significant digits to be shown in dynamic diagram layer for y";

    Modelica.Blocks.Interfaces.BooleanVectorInput u[nu] 
    "Set y = expr[i], if u[i] = true";
  Modelica.Blocks.Interfaces.RealOutput y(start=y_default,fixed=true) 
    "Output depending on expression";

protected 
  Integer firstActiveIndex;
initial equation 
  pre(u) = fill(false,nu);
equation 
  firstActiveIndex = Modelica.Math.BooleanVectors.firstTrueIndex(
                                                  u);
   y = if firstActiveIndex == 0 then y_default else expr[firstActiveIndex];
end MultiSwitch;

Modelica.Blocks.Math.Sum

Information

This blocks computes output y as sum of the elements of the input signal vector u:

    y = u[1] + u[2] + ...;

Example:

     parameter:   nin = 3;

  results in the following equations:

     y = u[1] + u[2] + u[3];

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

Parameters

Type	Name	Default	Description
Integer	nin	1	Number of inputs
Real	k[nin]	ones(nin)	Optional: sum coefficients

Connectors

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

Modelica definition

block Sum "Output the sum of the elements of the input vector"
  extends Interfaces.MISO;
  parameter Real k[nin]=ones(nin) "Optional: sum coefficients";
equation 
  y = k*u;
end Sum;

Modelica.Blocks.Math.Feedback

Information

This blocks computes output y as difference of the commanded input u1 and the feedback input u2:

    y = u1 - u2;

Example:

     parameter:   n = 2

  results in the following equations:

     y = u1 - u2

Connectors

Type	Name	Description
input RealInput	u1
input RealInput	u2
output RealOutput	y

Modelica definition

block Feedback 
  "Output difference between commanded and feedback input"

  input Interfaces.RealInput u1;
  input Interfaces.RealInput u2;
  output Interfaces.RealOutput y;

equation 
  y = u1 - u2;
end Feedback;

Modelica.Blocks.Math.Add

Information

This blocks computes output y as sum of the two input signals u1 and u2:

    y = k1*u1 + k2*u2;

Example:

     parameter:   k1= +2, k2= -3

  results in the following equations:

     y = 2 * u1 - 3 * u2

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

Parameters

Type	Name	Default	Description
Real	k1	+1	Gain of upper input
Real	k2	+1	Gain of lower input

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 Add 
  "Output the sum of the two inputs (this is an obsolet block. Use instead MultiSum)"
  extends Interfaces.SI2SO;
  parameter Real k1=+1 "Gain of upper input";
  parameter Real k2=+1 "Gain of lower input";

equation 
  y = k1*u1 + k2*u2;
end Add;

Modelica.Blocks.Math.Add3

Information

This blocks computes output y as sum of the three input signals u1, u2 and u3:

    y = k1*u1 + k2*u2 + k3*u3;

Example:

     parameter:   k1= +2, k2= -3, k3=1;

  results in the following equations:

     y = 2 * u1 - 3 * u2 + u3;

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

Parameters

Type	Name	Default	Description
Real	k1	+1	Gain of upper input
Real	k2	+1	Gain of middle input
Real	k3	+1	Gain of lower input

Connectors

Type	Name	Description
input RealInput	u1	Connector 1 of Real input signals
input RealInput	u2	Connector 2 of Real input signals
input RealInput	u3	Connector 3 of Real input signals
output RealOutput	y	Connector of Real output signals

Modelica definition

block Add3 
  "Output the sum of the three inputs (this is an obsolet block. Use instead MultiSum)"
  extends Interfaces.BlockIcon;

  parameter Real k1=+1 "Gain of upper input";
  parameter Real k2=+1 "Gain of middle input";
  parameter Real k3=+1 "Gain of lower input";
  input Interfaces.RealInput u1 "Connector 1 of Real input signals";
  input Interfaces.RealInput u2 "Connector 2 of Real input signals";
  input Interfaces.RealInput u3 "Connector 3 of Real input signals";
  output Interfaces.RealOutput y "Connector of Real output signals";

equation 
  y = k1*u1 + k2*u2 + k3*u3;
end Add3;

