Package Modelica.Blocks.TablesLibrary of blocks to interpolate in one and two-dimensional tables
Package Modelica.Blocks.Tables
This package contains blocks for one- and two-dimensional interpolation in tables.
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="../../../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="3.2.3")));
end Test25_usertab;
Extends from Modelica.Icons.Package (Icon for standard packages).
| 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 |
Block Modelica.Blocks.Tables.CombiTable1D
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).
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.
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
The table matrix can be defined in the following ways:
tableName is "NoName" or has only blanks, fileName is "NoName" or has only blanks.
save tables.mat tab1 tab2 tab3or Scilab by command
savematfile tables.mat tab1 tab2 tab3when the three tables tab1, tab2, tab3 should be used from the model.
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).
| Type | Name | Default | Description |
|---|---|---|---|
final Integer | n | size(columns, 1) | Number of inputs (= number of outputs) |
Boolean | tableOnFile | false | = true, if table is defined on file or in function usertab |
Real | table[:,:] | fill(0, 0, 2) | Table matrix (grid = first column; e.g., table=[0, 0; 1, 1; 2, 4]) |
String | tableName | "NoName" | Table name on file or in function usertab (see docu) |
String | fileName | "NoName" | File where matrix is stored |
Boolean | verboseRead | true | = true, if info message that file is loading is to be printed |
Integer | columns[:] | 2:size(table, 2) | Columns of table to be interpolated |
Smoothness | smoothness | Modelica.Blocks.Types.Smoothness.LinearSegments | Smoothness of table interpolation |
Extrapolation | extrapolation | Modelica.Blocks.Types.Extrapolation.LastTwoPoints | Extrapolation of data outside the definition range |
Boolean | verboseExtrapolation | false | = true, if warning messages are to be printed if table input is outside the definition range |
final Real | u_min | Internal.getTable1DAbscissaUmin(tableID) | Minimum abscissa value defined in table |
final Real | u_max | Internal.getTable1DAbscissaUmax(tableID) | Maximum abscissa value defined in table |
| Type | Name | Description |
|---|---|---|
input RealInput | u[n] | Connector of Real input signals |
output RealOutput | y[n] | Connector of Real output signals |
Block Modelica.Blocks.Tables.CombiTable1Ds
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.
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).
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.
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
The table matrix can be defined in the following ways:
tableName is "NoName" or has only blanks, fileName is "NoName" or has only blanks.
save tables.mat tab1 tab2 tab3or Scilab by command
savematfile tables.mat tab1 tab2 tab3when the three tables tab1, tab2, tab3 should be used from the model.
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.SIMO (Single Input Multiple Output continuous control block).
| Type | Name | Default | Description |
|---|---|---|---|
final Integer | nout | size(columns, 1) | Number of outputs |
Boolean | tableOnFile | false | = true, if table is defined on file or in function usertab |
Real | table[:,:] | fill(0, 0, 2) | Table matrix (grid = first column; e.g., table=[0, 0; 1, 1; 2, 4]) |
String | tableName | "NoName" | Table name on file or in function usertab (see docu) |
String | fileName | "NoName" | File where matrix is stored |
Boolean | verboseRead | true | = true, if info message that file is loading is to be printed |
Integer | columns[:] | 2:size(table, 2) | Columns of table to be interpolated |
Smoothness | smoothness | Modelica.Blocks.Types.Smoothness.LinearSegments | Smoothness of table interpolation |
Extrapolation | extrapolation | Modelica.Blocks.Types.Extrapolation.LastTwoPoints | Extrapolation of data outside the definition range |
Boolean | verboseExtrapolation | false | = true, if warning messages are to be printed if table input is outside the definition range |
final Real | u_min | Internal.getTable1DAbscissaUmin(tableID) | Minimum abscissa value defined in table |
final Real | u_max | Internal.getTable1DAbscissaUmax(tableID) | Maximum abscissa value defined in table |
| Type | Name | Description |
|---|---|---|
input RealInput | u | Connector of Real input signal |
output RealOutput | y[nout] | Connector of Real output signals |
Block Modelica.Blocks.Tables.CombiTable2D
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:
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.
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
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
The table matrix can be defined in the following ways:
tableName is "NoName" or has only blanks, fileName is "NoName" or has only blanks.
save tables.mat tab1 tab2 tab3or Scilab by command
savematfile tables.mat tab1 tab2 tab3when the three tables tab1, tab2, tab3 should be used from the model.
