Modelica.Blocks.Math

Library of Real 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
Modelica.Blocks.Math.UnitConversions UnitConversions Conversion blocks to convert between SI and non-SI unit signals
Modelica.Blocks.Math.InverseBlockConstraints InverseBlockConstraints Construct inverse model by requiring that two inputs and two outputs are identical
Modelica.Blocks.Math.Gain Gain Output the product of a gain value with the input signal
Modelica.Blocks.Math.MatrixGain MatrixGain Output the product of a gain matrix with the input signal vector
Modelica.Blocks.Math.MultiSum MultiSum Sum of Reals: y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]
Modelica.Blocks.Math.MultiProduct MultiProduct Product of Reals: y = u[1]*u[2]* ... *u[n]
Modelica.Blocks.Math.MultiSwitch MultiSwitch Set Real expression that is associated with the first active input signal
Modelica.Blocks.Math.Sum Sum Output the sum of the elements of the input vector
Modelica.Blocks.Math.Feedback Feedback Output difference between commanded and feedback input
Modelica.Blocks.Math.Add Add Output the sum of the two inputs
Modelica.Blocks.Math.Add3 Add3 Output the sum of the three inputs
Modelica.Blocks.Math.Product Product Output product of the two inputs
Modelica.Blocks.Math.Division Division Output first input divided by second input
Modelica.Blocks.Math.Abs Abs Output the absolute value of the input
Modelica.Blocks.Math.Sign Sign Output the sign of the input
Modelica.Blocks.Math.Sqrt Sqrt Output the square root of the input (input >= 0 required)
Modelica.Blocks.Math.Sin Sin Output the sine of the input
Modelica.Blocks.Math.Cos Cos Output the cosine of the input
Modelica.Blocks.Math.Tan Tan Output the tangent of the input
Modelica.Blocks.Math.Asin Asin Output the arc sine of the input
Modelica.Blocks.Math.Acos Acos Output the arc cosine of the input
Modelica.Blocks.Math.Atan Atan Output the arc tangent of the input
Modelica.Blocks.Math.Atan2 Atan2 Output atan(u1/u2) of the inputs u1 and u2
Modelica.Blocks.Math.Sinh Sinh Output the hyperbolic sine of the input
Modelica.Blocks.Math.Cosh Cosh Output the hyperbolic cosine of the input
Modelica.Blocks.Math.Tanh Tanh Output the hyperbolic tangent of the input
Modelica.Blocks.Math.Exp Exp Output the exponential (base e) of the input
Modelica.Blocks.Math.Log Log Output the natural (base e) logarithm of the input (input > 0 required)
Modelica.Blocks.Math.Log10 Log10 Output the base 10 logarithm of the input (input > 0 required)
Modelica.Blocks.Math.RealToInteger RealToInteger Convert Real to Integer signal
Modelica.Blocks.Math.IntegerToReal IntegerToReal Convert Integer to Real signals
Modelica.Blocks.Math.BooleanToReal BooleanToReal Convert Boolean to Real signal
Modelica.Blocks.Math.BooleanToInteger BooleanToInteger Convert Boolean to Integer signal
Modelica.Blocks.Math.RealToBoolean RealToBoolean Convert Real to Boolean signal
Modelica.Blocks.Math.IntegerToBoolean IntegerToBoolean Convert Integer to Boolean signal
Modelica.Blocks.Math.RectangularToPolar RectangularToPolar Convert rectangular coordinates to polar coordinates
Modelica.Blocks.Math.PolarToRectangular PolarToRectangular Convert polar coordinates to rectangular coordinates
Modelica.Blocks.Math.Mean Mean Calculate mean over period 1/f
Modelica.Blocks.Math.RectifiedMean RectifiedMean Calculate rectified mean over period 1/f
Modelica.Blocks.Math.ContinuousMean ContinuousMean Calculates the empirical expectation (mean) value of its input signal
Modelica.Blocks.Math.RootMeanSquare RootMeanSquare Calculate root mean square over period 1/f
Modelica.Blocks.Math.Variance Variance Calculates the empirical variance of its input signal
Modelica.Blocks.Math.StandardDeviation StandardDeviation Calculates the empirical standard deviation of its input signal
Modelica.Blocks.Math.Harmonic Harmonic Calculate harmonic over period 1/f
Modelica.Blocks.Math.Max Max Pass through the largest signal
Modelica.Blocks.Math.Min Min Pass through the smallest signal
Modelica.Blocks.Math.MinMax MinMax Output the minimum and the maximum element of the input vector
Modelica.Blocks.Math.LinearDependency LinearDependency Output a linear combination of the two inputs
Modelica.Blocks.Math.Edge Edge Indicates rising edge of Boolean signal
Modelica.Blocks.Math.BooleanChange BooleanChange Indicates Boolean signal changing
Modelica.Blocks.Math.IntegerChange IntegerChange Indicates integer signal changing

