.ModelicaAdditions.Tables.CombiTable2D

Information

Linear interpolation in two dimensions of a table. The grid points and function values are stored in a matrix "table[i,j]", where:

• the first column "table[2:,1]" contains the u[1] grid points,
• the first row "table[1,2:]" contains the u[2] 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 u is [1.0;1.0], the output y is 1.0,
       e.g. the input u is [2.0;1.5], the output y is 3.0.

• The interpolation is efficient, because a search for a new interpolation starts at the interval used in the last call.
• If the table has only one element, the table value is returned, independent of the value of the input signal.
• If the input signal u 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 strict monotonically increasing.

The table matrix can be defined in the following ways:

1. 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.
   

2. Read from a file "fileName" where the matrix is stored as "tableName". Both ASCII and binary file format is possible. (the ASCII format is described below). It is most convenient to generate the binary file from Matlab (Matlab 4 storage format), e.g., by command

      save tables.mat tab1 tab2 tab3 -V4
   

   when the three tables tab1, tab2, tab3 should be used from the model.
3. Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks.

Table definition methods (1) and (3) do not allocate dynamic memory, and do not access files, whereas method (2) does. Therefore (1) and (3) are suited for hardware-in-the-loop simulation (e.g. with dSpace hardware). When the constant "NO_FILE" is defined, all parts of the source code of method (2) are removed by the C-preprocessor, such that no dynamic memory allocation and no access to files takes place.

If tables are read from an ASCII-file, the file need 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". Afterwards, the corresponding matrix has to be declared with type, name and actual dimensions. Finally, in successive rows of the file, the elements of the matrix have to be given. Several matrices may be defined one after another.