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.

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

Name	Description
k	Gain value multiplied with input signal

Connectors

Name	Description
u	Input signal connector
y	Output signal connector

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];

Parameters

Name	Description
nin	Number of inputs
k[nin]	Optional: sum coefficients

Connectors

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

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

Name	Description
u1
u2
y

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

Parameters

Name	Description
k1	Gain of upper input
k2	Gain of lower input

Connectors

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

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;

Parameters

Name	Description
k1	Gain of upper input
k2	Gain of middle input
k3	Gain of lower input

Connectors

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

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;

Connectors

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

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;

Connectors

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

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.

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Sin

Information

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

    y = sin( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Cos

Information

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

    y = cos( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Tan

Information

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

    y = tan( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

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.

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

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.

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Atan

Information

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

    y= atan( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Sinh

Information

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

    y = sinh( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Cosh

Information

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

    y = cosh( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Tanh

Information

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

    y = tanh( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.Exp

Information

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

    y = exp( u );

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

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.

Connectors

Name	Description
u	Connector of Complex input signal
y	Connector of Complex output signal

Modelica.ComplexBlocks.ComplexMath.RealToComplex

Information

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

Connectors

Name	Description
y	Connector of Complex output signal
re
im

Modelica.ComplexBlocks.ComplexMath.PolarToComplex

Information

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

Connectors

Name	Description
y	Connector of Complex output signal
len
phi

Modelica.ComplexBlocks.ComplexMath.ComplexToReal

Information

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

Connectors

Name	Description
re
im
u

Modelica.ComplexBlocks.ComplexMath.ComplexToPolar

Information

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

Connectors

Name	Description
len
phi
u