Modelica.Blocks.Math.Product

Information

This blocks computes the output y (element-wise) as product of the corresponding elements of the two inputs u1 and u2:

    y = u1 * u2;

Extends from 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 Product 
  "Output product of the two inputs (this is an obsolet block. Use instead MultiProduct)"
  extends Interfaces.SI2SO;

equation 
  y = u1*u2;
end Product;

Modelica.Blocks.Math.Division

Information

This block computes the output y (element-wise) by dividing the corresponding elements of the two inputs u1 and u2:

    y = u1 / u2;

Extends from 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 Division "Output first input divided by second input"
  extends Interfaces.SI2SO;

equation 
  y = u1/u2;
end Division;

Modelica.Blocks.Math.Abs

Information

This blocks computes the output y as absolute value of the input u:

    y = abs( u );

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

Connectors

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

Modelica definition

block Abs "Output the absolute value of the input"
  extends Interfaces.SISO;
equation 
  y = abs(u);
end Abs;

Modelica.Blocks.Math.Sign

Information

This blocks computes the output y as sign of the input u:

         1  if u > 0
    y =  0  if u == 0
        -1  if u < 0

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

Connectors

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

Modelica definition

block Sign "Output the sign of the input"
  extends Interfaces.SISO;
equation 
  y = sign(u);
end Sign;

Modelica.Blocks.Math.Sqrt

Information

This blocks computes the output y as square root of the input u:

    y = sqrt( u );

All elements of the input vector shall be zero or positive. Otherwise an error occurs.

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

Connectors

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

Modelica definition

block Sqrt 
  "Output the square root of the input (input >= 0 required)"
  extends Interfaces.SISO;

equation 
  y = sqrt(u);
end Sqrt;

Modelica.Blocks.Math.Sin

Information

This blocks computes the output y as sine of the input u:

    y = sin( u );

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

Connectors

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

Modelica definition

block Sin "Output the sine of the input"
  extends Interfaces.SISO;
equation 
  y = Modelica.Math.sin(u);
end Sin;

Modelica.Blocks.Math.Cos

Information

This blocks computes the output y as cos of the input u:

    y = cos( u );

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

Connectors

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

Modelica definition

block Cos "Output the cosine of the input"
  extends Interfaces.SISO;

equation 
  y = Modelica.Math.cos(u);
end Cos;

Modelica.Blocks.Math.Tan

Information

This blocks computes the output y as tan of the input u:

    y = tan( u );

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

Connectors

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

Modelica definition

block Tan "Output the tangent of the input"
  extends Interfaces.SISO;

equation 
  y = Modelica.Math.tan(u);
end Tan;

Modelica.Blocks.Math.Asin

Information

This blocks computes the output y as the sine-inverse of the input u:

    y = asin( u );

The absolute values of the elements of the input u need to be less or equal to one (abs( u ) <= 1). Otherwise an error occurs.

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

Connectors

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

Modelica definition

block Asin "Output the arc sine of the input"
  extends Interfaces.SISO;

equation 
  y = Modelica.Math.asin(u);
end Asin;

Modelica.Blocks.Math.Acos

Information

This blocks computes the output y as the cosine-inverse of the input u:

    y = acos( u );

The absolute values of the elements of the input u need to be less or equal to one (abs( u ) <= 1). Otherwise an error occurs.

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

Connectors

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

Modelica definition

block Acos "Output the arc cosine of the input"
  extends Interfaces.SISO;
equation 
  y = Modelica.Math.acos(u);
end Acos;

Modelica.Blocks.Math.Atan

Information

This blocks computes the output y as the tangent-inverse of the input u:

    y= atan( u );

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

Connectors

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

Modelica definition

block Atan "Output the arc tangent of the input"
  extends Interfaces.SISO;
equation 
  y = Modelica.Math.atan(u);
end Atan;

Modelica.Blocks.Math.Atan2

Information

This blocks computes the output y as the tangent-inverse of the input u1 divided by input u2:

    y = atan2( u1, u2 );

u1 and u2 shall not be zero at the same time instant. Atan2 uses the sign of u1 and u2 in order to construct the solution in the range -180 deg ≤ y ≤ 180 deg, whereas block Atan gives a solution in the range -90 deg ≤ y ≤ 90 deg.

