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. In particular the following operations and functions are provided:

   Gain          Output the input multiplied by a scalar gain           
   MatrixGain    Output the product of a gain matrix with the input
   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 
   Add3          Output the sum of the three inputs 
   Product       Output product of the two inputs 
   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
   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 
   Log10         Output the base 10 logarithm of the input    

Main Author:

Martin Otter
Deutsches Zentrum fuer Luft und Raumfahrt e.V. (DLR)
Oberpfaffenhofen
Postfach 1116
D-82230 Wessling
email: Martin.Otter@dlr.de

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized (partly based on an existing Dymola library of Dieter Moormann and Hilding Elmqvist).

Copyright (C) 1999-2000, Modelica Association and DLR.

The Modelica package is free software; it can be redistributed and/or modified under the terms of the Modelica license, see the license conditions and the accompanying disclaimer in the documentation of package Modelica in file "Modelica/package.mo".

Modelica.Blocks.Math.Gain

Information

This blocks computes output y=outPort.signal as element-wise product of gain k with the input u = inPort.signal:

    y[i] = k[i] * u[i];

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
k[:]	{1}	Gain vector multiplied element-wise with input vector

Modelica definition

block Gain 
  "Output the element-wise product of a gain vector with the input signal vector"
   
  
  parameter Real k[:]={1} 
    "Gain vector multiplied element-wise with input vector";
protected 
  Real u[size(k, 1)] "Input signals";
  Real y[size(k, 1)] "Output signals";
public 
  Interfaces.InPort inPort(final n=size(k, 1)) 
    "Input signal connector";
  Interfaces.OutPort outPort(final n=size(k, 1)) 
    "Output signal connector";
equation 
  u = inPort.signal;
  y = outPort.signal;
  for i in 1:size(k, 1) loop
    y[i] = k[i]*u[i];
  end for;
end Gain;

Modelica.Blocks.Math.Add3

Information

This blocks computes output y=outPort.signal as sum of the three input signals u1=inPort1.signal, u2=inPort2.signal and u3=inPort3.signal:

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

Example:

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

  results in the following equations:
     
     y[1] = 2 * u1[1] - 3 * u2[1] + u3[1]; 
     y[2] = 2 * u1[2] - 3 * u2[2] + u3[2];

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
k1	+1	Gain of upper input
k2	+1	Gain of middle input
k3	+1	Gain of lower input
n	1	Dimension of input and output vectors.

Modelica definition

block Add3 "Output the sum of the three inputs" 
  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";
  parameter Integer n=1 "Dimension of input and output vectors.";
  Interfaces.InPort inPort1(final n=n) 
    "Connector 1 of Real input signals";
  Interfaces.InPort inPort2(final n=n) 
    "Connector 2 of Real input signals";
  Interfaces.InPort inPort3(final n=n) 
    "Connector 3 of Real input signals";
  Interfaces.OutPort outPort(final n=n) 
    "Connector of Real output signals";
equation 
  outPort.signal = k1*inPort1.signal + k2*inPort2.signal + k3*inPort3.signal;
end Add3;

Modelica.Blocks.Math.Add

Information

This blocks computes output y=outPort.signal as sum of the two input signals u1=inPort1.signal and u2=inPort2.signal:

    y = k1*u1 + k2*u2;

Example:

     parameter:   n = 2, k1= +2, k2= -3

  results in the following equations:
     
     y[1] = 2 * u1[1] - 3 * u2[1] 
     y[2] = 2 * u1[2] - 3 * u2[2]

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Dimension of input and output vectors.
k1	+1	Gain of upper input
k2	+1	Gain of lower input

Modelica definition

block Add "Output the sum of the two inputs" 
  extends Interfaces.MI2MO;
  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.MatrixGain

Information

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

    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] |

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
K[:, :]	[1, 0; 0, 1]	Gain matrix which is multiplied with the input

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.Sum

Information

This blocks computes output y=outPort.signal[1] as sum of the elements of the input signal vector u=inPort.signal:

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

Example:

     parameter:   nin = 3;

  results in the following equations:
     
     y = u[1] + u[2] + u[3];

Release Notes:

• Oct. 24, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
nin	1	Number of inputs

Modelica definition

block Sum "Output the sum of the elements of the input vector" 
  extends Interfaces.MISO;
algorithm 
  y := u[1];
  for i in 2:nin loop
    y := y + u[i];
  end for;
end Sum;

Modelica.Blocks.Math.Feedback

Information

This blocks computes output y=outPort.signal as difference of the commanded input u1=inPort1.signal and the feedback input u2=inPort2.signal:

    y = u1 - u2;

