Zbigniew,
there is << (quote) the package COMA (COntrol engineering with MAxima)
COMA is a well designed package for (wx)Maxima. It has functions for studies
of linear continuous systems in the time domain and Laplace domain. It
contains state space methods and functions for optimizing and computing
stability limits and stability areas.
The newest version can be found at>>
http://sourceforge.net/apps/phpbb/maxima/viewforum.php?f=3
It comes withe a very fine documentation.
best
Wolfgang Lindner
-----Urspr?ngliche Nachricht-----
Von: Zbigniew Komarnicki <cblasius at gmail.com>
An: maxima at math.utexas.edu <maxima at math.utexas.edu>
Datum: Montag, 12. Juli 2010 10:51
Betreff: [Maxima] Two questions
|Hello,
|
|is there any possibility to write a package which will be special type of
|symbolic expression for *control theory* (or maybe not only)? I especially
|think here about introducing special types, for example, 'control_matrix'
|and 'control_vector' as e.g.
|
|size_of_matrix: [3, 4];
|C: control_matrix(size_of_matrix);
|
|size_of_vector: [4, 1]
|indices_of_vector: [r, k];
|x: control_vector(size_of_vector, indices_of_vector);
|
|Then when I write:
|y: C . x(r+1,k) - C . x(r,k);
|
|then we tell maxima, that:
|- x is special type of vector and we can check it size and set it also to y
|and maxima will be know that x is indexed by indices r and k, so maxima
could
|be able to do some simplification on the special vector x
|
|- C is special type of matrix and maxima could be able to perform some
checks
|about sizes of matrices and vectors included in multiplications and
additions
|and so on.
|
|Then as a result we obtain this
| C . ( x(r+1,k) - x(r,k) );
|because maxima will be known, that here is a special type of matrix and
|vectors (control_matrix and control_vector)
|
|and not as now, where is no simplifications made
| C . x(r+1,k) - C . x(r,k);
|
|Of course instead of writing the vector x as x(r+1,k) we can operate for
|example on the list notation, e.i.
|y: C . x[r+1,k] - C . x[r,k];
|
|This gives our such output, but still without simplification
| C . x - C . x
| r + 1, k r, k
|
|it should be:
| C . (x - x )
| r + 1, k r, k
|
|Is this possible to create such package to manipulate on matrices as in
|control theory, not on real values in these matrices of vectors but in
|symbolic way? Of course after doing some operations we can in the finall
step
|assign values to this matrices for example by function
|assign_values(C, [[1,2,3,4],[1,2,3,4],[1,2,3,4]]);
|
|and for vectors, but first define range for index r and index k in vector
x,
|e.g.:
|
|set_range_on_vector(x, [r, 1, 10], [k, 1, 10])
|
|and assign for index 'r'
|assign_values(x[r,k], [1,2,3,4]);
|assign_values(x[r+1,k], [1,2,3,4]);
|...
|assign_values(x[r+9,k], [1,2,3,4]);
|
|and for index 'k'
|assign_values(x[r,k], [1,2,3,4]);
|assign_values(x[r,k+1], [1,2,3,4]);
|...
|assign_values(x[r,k+9], [1,2,3,4]);
|and so on
|
|or on real indices values
|assign_values(x[1,1], [1,2,3,4]);
|assign_values(x[2,1], [1,2,3,4]);
|...
|assign_values(x[10,1], [1,2,3,4]);
|
|of course for the vector x it must by created an array or list of list from
|the values will be taken or stored at given indices.
|
|What do you thinking about this? Is this possible to write such package in
|maxima? I haven't much knowledge about implement such project in maxima but
I
|think that such package will be very usefull for people who working in
|control theory field/research. As I know currently no such package even in
|commercial software (or maybe I am wrong?).
|
|
|------------------------------------------
|And second question:
|------------------------------------------
|I checked also that when I write:
|eq: transpose(A . B . C);
|I obtain as expected
| transpose(C) . transpose(B) . transpose(A)
|
|Is this possible to do it in back, e.g.:
|eq1: transpose(C) . transpose(B) . transpose(A)
|and get:
| transpose(A . B . C)
|
|Is this possible ?
|
|
|I'm sorry for my English language.
|Thank you for your time.
|
|Zbigniew
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