tfdata

Access transfer function data

Syntax

[num,den] = tfdata(sys)

[num,den,ts] = tfdata(sys)

[num,den,ts,sdnum,sdden] = tfdata(sys)

___ = tfdata(sys,J1,...,JN)

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

Description

[num,den] = tfdata(sys) returns the numerator and denominator coefficients of the transfer function for the tf (Control System Toolbox), ss (Control System Toolbox) and zpk (Control System Toolbox) model objects or the array of model objects represented by sys.

The outputs num and den are two-dimensional cell arrays if sys contains a single LTI model. When sys is an array of models, num and den are returned as multidimensional cell arrays.

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

[num,den,ts,sdnum,sdden] = tfdata(sys) also returns the uncertainties in the numerator and denominator coefficients of identified system sys. sdnum{i,j}(k) is the 1 standard uncertainty in the value num{i,j}(k) and sdden{i,j}(k) is the 1 standard uncertainty in the value den{i,j}(k). If sys does not contain uncertainty information, sdnum and sdden are empty [].

___ = tfdata(sys,J1,...,JN) extracts the data for the J1,...,JN entry in the model array sys.

[num,den] = tfdata(sys,'v') returns the numerator and denominator coefficients as row vectors rather than cell arrays for a SISO transfer function represented by sys.

Examples

Extract Numerator and Denominator Coefficients from Transfer Function

For this example, consider tfData.mat which contains a continuous-time SISO transfer function sys1.

Load the data and use tfdata to extract the numerator and denominator coefficients.

load('tfData.mat','sys1');
[num,den] = tfdata(sys1);

num and den are returned as cell arrays. To display data, use celldisp.

celldisp(num)

 
num{1} =
 
     0     1     5     2

 

celldisp(den)

 
den{1} =
 
     7     4     2     1

 

You can also extract the numerator and denominator coefficients as row vectors with the following syntax.

[num,den] = tfdata(sys1,'v');

Extract Discrete-Time Transfer Function Data

For this example, consider tfData.mat which contains a discrete-time SISO transfer function sys2.

Load the data and use tfdata to extract the numerator and denominator coefficients along with the sample time.

load('tfData.mat','sys2');
[num,den,ts] = tfdata(sys2)

num = 1x1 cell array
    {[0 0 2 0]}

den = 1x1 cell array
    {[4 0 3 -1]}

ts = 
0.1000

num and den are returned as cell arrays. To display data, use celldisp.

celldisp(num)

 
num{1} =
 
     0     0     2     0

 

celldisp(den)

 
den{1} =
 
     4     0     3    -1

 

Extract Identified Transfer Function Data

For this example, estimate a transfer function with 2 poles and 1 zero from identified data contained in iddata7.mat with an input delay value.

Load the identified data and estimate the transfer function.

load('iddata7.mat');
sys = tfest(z7,2,1,'InputDelay',[1 0]);

Extract the numerator, denominator and their standard deviations for the 2-input, 1 output identified transfer function.

[num,den,~,sdnum,sdden] = tfdata(sys)

num=1×2 cell array
    {[0 -0.5212 1.1886]}    {[0 0.0552 -0.0013]}

den=1×2 cell array
    {[1 0.3390 0.2353]}    {[1 0.0360 0.0314]}

sdnum=1×2 cell array
    {[0 0.1311 0.0494]}    {[0 0.0246 0.0033]}

sdden=1×2 cell array
    {[0 0.0183 0.0085]}    {[0 0.0278 0.0048]}

Extract Data from Specific Model in Transfer Function Array

For this example, extract numerator and denominator coefficients for a specific transfer function contained in the 3x1 array of continuous-time transfer functions sys.

Load the data and extract the numerator and denominator coefficients of the second model in the array.

load('tfArray.mat','sys');
[num,den] = tfdata(sys,2);

Use celldisp to visualize the data in the cell array num and den.

celldisp(num)

 
num{1} =
 
     0     0     2

 

celldisp(den)

 
den{1} =
 
     1     1     2

 

Input Arguments

sys — Dynamic system

dynamic system model | model array

Dynamic system, specified as a SISO or MIMO dynamic system model, or an array of SISO or MIMO dynamic system models. Dynamic systems that you can use include continuous-time or discrete-time numeric LTI models such as tf (Control System Toolbox), ss (Control System Toolbox) and zpk (Control System Toolbox) models.

If sys is a state-space or zero-pole-gain model, it is first converted to transfer function form using tf (Control System Toolbox). For more information on the format of transfer function model data, see the tf (Control System Toolbox) reference page.

For SISO transfer functions, use the following syntax to return the numerator and denominator coefficients directly as row vectors rather than as cell arrays:

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

J1,...,JN — Indices of models in array whose data you want to access

positive integer

Indices of models in array whose data you want to access, specified as a positive integer. You can provide as many indices as there are array dimensions in sys. For example, if sys is a 4-by-5 array of transfer functions, the following command accesses the data for entry (2,3) in the array.

[num,den] = tfdata(sys,2,3);

Output Arguments

num — Coefficients of the numerator

cell array | row vector

Coefficients of the numerator of the transfer function, returned as a cell array or row vector.

When sys contains a single LTI model, the output num is returned as a cell array with the following characteristics:

• num has as many rows as outputs and as many columns as inputs of sys.

• The (i,j) entries in num{i,j} are row vectors specifying the numerator coefficients of the transfer function from input j to output i. tfdata orders these coefficients in descending powers of s or z.

When sys contains an array of LTI models, num is returned as a multidimensional cell array of the same size as sys.

den — Coefficients of the denominator

cell array | row vector

Coefficients of the denominator of the transfer function, returned as a cell array or row vector.

When sys contains a single LTI model, the output den is returned as a cell array with the following characteristics:

• den has as many rows as outputs and as many columns as inputs of sys.

• The (i,j) entries in den{i,j} are row vectors specifying the denominator coefficients of the transfer function from input j to output i. tfdata orders these coefficients in descending powers of s or z.

When sys contains an array of LTI models, den is returned as a multidimensional cell array of the same size as sys.

ts — Sample time

non-negative scalar

Sample time, returned as a non-negative scalar.

sdnum — Standard uncertainty of the numerator coefficients

cell array

Standard uncertainty of the numerator coefficients of the identified system sys, returned as a cell array of the same size as num. sdnum{i,j}(k) is the 1 standard uncertainty in the value num{i,j}(k). If sys does not contain uncertainty information, sdnum is empty [].

sdden — Standard uncertainty the denominator coefficients

cell array

Standard uncertainty of the denominator coefficients of the identified system sys, returned as a cell array of the same size as den. sdden{i,j}(k) is the 1 standard uncertainty in the value den{i,j}(k). If sys does not contain uncertainty information, sdden is empty [].

Version History

Introduced before R2006a