Modelica.ComplexBlocks.ComplexMath

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
Gain	Output the product of a gain value with the 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
Add3	Output the sum of the three inputs
Product	Output product of the two inputs
Division	Output first input divided by second 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
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)
RealToComplex	Converts cartesian representation to complex
PolarToComplex	Converts polar representation to complex
ComplexToReal	Converts complex to cartesian representation
ComplexToPolar	Converts complex to polar representation

Modelica.ComplexBlocks.ComplexMath.Gain

Information

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

    y = k * u;

Parameters

Type	Name	Default	Description
Complex	k		Gain value multiplied with input signal

Connectors

Type	Name	Description
input ComplexInput	u	Input signal connector
output ComplexOutput	y	Output signal connector

Modelica definition

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

  parameter Complex k(re(start=1), im(start=0)) 
    "Gain value multiplied with input signal";
public 
  Interfaces.ComplexInput u "Input signal connector";
  Interfaces.ComplexOutput y "Output signal connector";

equation 
  y = k*u;
end Gain;

Modelica.ComplexBlocks.ComplexMath.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.ComplexMISO (Multiple Input Single Output continuous control block).

Parameters

Type	Name	Default	Description
Integer	nin	1	Number of inputs
Complex	k[nin]	fill(Complex(1, 0), nin)	Optional: sum coefficients

Connectors

Type	Name	Description
input ComplexInput	u[nin]	Connector of Complex input signals
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

block Sum "Output the sum of the elements of the input vector"
  extends Interfaces.ComplexMISO;
  parameter Complex k[nin]=fill(Complex(1,0), nin) "Optional: sum coefficients";
equation 
  y = k*u;
end Sum;

Modelica.ComplexBlocks.ComplexMath.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 ComplexInput	u1
input ComplexInput	u2
output ComplexOutput	y

Modelica definition

block Feedback 
  "Output difference between commanded and feedback input"

  Interfaces.ComplexInput u1;
  Interfaces.ComplexInput u2;
  Interfaces.ComplexOutput y;

equation 
  y = u1 - u2;
end Feedback;

Modelica.ComplexBlocks.ComplexMath.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.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

Type	Name	Default	Description
Complex	k1	Complex(1, 0)	Gain of upper input
Complex	k2	Complex(1, 0)	Gain of lower input

Connectors

Type	Name	Description
input ComplexInput	u1	Connector of Complex input signal 1
input ComplexInput	u2	Connector of Complex input signal 2
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

block Add "Output the sum of the two inputs"
  extends Interfaces.ComplexSI2SO;
  parameter Complex k1=Complex(1,0) "Gain of upper input";
  parameter Complex k2=Complex(1,0) "Gain of lower input";

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

Modelica.ComplexBlocks.ComplexMath.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 Blocks.Interfaces.BlockIcon (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
Complex	k1	Complex(1, 0)	Gain of upper input
Complex	k2	Complex(1, 0)	Gain of middle input
Complex	k3	Complex(1, 0)	Gain of lower input

Connectors

Type	Name	Description
input ComplexInput	u1	Connector 1 of Complex input signals
input ComplexInput	u2	Connector 2 of Complex input signals
input ComplexInput	u3	Connector 3 of Complex input signals
output ComplexOutput	y	Connector of Complex output signals

Modelica definition

block Add3 "Output the sum of the three inputs"
  extends Blocks.Interfaces.BlockIcon;

  parameter Complex k1=Complex(1,0) "Gain of upper input";
  parameter Complex k2=Complex(1,0) "Gain of middle input";
  parameter Complex k3=Complex(1,0) "Gain of lower input";
  Interfaces.ComplexInput u1 "Connector 1 of Complex input signals";
  Interfaces.ComplexInput u2 "Connector 2 of Complex input signals";
  Interfaces.ComplexInput u3 "Connector 3 of Complex input signals";
  Interfaces.ComplexOutput y "Connector of Complex output signals";