Modelica.Blocks.Math.InverseBlockConstraints Modelica.Blocks.Math.InverseBlockConstraints

Construct inverse model by requiring that two inputs and two outputs are identical

Information

Exchange input and output 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

NameDescription
u1Input signal 1 (u1 = u2)
u2Input signal 2 (u1 = u2)
y1Output signal 1 (y1 = y2)
y2Output signal 2 (y1 = y2)

Modelica.Blocks.Math.Gain Modelica.Blocks.Math.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:

    y = k * u;

Parameters

NameDescription
kGain value multiplied with input signal [1]

Connectors

NameDescription
uInput signal connector
yOutput signal connector

Modelica.Blocks.Math.MatrixGain Modelica.Blocks.Math.MatrixGain

Output the product of a gain matrix with the input signal vector

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

NameDescription
K[:, :]Gain matrix which is multiplied with the input
ninNumber of inputs
noutNumber of outputs

Connectors

NameDescription
u[nin]Connector of Real input signals
y[nout]Connector of Real output signals

Modelica.Blocks.Math.MultiSum Modelica.Blocks.Math.MultiSum

Sum of Reals: y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]

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

NameDescription
k[nu]Input gains
Advanced
significantDigitsNumber of significant digits to be shown in dynamic diagram layer for y

Connectors

NameDescription
u[nu] 
y 

Modelica.Blocks.Math.MultiProduct Modelica.Blocks.Math.MultiProduct

Product of Reals: y = u[1]*u[2]* ... *u[n]

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

NameDescription
Advanced
significantDigitsNumber of significant digits to be shown in dynamic diagram layer for y

Connectors

NameDescription
u[nu] 
y 

Modelica.Blocks.Math.MultiSwitch Modelica.Blocks.Math.MultiSwitch

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

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

NameDescription
expr[nu]y = if u[i] then expr[i] else y_default (time varying)
y_defaultDefault value of output y if all u[i] = false
Advanced
precisionNumber of significant digits to be shown in dynamic diagram layer for y

Connectors

NameDescription
u[nu]Set y = expr[i], if u[i] = true
yOutput depending on expression

Modelica.Blocks.Math.Sum Modelica.Blocks.Math.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.MISO (Multiple Input Single Output continuous control block).

Parameters

NameDescription
ninNumber of inputs
k[nin]Optional: sum coefficients

Connectors

NameDescription
u[nin]Connector of Real input signals
yConnector of Real output signal

Modelica.Blocks.Math.Feedback Modelica.Blocks.Math.Feedback

Output difference between commanded and feedback input

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

NameDescription
u1 
u2 
y 

Modelica.Blocks.Math.Add Modelica.Blocks.Math.Add

Output the sum of the two inputs

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

NameDescription
k1Gain of upper input
k2Gain of lower input

Connectors

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Add3 Modelica.Blocks.Math.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:

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

Parameters

NameDescription
k1Gain of upper input
k2Gain of middle input
k3Gain of lower input

Connectors

NameDescription
u1Connector 1 of Real input signals
u2Connector 2 of Real input signals
u3Connector 3 of Real input signals
yConnector of Real output signals

Modelica.Blocks.Math.Product Modelica.Blocks.Math.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:

    y = u1 * u2;

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

Connectors

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Division Modelica.Blocks.Math.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:

    y = u1 / u2;

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

Connectors

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Abs Modelica.Blocks.Math.Abs

Output the absolute value of the input

Information

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

    y = abs( u );

The Boolean parameter generateEvent decides whether Events are generated at zero crossing (Modelica specification before 3) or not.

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

Parameters

NameDescription
generateEventChoose whether events shall be generated

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Sign Modelica.Blocks.Math.Sign

Output the sign of the input

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

The Boolean parameter generateEvent decides whether Events are generated at zero crossing (Modelica specification before 3) or not.

