Modelica.Blocks.Tables

Library of blocks to interpolate in one and two-dimensional tables

Information

This package contains blocks for one- and two-dimensional interpolation in tables.

Special interest topic: Statically stored tables for real-time simulation targets

Especially for use on real-time platform targets (e.g., HIL-simulators) with no file system, it is possible to statically store tables using a function "usertab" in a file conventionally named "usertab.c". This can be more efficient than providing the tables as Modelica parameter arrays.

This is achieved by providing the tables in a specific structure as C-code and compiling that C-code together with the rest of the simulation model into a binary that can be executed on the target platform. The "Resources/Data/Tables/" subdirectory of the MSL installation directory contains the files "usertab.c" and "usertab.h" that can be used as a template for own developments. While "usertab.c" would be typically used unmodified, the "usertab.h" needs to adapted for the own needs.

In order to work it is necessary that the compiler pulls in the "usertab.c" file. Different Modelica tools might provide different mechanisms to do so. Please consult the respective documentation/support for your Modelica tool.

A possible (though a bit "hackish") Modelica standard conformant approach is to pull in the required files by utilizing a "dummy"-function that uses the Modelica external function interface to pull in the required "usertab.c". An example how this can be done is given below.

model Test25_usertab "Test utilizing the usertab.c interface"
  extends Modelica.Icons.Example;
public
  Modelica.Blocks.Sources.RealExpression realExpression(y=getUsertab(t_new.y))
    annotation (Placement(transformation(extent={{-40,-34},{-10,-14}})));
  Modelica.Blocks.Tables.CombiTable1D t_new(tableOnFile=true, tableName="TestTable_1D_a")
    annotation (Placement(transformation(extent={{-40,0},{-20,20}})));
  Modelica.Blocks.Sources.Clock clock
    annotation (Placement(transformation(extent={{-80,0},{-60,20}})));
protected
  encapsulated function getUsertab
    input Real dummy_u[:];
    output Real dummy_y;
    external "C" dummy_y=  mydummyfunc(dummy_u);
    annotation(IncludeDirectory="modelica://Modelica/Resources/Data/Tables",
           Include = "#include "usertab.c"
double mydummyfunc(double* dummy_in) {
   return 0;
}
");
  end getUsertab;
equation
  connect(clock.y,t_new. u[1]) annotation (Line(
      points={{-59,10},{-42,10}}, color={0,0,127}));
  annotation (experiment(StartTime=0, StopTime=5), uses(Modelica(version="3.2.2")));
end Test25_usertab;

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
CombiTable1D	Table look-up in one dimension (matrix/file) with n inputs and n outputs
CombiTable1Ds	Table look-up in one dimension (matrix/file) with one input and n outputs
CombiTable2D	Table look-up in two dimensions (matrix/file)
CombiTable2Dv	Table look-up in two dimensions (matrix/file) with vector inputs and vector output of size n
Internal	Internal external object definitions for table functions that should not be directly utilized by the user

Modelica.Blocks.Tables.CombiTable1D

Table look-up in one dimension (matrix/file) with n inputs and n outputs

Information

Univariate constant, linear or cubic Hermite spline interpolation in one dimension of a table. Via parameter columns it can be defined how many columns of the table are interpolated. If, e.g., columns={2,4}, it is assumed that 2 input and 2 output signals are present and that the first output interpolates the first input via column 2 and the second output interpolates the second input via column 4 of the table matrix.

The grid points and function values are stored in a matrix "table[i,j]", where the first column "table[:,1]" contains the grid points and the other columns contain the data to be interpolated. Example:

   table = [0,  0;
            1,  1;
            2,  4;
            4, 16]
   If, e.g., the input u = 1.0, the output y =  1.0,
       e.g., the input u = 1.5, the output y =  2.5,
       e.g., the input u = 2.0, the output y =  4.0,
       e.g., the input u =-1.0, the output y = -1.0 (i.e., extrapolation).

The interpolation interval is found by a binary search where the interval used in the last call is used as start interval.

Via parameter smoothness it is defined how the data is interpolated:

  smoothness = 1: Linear interpolation
             = 2: Akima interpolation: Smooth interpolation by cubic Hermite
                  splines such that der(y) is continuous, also if extrapolated.
             = 3: Constant segments
             = 4: Fritsch-Butland interpolation: Smooth interpolation by cubic
                  Hermite splines such that y preserves the monotonicity and
                  der(y) is continuous, also if extrapolated.
             = 5: Steffen interpolation: Smooth interpolation by cubic Hermite
                  splines such that y preserves the monotonicity and der(y)
                  is continuous, also if extrapolated.

