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## Copyright (C) 2009, 2010, 2011, 2012 Lukas F. Reichlin
##
## This file is part of LTI Syncope.
##
## LTI Syncope is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## LTI Syncope is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{s} =} tf (@var{'s'})
## @deftypefnx {Function File} {@var{z} =} tf (@var{'z'}, @var{tsam})
## @deftypefnx {Function File} {@var{sys} =} tf (@var{sys})
## @deftypefnx {Function File} {@var{sys} =} tf (@var{num}, @var{den}, @dots{})
## @deftypefnx {Function File} {@var{sys} =} tf (@var{num}, @var{den}, @var{tsam}, @dots{})
## Create or convert to transfer function model.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model to be converted to transfer function.
## @item num
## Numerator or cell of numerators. Each numerator must be a row vector
## containing the coefficients of the polynomial in descending powers of
## the transfer function variable.
## num@{i,j@} contains the numerator polynomial from input j to output i.
## In the SISO case, a single vector is accepted as well.
## @item den
## Denominator or cell of denominators. Each denominator must be a row vector
## containing the coefficients of the polynomial in descending powers of
## the transfer function variable.
## den@{i,j@} contains the denominator polynomial from input j to output i.
## In the SISO case, a single vector is accepted as well.
## @item tsam
## Sampling time in seconds. If @var{tsam} is not specified, a continuous-time
## model is assumed.
## @item @dots{}
## Optional pairs of properties and values.
## Type @command{set (tf)} for more information.
## @end table
##
## @strong{Outputs}
## @table @var
## @item sys
## Transfer function model.
## @end table
##
## @strong{Option Keys and Values}
## @table @var
## @item 'num'
## Numerator. See 'Inputs' for details.
##
## @item 'den'
## Denominator. See 'Inputs' for details.
##
## @item 'tfvar'
## String containing the transfer function variable.
##
## @item 'inv'
## Logical. True for negative powers of the transfer function variable.
##
## @item 'tsam'
## Sampling time. See 'Inputs' for details.
##
## @item 'inname'
## The name of the input channels in @var{sys}.
## Cell vector of length m containing strings.
## Default names are @code{@{'u1', 'u2', ...@}}
##
## @item 'outname'
## The name of the output channels in @var{sys}.
## Cell vector of length p containing strings.
## Default names are @code{@{'y1', 'y2', ...@}}
##
## @item 'ingroup'
## Struct with input group names as field names and
## vectors of input indices as field values.
## Default is an empty struct.
##
## @item 'outgroup'
## Struct with output group names as field names and
## vectors of output indices as field values.
## Default is an empty struct.
##
## @item 'name'
## String containing the name of the model.
##
## @item 'notes'
## String or cell of string containing comments.
##
## @item 'userdata'
## Any data type.
## @end table
##
## @strong{Example}
## @example
## @group
## octave:1> s = tf ('s');
## octave:2> G = 1/(s+1)
##
## Transfer function 'G' from input 'u1' to output ...
##
## 1
## y1: -----
## s + 1
##
## Continuous-time model.
## @end group
## @end example
## @example
## @group
## octave:3> z = tf ('z', 0.2);
## octave:4> H = 0.095/(z-0.9)
##
## Transfer function 'H' from input 'u1' to output ...
##
## 0.095
## y1: -------
## z - 0.9
##
## Sampling time: 0.2 s
## Discrete-time model.
## @end group
## @end example
## @example
## @group
## octave:5> num = @{[1, 5, 7], [1]; [1, 7], [1, 5, 5]@};
## octave:6> den = @{[1, 5, 6], [1, 2]; [1, 8, 6], [1, 3, 2]@};
## octave:7> sys = tf (num, den)
## @end group
## @end example
##
## @example
## @group
## Transfer function 'sys' from input 'u1' to output ...
##
## s^2 + 5 s + 7
## y1: -------------
## s^2 + 5 s + 6
##
## s + 7
## y2: -------------
## s^2 + 8 s + 6
## @end group
## @end example
##
## @example
## @group
## Transfer function 'sys' from input 'u2' to output ...
##
## 1
## y1: -----
## s + 2
##
## s^2 + 5 s + 5
## y2: -------------
## s^2 + 3 s + 2
##
## Continuous-time model.
## octave:8>
## @end group
## @end example
##
## @seealso{filt, ss, dss}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: September 2009
## Version: 0.3
function sys = tf (num = {}, den = {}, varargin)
## model precedence: frd > ss > zpk > tf > double
## inferiorto ("frd", "ss", "zpk"); # error if de-commented. bug in octave?
superiorto ("double");
argc = 0; # initialize argument count
switch (nargin)
case 0 # sys = tf ()
tsam = -2; # undefined sampling time
tfvar = "x"; # undefined transfer function variable
case 1
if (isa (num, "tf")) # already in tf form sys = tf (tfsys)
sys = num;
return;
elseif (isa (num, "lti")) # another lti object sys = tf (sys)
[sys, numlti] = __sys2tf__ (num);
sys.lti = numlti; # preserve lti properties
return;
elseif (is_real_matrix (num)) # static gain sys = tf (4), sys = tf (matrix)
num = num2cell (num);
num = __vec2tfpoly__ (num);
[p, m] = size (num);
den = tfpolyones (p, m); # denominators are all 1
tsam = -2; # undefined sampling time
tfvar = "x"; # undefined transfer function variable
elseif (ischar (num)) # s = tf ("s")
tfvar = num;
num = __vec2tfpoly__ ([1, 0]);
den = __vec2tfpoly__ ([1]);
tsam = 0;
else
print_usage ();
endif
case 2
if (ischar (num) && issample (den, -1)) # z = tf ("z", 0.3)
tfvar = num;
tsam = den;
num = __vec2tfpoly__ ([1, 0]);
den = __vec2tfpoly__ ([1]);
else # sys = tf (num, den)
num = __vec2tfpoly__ (num);
den = __vec2tfpoly__ (den);
tfvar = "s";
tsam = 0;
endif
otherwise # default case sys = tf (num, den, ...)
num = __vec2tfpoly__ (num);
den = __vec2tfpoly__ (den);
argc = numel (varargin); # number of additional arguments after num and den
if (issample (varargin{1}, -10)) # sys = tf (num, den, tsam, "prop1", val1, ...)
tsam = varargin{1}; # sampling time, could be 0 as well
argc--; # tsam is not a property-value pair
if (tsam == 0)
tfvar = "s";
else
tfvar = "z";
endif
if (argc > 0) # if there are any properties and values ...
varargin = varargin(2:end); # remove tsam from property-value list
endif
else # sys = tf (num, den, "prop1", val1, ...)
tsam = 0; # continuous-time
tfvar = "s";
endif
endswitch
[p, m] = __tf_dim__ (num, den); # determine number of outputs and inputs
tfdata = struct ("num", {num},
"den", {den},
"tfvar", tfvar,
"inv", false); # struct for tf-specific data
ltisys = lti (p, m, tsam); # parent class for general lti data
sys = class (tfdata, "tf", ltisys); # create tf object
if (argc > 0) # if there are any properties and values, ...
sys = set (sys, varargin{:}); # use the general set function
endif
endfunction

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