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

Parameters

NameDescription
generateEventChoose whether events shall be generated

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Sqrt Modelica.Blocks.Math.Sqrt

Output the square root of the input (input >= 0 required)

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

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Sin Modelica.Blocks.Math.Sin

Output the sine of the input

Information

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

    y = sin( u );

sin.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Cos Modelica.Blocks.Math.Cos

Output the cosine of the input

Information

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

    y = cos( u );

cos.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Tan Modelica.Blocks.Math.Tan

Output the tangent of the input

Information

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

    y = tan( u );

tan.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Asin Modelica.Blocks.Math.Asin

Output the arc sine of the input

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.

atan.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Acos Modelica.Blocks.Math.Acos

Output the arc cosine of the input

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.

acos.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Atan Modelica.Blocks.Math.Atan

Output the arc tangent of the input

Information

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

    y= atan( u );

atan.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Atan2 Modelica.Blocks.Math.Atan2

Output atan(u1/u2) of the inputs u1 and u2

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.

atan2.png

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

Connectors

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Sinh Modelica.Blocks.Math.Sinh

Output the hyperbolic sine of the input

Information

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

    y = sinh( u );

sinh.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Cosh Modelica.Blocks.Math.Cosh

Output the hyperbolic cosine of the input

Information

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

    y = cosh( u );

cosh.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Tanh Modelica.Blocks.Math.Tanh

Output the hyperbolic tangent of the input

Information

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

    y = tanh( u );

tanh.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Exp Modelica.Blocks.Math.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:

    y = exp( u );

exp.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Log Modelica.Blocks.Math.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:

    y = log( u );

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

log.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Log10 Modelica.Blocks.Math.Log10

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

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.

log10.png

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

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.RealToInteger Modelica.Blocks.Math.RealToInteger

Convert Real to Integer signal

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 Modelica.Blocks.Icons.IntegerBlock (Basic graphical layout of Integer block).

Connectors

NameDescription
uConnector of Real input signal
yConnector of Integer output signal

Modelica.Blocks.Math.IntegerToReal Modelica.Blocks.Math.IntegerToReal

Convert Integer to Real signals

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

Connectors

NameDescription
uConnector of Integer input signal
yConnector of Real output signal

Modelica.Blocks.Math.BooleanToReal Modelica.Blocks.Math.BooleanToReal

Convert Boolean to Real signal

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

NameDescription
realTrueOutput signal for true Boolean input
realFalseOutput signal for false Boolean input

Connectors

NameDescription
uConnector of Boolean input signal
yConnector of Real output signal

Modelica.Blocks.Math.BooleanToInteger Modelica.Blocks.Math.BooleanToInteger

Convert Boolean to Integer signal

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

NameDescription
integerTrueOutput signal for true Boolean input
integerFalseOutput signal for false Boolean input

Connectors

NameDescription
uConnector of Boolean input signal
yConnector of Integer output signal

Modelica.Blocks.Math.RealToBoolean Modelica.Blocks.Math.RealToBoolean

Convert Real to Boolean signal

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

NameDescription
thresholdOutput signal y is true, if input u >= threshold

Connectors

NameDescription
uConnector of Real input signal
yConnector of Boolean output signal

Modelica.Blocks.Math.IntegerToBoolean Modelica.Blocks.Math.IntegerToBoolean

Convert Integer to Boolean signal

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

NameDescription
thresholdOutput signal y is true, if input u >= threshold

Connectors

NameDescription
uConnector of Integer input signal
yConnector of Boolean output signal

Modelica.Blocks.Math.RectangularToPolar Modelica.Blocks.Math.RectangularToPolar

Convert rectangular coordinates to polar coordinates

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.Icons.Block (Basic graphical layout of input/output block).

Connectors

NameDescription
u_reReal part of rectangular representation
u_imImaginary part of rectangular representation
y_absLength of polar representation
y_argAngle of polar representation

Modelica.Blocks.Math.PolarToRectangular Modelica.Blocks.Math.PolarToRectangular

Convert polar coordinates to rectangular coordinates

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.Icons.Block (Basic graphical layout of input/output block).

Connectors

NameDescription
u_absLength of polar representation
u_argAngle of polar representation
y_reReal part of rectangular representation
y_imImaginary part of rectangular representation

Modelica.Blocks.Math.Mean Modelica.Blocks.Math.Mean

Calculate mean over period 1/f

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.

If parameter yGreaterOrEqualZero in the Advanced tab is true (default = false), then the modeller provides the information that the mean of the input signal is guaranteed to be ≥ 0 for the exact solution. However, due to inaccuracies in the numerical integration scheme, the output might be slightly negative. If this parameter is set to true, then the output is explicitly set to 0.0, if the mean value results in a negative value.

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

Parameters

NameDescription
fBase frequency [Hz]
x0Start value of integrator state
Advanced
yGreaterOrEqualZero=true, if output y is guaranteed to be >= 0 for the exact solution

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.RectifiedMean Modelica.Blocks.Math.RectifiedMean

Calculate rectified mean over period 1/f

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

NameDescription
fBase frequency [Hz]
x0Start value of integrator state

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.ContinuousMean Modelica.Blocks.Math.ContinuousMean

Calculates the empirical expectation (mean) value of its input signal

Information

This block continuously calculates the mean value of its input signal. It uses the function:

    integral( u over time)
y = ----------------------
      time - startTime

This can be used to determine the empirical expectation value of a random signal, such as generated by the Noise blocks.