Values outside of the table range, are computed by extrapolation according to the setting of parameter extrapolation:

  extrapolation = 1: Hold the first or last value of the table,
                     if outside of the table scope.
                = 2: Extrapolate by using the derivative at the first/last table
                     points if outside of the table scope.
                     (If smoothness is LinearSegments or ConstantSegments
                     this means to extrapolate linearly through the first/last
                     two table points.).
                = 3: Periodically repeat the table data (periodical function).
                = 4: No extrapolation, i.e. extrapolation triggers an error

If the table has only one row, the table value is returned, independent of the value of the input signal.
The grid values (first column) have to be strictly increasing.

The table matrix can be defined in the following ways:

Explicitly supplied as parameter matrix "table", and the other parameters have the following values:
```
   tableName is "NoName" or has only blanks,
   fileName  is "NoName" or has only blanks.
```
Read from a file "fileName" where the matrix is stored as "tableName". Both text and MATLAB MAT-file format is possible. (The text format is described below). The MAT-file format comes in four different versions: v4, v6, v7 and v7.3. The library supports at least v4, v6 and v7 whereas v7.3 is optional. It is most convenient to generate the MAT-file from FreeMat or MATLAB® by command
```
   save tables.mat tab1 tab2 tab3
```
or Scilab by command
```
   savematfile tables.mat tab1 tab2 tab3
```
when the three tables tab1, tab2, tab3 should be used from the model.
Note, a fileName can be defined as URI by using the helper function loadResource.
Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks. Row-wise storage is always to be preferred as otherwise the table is reallocated and transposed. See the Tables package documentation for more details.

When the constant "NO_FILE_SYSTEM" is defined, all file I/O related parts of the source code are removed by the C-preprocessor, such that no access to files takes place.

If tables are read from a text file, the file needs to have the following structure ("-----" is not part of the file content):

-----------------------------------------------------
#1
double tab1(5,2)   # comment line
  0   0
  1   1
  2   4
  3   9
  4  16
double tab2(5,2)   # another comment line
  0   0
  2   2
  4   8
  6  18
  8  32
-----------------------------------------------------

Note, that the first two characters in the file need to be "#1" (a line comment defining the version number of the file format). Afterwards, the corresponding matrix has to be declared with type (= "double" or "float"), name and actual dimensions. Finally, in successive rows of the file, the elements of the matrix have to be given. The elements have to be provided as a sequence of numbers in row-wise order (therefore a matrix row can span several lines in the file and need not start at the beginning of a line). Numbers have to be given according to C syntax (such as 2.3, -2, +2.e4). Number separators are spaces, tab (\t), comma (,), or semicolon (;). Several matrices may be defined one after another. Line comments start with the hash symbol (#) and can appear everywhere. Text files should either be ASCII or UTF-8 encoded, where UTF-8 encoded strings are only allowed in line comments and an optional UTF-8 BOM at the start of the text file is ignored. Other characters, like trailing non comments, are not allowed in the file.

MATLAB is a registered trademark of The MathWorks, Inc.

Extends from Modelica.Blocks.Interfaces.MIMOs (Multiple Input Multiple Output continuous control block with same number of inputs and outputs).

Parameters

Name	Description
n	Number of inputs (= number of outputs)
Table data definition
tableOnFile	= true, if table is defined on file or in function usertab
table[:, :]	Table matrix (grid = first column; e.g., table=[0, 0; 1, 1; 2, 4])
tableName	Table name on file or in function usertab (see docu)
fileName	File where matrix is stored
verboseRead	= true, if info message that file is loading is to be printed
Table data interpretation
columns[:]	Columns of table to be interpolated
smoothness	Smoothness of table interpolation
extrapolation	Extrapolation of data outside the definition range
verboseExtrapolation	= true, if warning messages are to be printed if table input is outside the definition range

Connectors

Name	Description
u[n]	Connector of Real input signals
y[n]	Connector of Real output signals

Modelica.Blocks.Tables.CombiTable1Ds

Table look-up in one dimension (matrix/file) with one input and n outputs

Information

Univariate constant, linear or cubic Hermite spline interpolation in one dimension of a table. Via parameter columns it can be defined how many columns of the table are interpolated. If, e.g., columns={2,4}, it is assumed that 2 output signals are present and that the first output interpolates via column 2 and the second output interpolates via column 4 of the table matrix.

   table = [0,  0;
            1,  1;
            2,  4;
            4, 16]
   If, e.g., the input u = 1.0, the output y =  1.0,
       e.g., the input u = 1.5, the output y =  2.5,
       e.g., the input u = 2.0, the output y =  4.0,
       e.g., the input u =-1.0, the output y = -1.0 (i.e., extrapolation).