Extends from 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 Atan2 "Output atan(u1/u2) of the inputs u1 and u2"
  extends Interfaces.SI2SO;
equation 
  y = Modelica.Math.atan2(u1, u2);
end Atan2;

Modelica.Blocks.Math.Sinh

Information

This blocks computes the output y as the hyperbolic sine of the input u:

    y = sinh( u );

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

Connectors

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

Modelica definition

block Sinh "Output the hyperbolic sine of the input"
  extends Interfaces.SISO;

equation 
  y = Modelica.Math.sinh(u);
end Sinh;

Modelica.Blocks.Math.Cosh

Information

This blocks computes the output y as the hyperbolic cosine of the input u:

    y = cosh( u );

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

Connectors

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

Modelica definition

block Cosh "Output the hyperbolic cosine of the input"
  extends Interfaces.SISO;
equation 
  y = Modelica.Math.cosh(u);
end Cosh;

Modelica.Blocks.Math.Tanh

Information

This blocks computes the output y as the hyperbolic tangent of the input u:

    y = tanh( u );

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

Connectors

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

Modelica definition

block Tanh "Output the hyperbolic tangent of the input"
  extends Interfaces.SISO;
equation 
  y = Modelica.Math.tanh(u);
end Tanh;

Modelica.Blocks.Math.Exp

Information

This blocks computes the output y as the exponential (of base e) of the input u:

    y = exp( u );

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

Connectors

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

Modelica definition

block Exp "Output the exponential (base e) of the input"
  extends Interfaces.SISO;

equation 
  y = Modelica.Math.exp(u);
end Exp;

Modelica.Blocks.Math.Log

Information

This blocks computes the output y as the natural (base e) logarithm of the input u:

    y = log( u );

An error occurs if the elements of the input u are zero or negative.

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

Connectors

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

Modelica definition

block Log 
  "Output the natural (base e) logarithm of the input (input > 0 required)"

  extends Interfaces.SISO;
equation 
  y = Modelica.Math.log(u);
end Log;

Modelica.Blocks.Math.Log10

Information

This blocks computes the output y as the base 10 logarithm of the input u:

    y = log10( u );

An error occurs if the elements of the input u are zero or negative.

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

Connectors

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

Modelica definition

block Log10 
  "Output the base 10 logarithm of the input (input > 0 required)"

  extends Interfaces.SISO;
equation 
  y = Modelica.Math.log10(u);
end Log10;

Modelica.Blocks.Math.RealToInteger

Information

This block computes the output y as nearest integer value of the input u:

    y = integer( floor( u + 0.5 ) )  for  u > 0;
    y = integer( ceil ( u - 0.5 ) )  for  u < 0;

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

Connectors

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

Modelica definition

block RealToInteger "Convert Real to Integer signal"
  extends Interfaces.IntegerBlockIcon;
public 
  Interfaces.RealInput u "Connector of Real input signal";
  Interfaces.IntegerOutput y "Connector of Integer output signal";
equation 
   y = if (u > 0) then integer(floor(u + 0.5)) else 
                       integer(ceil( u - 0.5));
end RealToInteger;

Modelica.Blocks.Math.IntegerToReal

Information

This block computes the output y as Real equivalent of the Integer input u:

    y = u;

where u is of Integer and y of Real type.

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

Connectors

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

Modelica definition

block IntegerToReal "Convert integer to real signals"
  extends Interfaces.BlockIcon;
  Interfaces.IntegerInput u "Connector of Integer input signal";
  Interfaces.RealOutput y "Connector of Real output signal";
equation 
  y = u;
end IntegerToReal;

Modelica.Blocks.Math.BooleanToReal

Information

This block computes the output y as Real equivalent of the Boolean input u:

    y = if u then realTrue else realFalse;

where u is of Boolean and y of Real type, and realTrue and realFalse are parameters.

Extends from Interfaces.partialBooleanSI (Partial block with 1 input Boolean signal).

