Function Reference: tf

Function File: s = tf ('s')

Function File: z = tf ('z', tsam)

Function File: sys = tf (sys)

Function File: sys = tf (mat, …)

Function File: sys = tf (num, den, …)

Function File: sys = tf (num, den, tsam, …)

Create or convert to transfer function model.

Inputs

sys: LTI model to be converted to transfer function.
mat: Gain matrix to be converted to static transfer function.
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.
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.
tsam: Sampling time in seconds. If tsam is not specified, a continuous-time model is assumed.
…: Optional pairs of properties and values. Type set (tf) for more information.

Outputs

sys: Transfer function model.

Option Keys and Values

’num’: Numerator. See ’Inputs’ for details.
’den’: Denominator. See ’Inputs’ for details.
’tfvar’: String containing the transfer function variable.
’inv’: Logical. True for negative powers of the transfer function variable.
’tsam’: Sampling time. See ’Inputs’ for details.
’inname’: The name of the input channels in sys. Cell vector of length m containing strings. Default names are {'u1', 'u2', ...}
’outname’: The name of the output channels in sys. Cell vector of length p containing strings. Default names are {'y1', 'y2', ...}
’ingroup’: Struct with input group names as field names and vectors of input indices as field values. Default is an empty struct.
’outgroup’: Struct with output group names as field names and vectors of output indices as field values. Default is an empty struct.
’name’: String containing the name of the model.
’notes’: String or cell of string containing comments.
’userdata’: Any data type.

Example

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.

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.

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)

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

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>

See also: filt, ss, dss.

Package: control