The interpolation interval is found by a binary search where the interval used in the last call is used as start interval.

Via parameter smoothness it is defined how the data is interpolated:

  smoothness = 1: Linear interpolation
             = 2: Akima interpolation: Smooth interpolation by cubic Hermite
                  splines such that der(y) is continuous, also if extrapolated.
             = 3: Constant segments
             = 4: Fritsch-Butland interpolation: Smooth interpolation by cubic
                  Hermite splines such that y preserves the monotonicity and
                  der(y) is continuous, also if extrapolated.
             = 5: Steffen interpolation: Smooth interpolation by cubic Hermite
                  splines such that y preserves the monotonicity and der(y)
                  is continuous, also if extrapolated.

Values outside of the table range, are computed by extrapolation according to the setting of parameter extrapolation:

  extrapolation = 1: Hold the first or last value of the table,
                     if outside of the table scope.
                = 2: Extrapolate by using the derivative at the first/last table
                     points if outside of the table scope.
                     (If smoothness is LinearSegments or ConstantSegments
                     this means to extrapolate linearly through the first/last
                     two table points.).
                = 3: Periodically repeat the table data (periodical function).
                = 4: No extrapolation, i.e. extrapolation triggers an error

If the table has only one row, the table value is returned, independent of the value of the input signal.
The grid values (first column) have to be strictly increasing.

The table matrix can be defined in the following ways:

Explicitly supplied as parameter matrix "table", and the other parameters have the following values:
```
   tableName is "NoName" or has only blanks,
   fileName  is "NoName" or has only blanks.
```
Read from a file "fileName" where the matrix is stored as "tableName". Both text and MATLAB MAT-file format is possible. (The text format is described below). The MAT-file format comes in four different versions: v4, v6, v7 and v7.3. The library supports at least v4, v6 and v7 whereas v7.3 is optional. It is most convenient to generate the MAT-file from FreeMat or MATLAB® by command
```
   save tables.mat tab1 tab2 tab3
```
or Scilab by command
```
   savematfile tables.mat tab1 tab2 tab3
```
when the three tables tab1, tab2, tab3 should be used from the model.
Note, a fileName can be defined as URI by using the helper function loadResource.
Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks. Row-wise storage is always to be preferred as otherwise the table is reallocated and transposed. See the Tables package documentation for more details.

When the constant "NO_FILE_SYSTEM" is defined, all file I/O related parts of the source code are removed by the C-preprocessor, such that no access to files takes place.

If tables are read from a text file, the file needs to have the following structure ("-----" is not part of the file content):

-----------------------------------------------------
#1
double tab1(5,2)   # comment line
  0   0
  1   1
  2   4
  3   9
  4  16
double tab2(5,2)   # another comment line
  0   0
  2   2
  4   8
  6  18
  8  32
-----------------------------------------------------

MATLAB is a registered trademark of The MathWorks, Inc.

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

Parameters

Name	Description
nout	Number of outputs
Table data definition
tableOnFile	= true, if table is defined on file or in function usertab
table[:, :]	Table matrix (grid = first column; e.g., table=[0, 0; 1, 1; 2, 4])
tableName	Table name on file or in function usertab (see docu)
fileName	File where matrix is stored
verboseRead	= true, if info message that file is loading is to be printed
Table data interpretation
columns[:]	Columns of table to be interpolated
smoothness	Smoothness of table interpolation
extrapolation	Extrapolation of data outside the definition range
verboseExtrapolation	= true, if warning messages are to be printed if table input is outside the definition range

Connectors

Name	Description
u	Connector of Real input signal
y[nout]	Connector of Real output signals

Modelica.Blocks.Tables.CombiTable2D

Table look-up in two dimensions (matrix/file)

Information

Bivariate constant, bilinear or bivariate Akima interpolation of a two-dimensional table. The grid points and function values are stored in a matrix "table[i,j]", where:

the first column "table[2:,1]" contains the u1 grid points,
the first row "table[1,2:]" contains the u2 grid points,
the other rows and columns contain the data to be interpolated.

Example:

           |       |       |       |
           |  1.0  |  2.0  |  3.0  |  // u2
       ----*-------*-------*-------*
       1.0 |  1.0  |  3.0  |  5.0  |
       ----*-------*-------*-------*
       2.0 |  2.0  |  4.0  |  6.0  |
       ----*-------*-------*-------*
     // u1
   is defined as
      table = [0.0,   1.0,   2.0,   3.0;
               1.0,   1.0,   3.0,   5.0;
               2.0,   2.0,   4.0,   6.0]
   If, e.g., the input u1 is 1.0, input u2 is 1.0 and smoothness is LinearSegments, the output y is 1.0,
       e.g., the input u1 is 2.0, input u2 is 1.5 and smoothness is LinearSegments, the output y is 3.0.