Parameters

Type	Name	Default	Description
Real	realTrue	1.0	Output signal for true Boolean input
Real	realFalse	0.0	Output signal for false Boolean input

Connectors

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

Modelica definition

block BooleanToReal "Convert Boolean to Real signal"
  extends Interfaces.partialBooleanSI;
  parameter Real realTrue=1.0 "Output signal for true Boolean input";
  parameter Real realFalse=0.0 "Output signal for false Boolean input";

  Blocks.Interfaces.RealOutput y "Connector of Real output signal";

equation 
  y = if u then realTrue else realFalse;
end BooleanToReal;

Modelica.Blocks.Math.BooleanToInteger

Information

This block computes the output y as Integer equivalent of the Boolean input u:

    y = if u then integerTrue else integerFalse;

where u is of Boolean and y of Integer type, and integerTrue and integerFalse are parameters.

Extends from Interfaces.partialBooleanSI (Partial block with 1 input Boolean signal).

Parameters

Type	Name	Default	Description
Integer	integerTrue	1	Output signal for true Boolean input
Integer	integerFalse	0	Output signal for false Boolean input

Connectors

Type	Name	Description
input BooleanInput	u	Connector of Boolean input signal
output IntegerOutput	y	Connector of Integer output signal

Modelica definition

block BooleanToInteger "Convert Boolean to Integer signal"
  extends Interfaces.partialBooleanSI;
  parameter Integer integerTrue=1 "Output signal for true Boolean input";
  parameter Integer integerFalse=0 "Output signal for false Boolean input";

  Blocks.Interfaces.IntegerOutput y "Connector of Integer output signal";

equation 
  y = if u then integerTrue else integerFalse;
end BooleanToInteger;

Modelica.Blocks.Math.RealToBoolean

Information

This block computes the Boolean output y from the Real input u by the equation:

    y = u ≥ threshold;

where threshold is a parameter.

Extends from Interfaces.partialBooleanSO (Partial block with 1 output Boolean signal).

Parameters

Type	Name	Default	Description
Real	threshold	0.5	Output signal y is true, if input u >= threshold

Connectors

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

Modelica definition

block RealToBoolean "Convert Real to Boolean signal"

  Blocks.Interfaces.RealInput u "Connector of Real input signal";
  extends Interfaces.partialBooleanSO;
  parameter Real threshold=0.5 
    "Output signal y is true, if input u >= threshold";

equation 
  y = u >= threshold;
end RealToBoolean;

Modelica.Blocks.Math.IntegerToBoolean

Information

This block computes the Boolean output y from the Integer input u by the equation:

    y = u ≥ threshold;

where threshold is a parameter.

Extends from Interfaces.partialBooleanSO (Partial block with 1 output Boolean signal).

Parameters

Type	Name	Default	Description
Integer	threshold	1	Output signal y is true, if input u >= threshold

Connectors

Type	Name	Description
input IntegerInput	u	Connector of Integer input signal
output BooleanOutput	y	Connector of Boolean output signal

Modelica definition

block IntegerToBoolean "Convert Integer to Boolean signal"

  Blocks.Interfaces.IntegerInput u "Connector of Integer input signal";
  extends Interfaces.partialBooleanSO;
  parameter Integer threshold=1 
    "Output signal y is true, if input u >= threshold";

equation 
  y = u >= threshold;
end IntegerToBoolean;

Modelica.Blocks.Math.RectangularToPolar

Information

The input values of this block are the rectangular components u_re and u_im of a phasor in two dimensions. This block calculates the length y_abs and the angle y_arg of the polar representation of this phasor.

  y_abs = abs(u_re + j*u_im) = sqrt( u_re2 + u_im2 )
  y_arg = arg(u_re + j*u_im) = atan2(u_im, u_re)

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

Connectors

Type	Name	Description
input RealInput	u_re	Real part of rectangular representation
input RealInput	u_im	Imaginary part of rectangular representation
output RealOutput	y_abs	Length of polar representation
output RealOutput	y_arg	Angle of polar representation

