## Control System Toolbox |

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

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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:

The

`get`commandStructure-like dot notation

Data retrieval commands

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

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

G = s + 2 exp(-3*s) * -------------- s^2 + 3 s + 10 Continuous-time transfer function.

To see all properties of the TF object `G`, type

get(G)

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

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 `help tf.num` to get more information on the "num" property and similarly for the other properties.

To retrieve the value of a particular property, use

```
G.InputDelay % get input delay value
```

ans = 3

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

```
G.iod % get transport delay value
```

ans = 0

```
G.var % get variable
```

ans = s

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

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

G,

G = z + 2 z^(-3) * -------------- z^2 + 3 z + 10 Sample time: 1 seconds Discrete-time transfer function.

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

```
G.Ts = 0.1;
G.Variable = 'q';
G,
```

G = q + 2 q^(-3) * -------------- q^2 + 3 q + 10 Sample time: 0.1 seconds Discrete-time transfer function.

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