The parameter t_eps is used to guard against division by zero (the mean value computation starts at startTime + t_eps and before that time instant y = u).

See also the Mean block for a sampled implementation.

This block is demonstrated in the examples UniformNoiseProperties, NormalNoiseProperties and WeibullNoiseProperties.

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

Parameters

NameDescription
Advanced
t_epsMean value calculation starts at startTime + t_eps [s]

Connectors

NameDescription
uNoisy input signal
yExpectation (mean) value of the input signal

Modelica.Blocks.Math.RootMeanSquare Modelica.Blocks.Math.RootMeanSquare

Calculate root mean square over period 1/f

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

NameDescription
fBase frequency [Hz]
x0Start value of integrator state

Connectors

NameDescription
uConnector of Real input signal
yConnector of Real output signal

Modelica.Blocks.Math.Variance Modelica.Blocks.Math.Variance

Calculates the empirical variance of its input signal

Information

This block calculates the empirical variance of its input signal. It is based on the formula (but implemented in a more reliable numerical way):

y = mean(  (u - mean(u))^2  )

The parameter t_eps is used to guard against division by zero (the variance computation starts at startTime + t_eps and before that time instant y = 0).

The variance of a signal is also equal to its mean power.

This block is demonstrated in the examples UniformNoiseProperties, NormalNoiseProperties and WeibullNoiseProperties.

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

Parameters

NameDescription
Advanced
t_epsVariance calculation starts at startTime + t_eps [s]

Connectors

NameDescription
uNoisy input signal
yVariance of the input signal

Modelica.Blocks.Math.StandardDeviation Modelica.Blocks.Math.StandardDeviation

Calculates the empirical standard deviation of its input signal

Information

This block calculates the standard deviation of its input signal. The standard deviation is the square root of the signal's variance:

y = sqrt( variance(u) )

The Variance block is used to calculate variance(u).

The parameter t_eps is used to guard against division by zero (the computation of the standard deviation starts at startTime + t_eps and before that time instant y = 0).

This block is demonstrated in the examples UniformNoiseProperties, NormalNoiseProperties and WeibullNoiseProperties.

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

Parameters

NameDescription
Advanced
t_epsStandard deviation calculation starts at startTime + t_eps [s]

Connectors

NameDescription
uNoisy input signal
yStandard deviation of the input signal

Modelica.Blocks.Math.Harmonic Modelica.Blocks.Math.Harmonic

Calculate harmonic over period 1/f

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.Icons.Block (Basic graphical layout of input/output block).

Parameters

NameDescription
fBase frequency [Hz]
kOrder of harmonic
x0CosStart value of cos integrator state
x0SinStart value of sin integrator state

Connectors

NameDescription
u 
y_rmsRoot mean square of polar representation
y_argAngle of polar representation

Modelica.Blocks.Math.Max Modelica.Blocks.Math.Max

Pass through the largest signal

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

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Min Modelica.Blocks.Math.Min

Pass through the smallest signal

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

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.MinMax Modelica.Blocks.Math.MinMax

Output the minimum and the maximum element of the input vector

Information

Determines the minimum and maximum element of the input vector and provide both values as output.

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

Connectors

NameDescription
u[nu] 
yMax 
yMin 

Modelica.Blocks.Math.LinearDependency Modelica.Blocks.Math.LinearDependency

Output a linear combination of the two inputs

Information

Determine the linear combination of the two inputs: y = y0*(1 + k1*u1 + k2*u2)

Note, for y0=0 the output is always zero.

To improve the implementation, the formula will be changed (non-backwards compatible) in the future: y = y0 + k1*u1 + k2*u2

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

Parameters

NameDescription
y0Initial value
k1u1 dependency
k2u2 dependency

Connectors

NameDescription
u1Connector of Real input signal 1
u2Connector of Real input signal 2
yConnector of Real output signal

Modelica.Blocks.Math.Edge Modelica.Blocks.Math.Edge

Indicates rising edge of Boolean signal

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

NameDescription
uConnector of Boolean input signal
yConnector of Boolean output signal

Modelica.Blocks.Math.BooleanChange Modelica.Blocks.Math.BooleanChange

Indicates Boolean signal changing

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

NameDescription
uConnector of Boolean input signal
yConnector of Boolean output signal

Modelica.Blocks.Math.IntegerChange Modelica.Blocks.Math.IntegerChange

Indicates integer signal changing

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

NameDescription
uConnector of Integer input signal
yConnector of Boolean output signal
Automatically generated Tue Apr 05 09:36:12 2016.