Modelica.ComplexBlocks.ComplexMath

Library of mathematical functions as input/output blocks

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
Conj	Output is equal to the conjugate complex input signal
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 input 1 and feedback input 2
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 (= principal square root of complex number)
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
TransferFunction

Modelica.ComplexBlocks.ComplexMath.Conj

Output is equal to the conjugate complex input signal

Information

This block computes output y as conjugate complex input u.

    y = Modelica.ComplexMath.conj(u)

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Gain

Output the product of a gain value with the input signal

Information

This block computes output y as product of gain k with the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput either the original or the conjugate complex input signal are processed.

    y = k * (if useConjugateInput then Modelica.ComplexMath.conj(u) else u);

Example: If useConjugateInput = true and k = 2 the output signal y = 2 * Modelica.ComplexMath.conj(u).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Sum

Output the sum of the elements of the input vector

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

Connectors

Modelica.ComplexBlocks.ComplexMath.Feedback

Output difference between commanded input 1 and feedback input 2

Information

This blocks computes output y as difference of the commanded input u1 and the feedback input u2. Optionally, either input u1 or u2 or both inputs can be processed conjugate complex, when parameters useConjugateInput1 and useConjugateInput2 are true, respectively.

  y = (if useConjugateInput1 then Modelica.ComplexMath.conj(u1) else u1)
    - (if useConjugateInput1 then Modelica.ComplexMath.conj(u2) else u2);

Example parameters:

• useConjugateInput1 = true,
• useConjugateInput2 = false

result in the following equation:

     y = Modelica.ComplexMath.conj(u1) - u2

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Add

Output the sum of the two inputs

Information

This blocks computes output y as sum of the two input signals u1 and u2. Optionally, either input u1 or u2 or both inputs can be processed conjugate complex, when parameters useConjugateInput1 and useConjugateInput2 are true, respectively.

  y = k1*u1Internal + k2*u2Internal;

Example parameters:

• k1 = +2,
• k2 = -3,
• useConjugateInput1 = true,
• useConjugateInput2 = false

result in the following equation:

     y = 2 * Modelica.ComplexMath.conj(u1) - 3 * u2

Extends from Interfaces.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Add3

Output the sum of the three inputs

Information

This blocks computes output y as sum of the three input signals u1, u2 and u3. Optionally, inputs u1 and u2 and u3 can be processed conjugate complex, when parameters useConjugateInput1 and useConjugateInput2 and useConjugateInput3 are true, respectively.

  y = k1*(if useConjugateInput1 then Modelica.ComplexMath.conj(u1) else u1)
    + k2*(if useConjugateInput2 then Modelica.ComplexMath.conj(u2) else u2)
    + k3*(if useConjugateInput3 then Modelica.ComplexMath.conj(u3) else u3);

Example parameters:

• k1 = +2,
• k2 = -3,
• k3 = +1,
• useConjugateInput1 = true,
• useConjugateInput2 = false
• useConjugateInput3 = false

result in the following equation:

     y = 2 * Modelica.ComplexMath.conj(u1) - 3 * u2 + u3;

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Product

Output product of the two inputs

Information

This blocks computes the output y (element-wise) as product of the corresponding elements of the two inputs u1 and u2. Optionally, either input u1 or u2 or both inputs can be processed conjugate complex, when parameters useConjugateInput1 and useConjugateInput2 are true, respectively. Depending on useConjugateInput1 and useConjugateInput2 the internal signals represent either the original or the conjugate complex input signal.

  y = u1Inernal * u2Internal;

Example: If useConjugateInput1 = true and useConjugateInput2 = false the output signal y = Modelica.ComplexMath.conj(u1) * u2.

Extends from Interfaces.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Division

Output first input divided by second input

Information

This block computes the output y (element-wise) by dividing the corresponding elements of the two inputs u1 and u2. Optionally, either input u1 or u2 or both inputs can be processed conjugate complex, when parameters useConjugateInput1 and useConjugateInput2 are true, respectively. Depending on useConjugateInput1 and useConjugateInput2 the internal signals represent either the original or the conjugate complex input signal.

    y = u1Internal / u2Internal;

Example: If useConjugateInput1 = true and useConjugateInput2 = false the output signal y = Modelica.ComplexMath.conj(u1) / u2.

Extends from Interfaces.ComplexSI2SO (2 Single Input / 1 Single Output continuous control block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Sqrt

Output the square root of the input (= principal square root of complex number)

Information

This blocks computes the output y as square root of the input u (= principal square root of the complex input). Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = sqrt(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Sin

Output the sine of the input

Information

This blocks computes the output y as sine of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = sin(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Cos

Output the cosine of the input

Information

This blocks computes the output y as cos of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = cos(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Tan

Output the tangent of the input

Information

This blocks computes the output y as tan of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = tan(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Asin

Output the arc sine of the input

Information

This blocks computes the output y as the sine-inverse of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = asin(uInternal);

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).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Acos

Output the arc cosine of the input

Information

This blocks computes the output y as the cosine-inverse of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = acos(uInternal);

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).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Atan

Output the arc tangent of the input

Information

This blocks computes the output y as the tangent-inverse of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y= atan(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Sinh

Output the hyperbolic sine of the input

Information

This blocks computes the output y as the hyperbolic sine of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = sinh(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Cosh

Output the hyperbolic cosine of the input

Information

This blocks computes the output y as the hyperbolic cosine of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = cosh(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Tanh

Output the hyperbolic tangent of the input

Information

This blocks computes the output y as the hyperbolic tangent of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = tanh(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Exp

Output the exponential (base e) of the input

Information

This blocks computes the output y as the exponential (of base e) of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = exp(uInternal);

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

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.Log

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

Information

This blocks computes the output y as the natural (base e) logarithm of the input u. Optionally, the input u can be processed conjugate complex, when parameter useConjugateInput is true. Depending on useConjugateInput the internal signal uInternal represents either the original or the conjugate complex input signal.

    y = log(uInternal);

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).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.RealToComplex

Converts Cartesian representation to complex

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

Modelica.ComplexBlocks.ComplexMath.PolarToComplex

Converts polar representation to complex

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

Modelica.ComplexBlocks.ComplexMath.ComplexToReal

Converts complex to Cartesian representation

Information

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

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.ComplexToPolar

Converts complex to polar representation

Information

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

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Connectors

Modelica.ComplexBlocks.ComplexMath.TransferFunction

Information

The complex input u is multiplied by the complex transfer function (depending on frequency input w) to obtain the complex output y (nb = dimension of b, na = dimension of a):

           b[1]*(jw)^[nb-1] + b[2]*(jw)^[nb-2] + ... + b[nb]
   y(jw) = ------------------------------------------------- * u(jw)
           a[1]*(jw)^[na-1] + a[2]*(jw)^[na-2] + ... + a[na]

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

Parameters

Connectors