Modelica definition

block RectangularToPolar 
  "Convert rectangular coordinates to polar coordinates"
  extends Modelica.Blocks.Interfaces.BlockIcon;
  Modelica.Blocks.Interfaces.RealInput u_re 
    "Real part of rectangular representation";
  Modelica.Blocks.Interfaces.RealInput u_im 
    "Imaginary part of rectangular representation";
  Modelica.Blocks.Interfaces.RealOutput y_abs "Length of polar representation";
  Modelica.Blocks.Interfaces.RealOutput y_arg "Angle of polar representation";

equation 
   y_abs = sqrt(u_re*u_re + u_im*u_im);
   y_arg = Modelica.Math.atan2(u_im, u_re);
end RectangularToPolar;

Modelica.Blocks.Math.PolarToRectangular

Information

The input values of this block are the polar components uabs and uarg of a phasor. This block calculates the components y_re and y_im of the rectangular representation of this phasor.

   y_re = u_abs * cos( u_arg )
   y_im = u_abs * sin( u_arg )

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

Connectors

Type	Name	Description
input RealInput	u_abs	Length of polar representation
input RealInput	u_arg	Angle of polar representation
output RealOutput	y_re	Real part of rectangular representation
output RealOutput	y_im	Imaginary part of rectangular representation

Modelica definition

block PolarToRectangular 
  "Convert polar coordinates to rectangular coordinates"
  extends Modelica.Blocks.Interfaces.BlockIcon;
  Modelica.Blocks.Interfaces.RealInput u_abs "Length of polar representation";
  Modelica.Blocks.Interfaces.RealInput u_arg "Angle of polar representation";
  Modelica.Blocks.Interfaces.RealOutput y_re 
    "Real part of rectangular representation";
  Modelica.Blocks.Interfaces.RealOutput y_im 
    "Imaginary part of rectangular representation";

equation 
  y_re = u_abs * Modelica.Math.cos(u_arg);
  y_im = u_abs * Modelica.Math.sin(u_arg);
end PolarToRectangular;

Modelica.Blocks.Math.Mean

Information

This block calculates the mean of the input signal u over the given period 1/f:

1 T
- ∫ u(t) dt
T 0

Note: The output is updated after each period defined by 1/f.

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

Parameters

Type	Name	Default	Description
Frequency	f		Base frequency [Hz]

Connectors

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

Modelica definition

block Mean "Calculate mean over period 1/f"
  extends Modelica.Blocks.Interfaces.SISO;
  parameter Modelica.SIunits.Frequency f(start=50) "Base frequency";
protected 
  discrete Modelica.SIunits.Time t0 "Start time of simulation";
  Real x(start=0) "Integrator state";
equation 
  when initial() then
      t0 = time;
  end when;
  der(x) = u;
  when sample(t0+1/f, 1/f) then
    y=f*x;
    reinit(x, 0);
  end when;
end Mean;

Modelica.Blocks.Math.RectifiedMean

Information

This block calculates the rectified mean of the input signal u over the given period 1/f, using the mean block.

Note: The output is updated after each period defined by 1/f.

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

Parameters

Type	Name	Default	Description
Frequency	f		Base frequency [Hz]

Connectors

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

Modelica definition

block RectifiedMean "Calculate refctified mean over period 1/f"
  extends Modelica.Blocks.Interfaces.SISO;
  parameter Modelica.SIunits.Frequency f(start=50) "Base frequency";
  Mean mean(final f=f);
  Blocks.Math.Abs abs1;
equation 
  connect(u, abs1.u);
  connect(abs1.y, mean.u);
  connect(mean.y, y);
end RectifiedMean;

Modelica.Blocks.Math.RootMeanSquare

Information

This block calculates the root mean square of the input signal u over the given period 1/f, using the mean block.

Note: The output is updated after each period defined by 1/f.

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

Parameters

Type	Name	Default	Description
Frequency	f		Base frequency [Hz]

Connectors

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

Modelica definition

block RootMeanSquare "Calculate root mean square over period 1/f"
  extends Modelica.Blocks.Interfaces.SISO;
  parameter Modelica.SIunits.Frequency f(start=50) "Base frequency";
  Blocks.Math.Product product;
  Mean mean(final f=f);
  Blocks.Math.Sqrt sqrt1;
equation 

  connect(u, product.u1);
  connect(u, product.u2);
  connect(product.y, mean.u);
  connect(mean.y, sqrt1.u);
  connect(sqrt1.y, y);
end RootMeanSquare;

Modelica.Blocks.Math.Harmonic

Information

This block calculates the root mean square and the phase angle of a single harmonic k of the input signal u over the given period 1/f, using the mean block.

