Control System Toolbox Function Reference

tfdata

Quick access to transfer function data

Syntax

[num,den] = tfdata(sys)
[num,den] = tfdata(sys,'v')
[num,den,Ts] = tfdata(sys)

Description

[num,den] = tfdata(sys) returns the numerator(s) and denominator(s) of the transfer function for the TF, SS or ZPK model (or LTI array of TF, SS or ZPK models) sys. For single LTI models, the outputs num and den of tfdata are cell arrays with the following characteristics:

• num and den have as many rows as outputs and as many columns as inputs.
• The (i,j) entries num{i,j} and den{i,j} are row vectors specifying the numerator and denominator coefficients of the transfer function from input j to output i. These coefficients are ordered in descending powers of or .

For arrays sys of LTI models, num and den are multidimensional cell arrays with the same sizes as sys.

If sys is a state-space or zero-pole-gain model, it is first converted to transfer function form using tf. See Table 11-15, "LTI Properties," on page 11-194 for more information on the format of transfer function model data.

For SISO transfer functions, the syntax

[num,den] = tfdata(sys,'v')

forces tfdata to return the numerator and denominator directly as row vectors rather than as cell arrays (see example below).

[num,den,Ts] = tfdata(sys) also returns the sample time Ts.

You can access the remaining LTI properties of sys with get or by direct referencing, for example,

sys.Ts
sys.variable

Example

Given the SISO transfer function

h = tf([1 1],[1 2 5])

you can extract the numerator and denominator coefficients by typing

[num,den] = tfdata(h,'v')
num =
     0     1     1
 
den =
     1     2     5

This syntax returns two row vectors.

If you turn h into a MIMO transfer function by typing

H = [h ; tf(1,[1 1])]

the command

[num,den] = tfdata(H)

now returns two cell arrays with the numerator/denominator data for each SISO entry. Use celldisp to visualize this data. Type

celldisp(num)

and MATLAB returns the numerator vectors of the entries of H.

num{1} =
     0     1     1
 
num{2} =
     0     1

Similarly, for the denominators, type

celldisp(den)
den{1} =
     1     2     5
 
den{2} =
     1     1

See Also
get         Get properties of LTI models

ssdata      Quick access to state-space data

tf          Specify transfer functions

zpkdata     Quick access to zero-pole-gain data

tf

totaldelay