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

Modelica.ComplexBlocks.ComplexMath.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.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u1	Connector of Complex input signal 1
input ComplexInput	u2	Connector of Complex input signal 2
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

block Product "Output product of the two inputs"
  extends Interfaces.ComplexSI2SO;

equation 
  y = u1*u2;
end Product;

Modelica.ComplexBlocks.ComplexMath.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.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u1	Connector of Complex input signal 1
input ComplexInput	u2	Connector of Complex input signal 2
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

block Division "Output first input divided by second input"
  extends Interfaces.ComplexSI2SO;

equation 
  y = u1/u2;
end Division;

Modelica.ComplexBlocks.ComplexMath.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.ComplexSISO (Single Input Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Sin

Information

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

    y = sin( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Cos

Information

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

    y = cos( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Tan

Information

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

    y = tan( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.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.ComplexSISO (Single Input Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.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.ComplexSISO (Single Input Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Atan

Information

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

    y= atan( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Sinh

Information

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

    y = sinh( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Cosh

Information

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

    y = cosh( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Tanh

Information

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

    y = tanh( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.Exp

Information

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

    y = exp( u );

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

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.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.ComplexSISO (Single Input Single Output continuous control block).

Connectors

Type	Name	Description
input ComplexInput	u	Connector of Complex input signal
output ComplexOutput	y	Connector of Complex output signal

Modelica definition

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

Modelica.ComplexBlocks.ComplexMath.RealToComplex

Information

Converts the Real inputs re (real part) and im (imaginary part) to the Complex output y.

Extends from Modelica.ComplexBlocks.Interfaces.ComplexSO (Single Output continuous control block).

Connectors

Type	Name	Description
output ComplexOutput	y	Connector of Complex output signal
input RealInput	re
input RealInput	im

Modelica definition

block RealToComplex "Converts cartesian representation to complex"
  extends Modelica.ComplexBlocks.Interfaces.ComplexSO;
  Blocks.Interfaces.RealInput re;
  Blocks.Interfaces.RealInput im;
equation 
  y=Complex(re,im);
end RealToComplex;

Modelica.ComplexBlocks.ComplexMath.PolarToComplex

Information

Converts the Real inputs len (length, absolute) and phi (angle, argument) to the Complex output y.

Extends from Modelica.ComplexBlocks.Interfaces.ComplexSO (Single Output continuous control block).

Connectors

Type	Name	Description
output ComplexOutput	y	Connector of Complex output signal
input RealInput	len
input RealInput	phi

Modelica definition

block PolarToComplex "Converts polar representation to complex"
  extends Modelica.ComplexBlocks.Interfaces.ComplexSO;
  Blocks.Interfaces.RealInput len;
  Blocks.Interfaces.RealInput phi;
equation 
  y=Complex(len*cos(phi),len*sin(phi));
end PolarToComplex;

Modelica.ComplexBlocks.ComplexMath.ComplexToReal

Information

Converts the Complex input u to the Real outputs re (real part) and im (imaginary part).

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

Connectors

Type	Name	Description
output RealOutput	re
output RealOutput	im
input ComplexInput	u

Modelica definition

block ComplexToReal "Converts complex to cartesian representation"
  extends Modelica.Blocks.Interfaces.BlockIcon;
  Blocks.Interfaces.RealOutput re;
  Blocks.Interfaces.RealOutput im;
  Interfaces.ComplexInput u;
equation 
  re=u.re;
  im=u.im;
end ComplexToReal;

Modelica.ComplexBlocks.ComplexMath.ComplexToPolar

Information

Converts the Complex input u to the Real outputs len (length, absolute) and phi (angle, argument).

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

Connectors

Type	Name	Description
output RealOutput	len
output RealOutput	phi
input ComplexInput	u

Modelica definition

block ComplexToPolar "Converts complex to polar representation"
  extends Modelica.Blocks.Interfaces.BlockIcon;
  Blocks.Interfaces.RealOutput len;
  Blocks.Interfaces.RealOutput phi;
  Interfaces.ComplexInput u;
equation 
  len=(u.re^2 + u.im^2)^0.5;
  phi=Modelica.Math.atan2(u.im,u.re);
end ComplexToPolar;