Example:

     parameter:   n = 2

  results in the following equations:
     
     y[1] = u1[1] - u2[1] 
     y[2] = u1[2] - u2[2]

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	size of input and feedback signal

Modelica definition

block Feedback 
  "Output difference between commanded and feedback input" 
  parameter Integer n=1 "size of input and feedback signal";
  Interfaces.InPort inPort1(final n=n);
  Interfaces.InPort inPort2(final n=n);
  Interfaces.OutPort outPort(final n=n);
equation 
  outPort.signal = inPort1.signal - inPort2.signal;
end Feedback;

Modelica.Blocks.Math.Product

Information

This blocks computes the output y=outPort.signal element-wise as product of the corresponding elements of the two inputs u1=inPort1.signal and u2=inPort2.signal:

    y[i] = u1[i] * u2[i];

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Dimension of input and output vectors.

Modelica definition

block Product "Output product of the two inputs" 
  extends Interfaces.MI2MO;
equation 
  for i in 1:n loop
    y[i] = u1[i]*u2[i];
  end for;
end Product;

Modelica.Blocks.Math.Division

Information

This block computes the output y=outPort.signal element-wise by dividing the corresponding elements of the two inputs u1=inPort1.signal and u2=inPort2.signal:

    y[i] = u1[i] / u2[i];

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Dimension of input and output vectors.

Modelica definition

block Division "Output first input divided by second input" 
  extends Interfaces.MI2MO;
equation 
  for i in 1:n loop
    y[i] = u1[i]/u2[i];
  end for;
end Division;

Modelica.Blocks.Math.Abs

Information

This blocks computes the output y=outPort.signal element-wise as absolute value of the input u=inPort.signal:

    y[i] = abs( u[i] );

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

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

Modelica.Blocks.Math.Sign

Information

This blocks computes the output y=outPort.signal element-wise as sign of the input u=inPort.signal:

            1  if u[i] > 0
    y[i] =  0  if u[i] == 0
           -1  if u[i] < 0 

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

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

Modelica.Blocks.Math.Sqrt

Information

This blocks computes the output y=outPort.signal element-wise as square root of the input u=inPort.signal:

    y[i] = sqrt( u[i] );

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

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

block Sqrt 
  "Output the square root of the input (input >= 0 required)" 
  extends Interfaces.MIMOs;
equation 
  y = sqrt(u);
end Sqrt;

Modelica.Blocks.Math.Sin

Information

This blocks computes the output y=outPort.signal element-wise as sine of the input u=inPort.signal:

    y[i] = sin( u[i] );

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

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

Modelica.Blocks.Math.Cos

Information

This blocks computes the output y=outPort.signal element-wise as cos of the input u=inPort.signal:

    y[i] = cos( u[i] );

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

block Cos "Output the cosine of the input" 
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.cos(u);
end Cos;

Modelica.Blocks.Math.Tan

Information

This blocks computes the output y=outPort.signal element-wise as tan of the input u=inPort.signal:

    y[i] = tan( u[i] );

Release Notes:

• August 7, 1999 by Martin Otter:
  Realized.

Parameters

Name	Default	Description
n	1	Number of inputs (= number of outputs)

Modelica definition

block Tan "Output the tangent of the input" 
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.tan(u);
end Tan;

Modelica.Blocks.Math.Asin

Information

This blocks computes the output y=outPort.signal element-wise as the sine-inverse of the input u=inPort.signal:

    y[i] = asin( u[i] );

block Asin "Output the arc sine of the input" 
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.asin(u);
end Asin;

    y[i] = acos( u[i] );

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

    y[i] = atan( u[i] );

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

    y[i] = atan2( u1[i], u2[i] );

block Atan2 "Output atan(u1/u2) of the inputs u1 and u2" 
  extends Interfaces.MI2MO;
equation 
  y = Modelica.Math.atan2(u1, u2);
end Atan2;

    y[i] = sinh( u[i] );

block Sinh "Output the hyperbolic sine of the input" 
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.sinh(u);
end Sinh;

    y[i] = cosh( u[i] );

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

    y[i] = tanh( u[i] );

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

    y[i] = exp( u[i] );

block Exp "Output the exponential (base e) of the input" 
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.exp(u);
end Exp;

    y[i] = log( u[i] );

block Log 
  "Output the natural (base e) logarithm of the input (input > 0 required)"
   
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.log(u);
end Log;

    y[i] = log10( u[i] );

block Log10 
  "Output the base 10 logarithm of the input (input > 0 required)"
   
  
  extends Interfaces.MIMOs;
equation 
  y = Modelica.Math.log10(u);
end Log10;