.ModelicaAdditions.Tables.CombiTableTime

Information

Linear interpolation in a table with respect to time. Via parameter icol it can be defined how many columns of the table are interpolated. If, e.g., icol={2,4}, it is assumed that 2 output signals are present and that the first output is computed by interpolation of column 2 and the second output is computed by interpolation of column 4 of the table matrix.

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

   table = [0,  0;
            1,  0;
            1,  1;
            2,  4;
            3,  9;
            4, 16]

  If, e.g., time = 1.0, the output y =  0.0 (before event), 1.0 (after event)
      e.g., time = 1.5, the output y =  2.5,
      e.g., time = 2.0, the output y =  4.0,
      e.g., time = 5.0, the output y = 23.0 (i.e. extrapolation).

• If the table has only one row, the table value is returned, independently of time.
• If time is outside of the defined interval, i.e., time > table[size(table,1),1] or time < table[1,1], the corresponding value is also determined by linear interpolation through the last or first two points of the table.
• Two successive time instants may be identical (see table example) to define a discontinuous point in the function. At every defined time instant of the table, a time event occurs in order to not integrate over a discontinuous or not differentiable point. From the discussion follows that the time values in the first column of the table have to be monotonically (but NOT 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(6,2)   # comment line
  0   0
  1   0
  1   1
  2   4
  3   9
  4  16

double tab2(6,2)   # another comment line
  0   0
  2   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.