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 -----------------------------------------------------
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. The matrix elements are interpreted in exactly the same way as if the matrix is given as a parameter. For example, the first column "table2D_1[2:,1]" contains the u[1] grid points, and the first row "table2D_1[1,2:]" contains the u[2] grid points.
MATLAB is a registered trademark of The MathWorks, Inc.
Extends from Modelica.Blocks.Interfaces.SI2SO (2 Single Input / 1 Single Output continuous control block) and Modelica.Blocks.Tables.Internal.CombiTable2DBase (Base class for variants of CombiTable2D).
| Type | Name | Default | Description |
|---|---|---|---|
Boolean | tableOnFile | false | = true, if table is defined on file or in function usertab |
Real | table[:,:] | fill(0, 0, 2) | Table matrix (grid u1 = first column, grid u2 = first row; e.g., table=[0, 0; 0, 1]) |
String | tableName | "NoName" | Table name on file or in function usertab (see docu) |
String | fileName | "NoName" | File where matrix is stored |
Boolean | verboseRead | true | = true, if info message that file is loading is to be printed |
Smoothness | smoothness | Modelica.Blocks.Types.Smoothness.LinearSegments | Smoothness of table interpolation |
Extrapolation | extrapolation | Modelica.Blocks.Types.Extrapolation.LastTwoPoints | Extrapolation of data outside the definition range |
Boolean | verboseExtrapolation | false | = true, if warning messages are to be printed if table input is outside the definition range |
final Real | u_min[2] | getTable2DAbscissaUmin(tableID) | Minimum abscissa value defined in table |
final Real | u_max[2] | getTable2DAbscissaUmax(tableID) | Maximum abscissa value defined in table |
| Type | Name | Description |
|---|---|---|
input RealInput | u1 | Connector of Real input signal 1 |
input RealInput | u2 | Connector of Real input signal 2 |
output RealOutput | y | Connector of Real output signal |
Block Modelica.Blocks.Tables.CombiTable2Dv
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:
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}.
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
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
The table matrix can be defined in the following ways:
tableName is "NoName" or has only blanks, fileName is "NoName" or has only blanks.
save tables.mat tab1 tab2 tab3or Scilab by command
savematfile tables.mat tab1 tab2 tab3when the three tables tab1, tab2, tab3 should be used from the model.
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 -----------------------------------------------------
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. The matrix elements are interpreted in exactly the same way as if the matrix is given as a parameter. For example, the first column "table2D_1[2:,1]" contains the u[1] grid points, and the first row "table2D_1[1,2:]" contains the u[2] grid points.
MATLAB is a registered trademark of The MathWorks, Inc.
Extends from Modelica.Blocks.Interfaces.MI2MO (2 Multiple Input / Multiple Output continuous control block) and Modelica.Blocks.Tables.Internal.CombiTable2DBase (Base class for variants of CombiTable2D).
| Type | Name | Default | Description |
|---|---|---|---|
Integer | n | 1 | Dimension of input and output vectors. |
Boolean | tableOnFile | false | = true, if table is defined on file or in function usertab |
Real | table[:,:] | fill(0, 0, 2) | Table matrix (grid u1 = first column, grid u2 = first row; e.g., table=[0, 0; 0, 1]) |
String | tableName | "NoName" | Table name on file or in function usertab (see docu) |
String | fileName | "NoName" | File where matrix is stored |
Boolean | verboseRead | true | = true, if info message that file is loading is to be printed |
Smoothness | smoothness | Modelica.Blocks.Types.Smoothness.LinearSegments | Smoothness of table interpolation |
Extrapolation | extrapolation | Modelica.Blocks.Types.Extrapolation.LastTwoPoints | Extrapolation of data outside the definition range |
Boolean | verboseExtrapolation | false | = true, if warning messages are to be printed if table input is outside the definition range |
final Real | u_min[2] | getTable2DAbscissaUmin(tableID) | Minimum abscissa value defined in table |
final Real | u_max[2] | getTable2DAbscissaUmax(tableID) | Maximum abscissa value defined in table |
| Type | Name | Description |
|---|---|---|
input RealInput | u1[n] | Connector 1 of Real input signals |
input RealInput | u2[n] | Connector 2 of Real input signals |
output RealOutput | y[n] | Connector of Real output signals |