Note: The output is updated after each period defined by 1/f.

Note: The harmonic is defined by √2 rms cos(k 2 π f t - arg)

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

Parameters

Type	Name	Default	Description
Frequency	f		Base frequency [Hz]
Integer	k		Order of harmonic

Connectors

Type	Name	Description
input RealInput	u
output RealOutput	y_rms	Root mean square of polar representation
output RealOutput	y_arg	Angle of polar representation

Modelica definition

block Harmonic "Calculate harmonic over period 1/f"
  extends Modelica.Blocks.Interfaces.BlockIcon;
  parameter Modelica.SIunits.Frequency f(start=50) "Base frequency";
  parameter Integer k(start=1) "Order of harmonic";
  Blocks.Sources.Sine sin1(
    final amplitude=sqrt(2),
    final phase=Modelica.Constants.pi/2,
    final freqHz=k*f);
  Blocks.Sources.Sine sin2(                final amplitude=sqrt(2),
    final phase=0,
    final freqHz=k*f);
  Blocks.Math.Product product1;
  Blocks.Math.Product product2;
  Mean mean1(final f=f);
  Mean mean2(final f=f);
  Blocks.Interfaces.RealInput u;
  Blocks.Interfaces.RealOutput y_rms "Root mean square of polar representation";
  Blocks.Interfaces.RealOutput y_arg "Angle of polar representation";
  Blocks.Math.RectangularToPolar rectangularToPolar;
equation 

  connect(sin2.y, product2.u2);
  connect(sin1.y, product1.u1);
  connect(u, product1.u2);
  connect(u, product2.u1);
  connect(product2.y, mean2.u);
  connect(product1.y, mean1.u);
  connect(mean1.y, rectangularToPolar.u_re);
  connect(mean2.y, rectangularToPolar.u_im);
  connect(rectangularToPolar.y_abs, y_rms);
  connect(rectangularToPolar.y_arg, y_arg);
end Harmonic;

Modelica.Blocks.Math.Max

Information

This block computes the output y as maximum of the two Real inputs u1 and u2:

    y = max ( u1 , u2 );

Extends from 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 Max "Pass through the largest signal"
  extends Interfaces.SI2SO;
equation 
  y = max(u1, u2);
end Max;

Modelica.Blocks.Math.Min

Information

This block computes the output y as minimum of the two Real inputs u1 and u2:

    y = min ( u1 , u2 );

Extends from 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 Min "Pass through the smallest signal"
  extends Interfaces.SI2SO;
equation 
   y = min(u1, u2);
end Min;

Modelica.Blocks.Math.Edge

Information

This block sets the Boolean output y to true, when the Boolean input u shows a rising edge:

    y = edge( u );

Extends from Interfaces.BooleanSISO (Single Input Single Output control block with signals of type Boolean).

Connectors

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

Modelica definition

block Edge "Indicates rising edge of boolean signal"
  extends Interfaces.BooleanSISO;
equation 
  y = edge(u);
end Edge;

Modelica.Blocks.Math.BooleanChange

Information

This block sets the Boolean output y to true, when the Boolean input u shows a rising or falling edge, i.e., when the signal changes:

    y = change( u );

Extends from Interfaces.BooleanSISO (Single Input Single Output control block with signals of type Boolean).

Connectors

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

Modelica definition

block BooleanChange "Indicates boolean signal changing"
  extends Interfaces.BooleanSISO;
equation 
  y = change(u);
end BooleanChange;

Modelica.Blocks.Math.IntegerChange

Information

This block sets the Boolean output y to true, when the Integer input u changes:

    y = change( u );

Extends from Interfaces.IntegerSIBooleanSO (Integer Input Boolean Output continuous control block).

Connectors

Type	Name	Description
input IntegerInput	u	Connector of Integer input signal
output BooleanOutput	y	Connector of Boolean output signal

Modelica definition

block IntegerChange "Indicates integer signal changing"
  extends Interfaces.IntegerSIBooleanSO;
equation 
  y = change(u);
end IntegerChange;