Control System Toolbox 8.4

Accessing and Modifying the Model Data

This demo shows how to access or edit parameter values and metadata in LTI objects.

Contents

Accessing Data

The tf, zpk, ss, and frd commands create LTI objects that store model data in a single MATLAB® variable. This data includes model-specific parameters (e.g., A,B,C,D matrices for state-space models) as well as generic metadata such as input and output names. The data is arranged into a fixed set of data fields called properties.

You can access model data in the following ways:

For illustration purposes, create the SISO transfer function (TF):

G = tf([1 2],[1 3 10],'inputdelay',3)

Transfer function:
                s + 2
exp(-3*s) * --------------
            s^2 + 3 s + 10

To see all properties of the TF object G, type

get(G)

           num: {[0 1 2]}
           den: {[1 3 10]}
       ioDelay: 0
      Variable: 's'
            Ts: 0
    InputDelay: 3
   OutputDelay: 0
     InputName: {''}
    OutputName: {''}
    InputGroup: [1x1 struct]
   OutputGroup: [1x1 struct]
          Name: ''
         Notes: {}
      UserData: []

The first four properties num, den, ioDelay, and variable are specific to the TF representation. The remaining properties are common to all LTI representations. You can use ltiprops to get more information on specific properties.

To retrieve the value of a particular property, use get or dot notation:

get(G,'num')    % get numerator value

ans =

    [1x3 double]

G.InputDelay    % get input delay value

ans =

     3

You can use abbreviations for property names as long as they are unambiguous, for example:

get(G,'iod')    % get transport delay value

ans =

     0

G.var           % get variable

ans =

s

Quick Data Retrieval

You can also retrieve all model parameters at once using tfdata, zpkdata, ssdata, or frdata. For example:

[num,den,Ts] = tfdata(G)

num =

    [1x3 double]


den =

    [1x3 double]


Ts =

     0

Note that the numerator and denominator are returned as cell arrays. This is consistent with the MIMO case where num and den contain cell arrays of numerator and denominator polynomials (with one entry per I/O pair). For SISO transfer functions, you can return the numerator and denominator data as vectors by using a flag, for example:

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

num =

     0     1     2


den =

     1     3    10

Editing Data

You can modify the data stored in LTI objects by editing the corresponding property values with set or dot notation. For example, for the transfer function G created above,

G.Ts = 1;

changes the sampling time from 0 to 1, which redefines the model as discrete:

G,

Transfer function:
             z + 2
z^(-3) * --------------
         z^2 + 3 z + 10

Sampling time: 1

The set command is equivalent to dot assignment, but also lets you set multiple properties at once:

set(G,'Ts',0.1,'Variable','q')
G,

Transfer function:
             q + 2
q^(-3) * --------------
         q^2 + 3 q + 10

Sampling time: 0.1

Sensitivity Analysis Example

Using model editing together with LTI array support, you can easily investigate sensitivity to parameter variations. For example, consider the second-order transfer function

You can investigate the effect of the damping parameter zeta on the frequency response by creating three models with different zeta values and comparing their Bode responses:

s = tf('s');

% Create 3 transfer functions with num=s+1 and den=1
H = repsys(s+5,[1 1 3]);

% Specify denominators using 3 different zeta values
zeta = [1 .5 .2];
for k=1:3
  H(:,:,k).den = [1 2*zeta(k) 5];  % zeta(k) -> k-th model
end

% Plot Bode response
bode(H), grid