The interpolation interval is found by a binary search where the interval used in the last call is used as start interval.

Via parameter smoothness it is defined how the data is interpolated:

  smoothness = 1: Bilinear interpolation
             = 2: Bivariate Akima interpolation: Smooth interpolation by bicubic Hermite
                  splines such that der(y) is continuous, also if extrapolated.
             = 3: Constant segments
             = 4: Fritsch-Butland interpolation: Not supported
             = 5: Steffen interpolation: Not supported

Values outside of the table range, are computed by extrapolation according to the setting of parameter extrapolation:

  extrapolation = 1: Hold the first or last values of the table,
                     if outside of the table scope.
                = 2: Extrapolate by using the derivative at the first/last table
                     points if outside of the table scope.
                     (If smoothness is LinearSegments or ConstantSegments
                     this means to extrapolate linearly through the first/last
                     two table points.).
                = 3: Periodically repeat the table data (periodical function).
                = 4: No extrapolation, i.e. extrapolation triggers an error

If the table has only one element, the table value is returned, independent of the value of the input signal.
If the input signal u1 or u2 is outside of the defined interval, the corresponding value is also determined by linear interpolation through the last or first two points of the table.
The grid values (first column and first row) have to be strictly increasing.

The table matrix can be defined in the following ways:

Explicitly supplied as parameter matrix "table", and the other parameters have the following values:
```
   tableName is "NoName" or has only blanks,
   fileName  is "NoName" or has only blanks.
```
Read from a file "fileName" where the matrix is stored as "tableName". Both text and MATLAB MAT-file format is possible. (The text format is described below). The MAT-file format comes in four different versions: v4, v6, v7 and v7.3. The library supports at least v4, v6 and v7 whereas v7.3 is optional. It is most convenient to generate the MAT-file from FreeMat or MATLAB® by command
```
   save tables.mat tab1 tab2 tab3
```
or Scilab by command
```
   savematfile tables.mat tab1 tab2 tab3
```
when the three tables tab1, tab2, tab3 should be used from the model.
Note, a fileName can be defined as URI by using the helper function loadResource.
Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks. Row-wise storage is always to be preferred as otherwise the table is reallocated and transposed. See the Tables package documentation for more details.

When the constant "NO_FILE_SYSTEM" is defined, all file I/O related parts of the source code are removed by the C-preprocessor, such that no access to files takes place.

If tables are read from a text file, the file needs to have the following structure ("-----" is not part of the file content):

-----------------------------------------------------
#1
double table2D_1(3,4)   # comment line
0.0  1.0  2.0  3.0  # u[2] grid points
1.0  1.0  3.0  5.0
2.0  2.0  4.0  6.0

double table2D_2(4,4)   # comment line
0.0  1.0  2.0  3.0  # u[2] grid points
1.0  1.0  3.0  5.0
2.0  2.0  4.0  6.0
3.0  3.0  5.0  7.0
-----------------------------------------------------

MATLAB is a registered trademark of The MathWorks, Inc.

Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block), Internal.CombiTable2DBase (Base class for variants of CombiTable2D).

Parameters

Name	Description
Table data definition
tableOnFile	= true, if table is defined on file or in function usertab
table[:, :]	Table matrix (grid u1 = first column, grid u2 = first row; e.g., table=[0, 0; 0, 1])
tableName	Table name on file or in function usertab (see docu)
fileName	File where matrix is stored
verboseRead	= true, if info message that file is loading is to be printed
Table data interpretation
smoothness	Smoothness of table interpolation
extrapolation	Extrapolation of data outside the definition range
verboseExtrapolation	= true, if warning messages are to be printed if table input is outside the definition range

Connectors

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

Modelica.Blocks.Tables.CombiTable2Dv

Table look-up in two dimensions (matrix/file) with vector inputs and vector output of size n

Information

Bivariate constant, bilinear or bivariate Akima interpolation of a two-dimensional table. The grid points and function values are stored in a matrix "table[i,j]", where:

the first column "table[2:,1]" contains the u1 grid points,
the first row "table[1,2:]" contains the u2 grid points,
the other rows and columns contain the data to be interpolated.

Example:

           |       |       |       |
           |  1.0  |  2.0  |  3.0  |  // u2
       ----*-------*-------*-------*
       1.0 |  1.0  |  3.0  |  5.0  |
       ----*-------*-------*-------*
       2.0 |  2.0  |  4.0  |  6.0  |
       ----*-------*-------*-------*
     // u1
   is defined as
      table = [0.0,   1.0,   2.0,   3.0;
               1.0,   1.0,   3.0,   5.0;
               2.0,   2.0,   4.0,   6.0]
   If, e.g., the input u1 is {1.0}, input u2 is {1.0} and smoothness is LinearSegments, the output y is {1.0},
       e.g., the input u1 is {2.0}, input u2 is {1.5} and smoothness is LinearSegments, the output y is {3.0}.

The interpolation interval is found by a binary search where the interval used in the last call is used as start interval.

Via parameter smoothness it is defined how the data is interpolated:

  smoothness = 1: Bilinear interpolation
             = 2: Bivariate Akima interpolation: Smooth interpolation by bicubic Hermite
                  splines such that der(y) is continuous, also if extrapolated.
             = 3: Constant segments
             = 4: Fritsch-Butland interpolation: Not supported
             = 5: Steffen interpolation: Not supported

Values outside of the table range, are computed by extrapolation according to the setting of parameter extrapolation:

  extrapolation = 1: Hold the first or last values of the table,
                     if outside of the table scope.
                = 2: Extrapolate by using the derivative at the first/last table
                     points if outside of the table scope.
                     (If smoothness is LinearSegments or ConstantSegments
                     this means to extrapolate linearly through the first/last
                     two table points.).
                = 3: Periodically repeat the table data (periodical function).
                = 4: No extrapolation, i.e. extrapolation triggers an error

If the table has only one element, the table value is returned, independent of the value of the input signal.
If the input signal u1 or u2 is outside of the defined interval, the corresponding value is also determined by linear interpolation through the last or first two points of the table.
The grid values (first column and first row) have to be strictly increasing.

The table matrix can be defined in the following ways:

Explicitly supplied as parameter matrix "table", and the other parameters have the following values:
```
   tableName is "NoName" or has only blanks,
   fileName  is "NoName" or has only blanks.
```
Read from a file "fileName" where the matrix is stored as "tableName". Both text and MATLAB MAT-file format is possible. (The text format is described below). The MAT-file format comes in four different versions: v4, v6, v7 and v7.3. The library supports at least v4, v6 and v7 whereas v7.3 is optional. It is most convenient to generate the MAT-file from FreeMat or MATLAB® by command
```
   save tables.mat tab1 tab2 tab3
```
or Scilab by command
```
   savematfile tables.mat tab1 tab2 tab3
```
when the three tables tab1, tab2, tab3 should be used from the model.
Note, a fileName can be defined as URI by using the helper function loadResource.
Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks. Row-wise storage is always to be preferred as otherwise the table is reallocated and transposed. See the Tables package documentation for more details.

When the constant "NO_FILE_SYSTEM" is defined, all file I/O related parts of the source code are removed by the C-preprocessor, such that no access to files takes place.

If tables are read from a text file, the file needs to have the following structure ("-----" is not part of the file content):

-----------------------------------------------------
#1
double table2D_1(3,4)   # comment line
0.0  1.0  2.0  3.0  # u[2] grid points
1.0  1.0  3.0  5.0
2.0  2.0  4.0  6.0

double table2D_2(4,4)   # comment line
0.0  1.0  2.0  3.0  # u[2] grid points
1.0  1.0  3.0  5.0
2.0  2.0  4.0  6.0
3.0  3.0  5.0  7.0
-----------------------------------------------------

MATLAB is a registered trademark of The MathWorks, Inc.

Extends from Modelica.Blocks.Interfaces.MI2MO (2 Multiple Input / Multiple Output continuous control block), Internal.CombiTable2DBase (Base class for variants of CombiTable2D).

Parameters

Name	Description
n	Dimension of input and output vectors.
Table data definition
tableOnFile	= true, if table is defined on file or in function usertab
table[:, :]	Table matrix (grid u1 = first column, grid u2 = first row; e.g., table=[0, 0; 0, 1])
tableName	Table name on file or in function usertab (see docu)
fileName	File where matrix is stored
verboseRead	= true, if info message that file is loading is to be printed
Table data interpretation
smoothness	Smoothness of table interpolation
extrapolation	Extrapolation of data outside the definition range
verboseExtrapolation	= true, if warning messages are to be printed if table input is outside the definition range

Connectors

Name	Description
u1[n]	Connector 1 of Real input signals
u2[n]	Connector 2 of Real input signals
y[n]	Connector of Real output signals

Automatically generated Thu Dec 19 17:19:52 2019.