System Identification Toolbox

Graphs of Model Properties

There are several commands in the toolbox for graphing model characteristics such as:

• bode
• compare
• ffplot
• impulse
• nyquist
• pzmap
• step

They have all the same basic syntax. To look at one model use

• command(Model)
  

where command is any of the functions listed above.

• command(Mod1,Mod2, ...,ModN)
  

shows a comparison of several models. Modk can be any idmodel models. They can be used with any of the Control System Toolbox's LTI models. For some commands Modk can also be idfrd and iddata objects. For multivariable models, the plots are grouped so that each input/output channel (for all models) are plotted together. The InputName and OutputName properties of the models are used for this. The number of channels need not be the same in the different models, which is quite useful when trying to find a good model of a multivariable system.

• command(Mod1,PlotStyle1,...,ModN,PlotStyleN)
  

allows you to define colors, linestyles and markers associated with the different models. PlotStyle takes values such as 'b' (for blue), 'b:' (for a blue dotted line) or 'b*-' (for a blue solid line with the points marked by a star). This is the same as for the usual plot command.

To also show the uncertainty of the model characteristics, use

• command(Mod1,...,ModN,'sd',SD)
  

This will mark, using dash-dotted lines, a confidence region around the nominal model corresponding to SD standard deviations (for the Gaussian distribution). This region is computed using the estimated covariance matrix for the estimated parameters.

• command(Mod1,...,ModN,'sd',SD,'fill')
  

shows the uncertainty region as a filled region instead.

The different commands have some further options to select time or frequency ranges and similar. See Function Reference.

If Model contains measured input channels, the plot shows just the transfer functions from these measured inputs to the outputs, that is G in (3-53). To graph the response from the noise sources, use

• command(Model('n'))
  

For the frequency response graphs, this shows the additive disturbance spectra, i.e., the spectra of the signal H(q)e(t) in Equation (3-53), so that the properties of the noise source e are included in the plot.

For the other graphs, the properties of the transfer function H are shown, i.e., no noise normalization is done. The same is true if Model is a time series and has no measured input channels. That means that, for example, step shows the step response of the transfer function H, without accounting for the size (covariance matrix) of e. To include such effects, the disturbances should first be converted to normalized noise sources, using the command noisecnv. See The Noise Channels.

Model Output

An important and visually suggestive plot, is to compare the measured output signal with the models' simulated or predicted outputs. This is achieved by

• compare(Data,model)
  

The input signal in Data is used by the model(s) to simulate the output. This simulated output is shown together with the measured output, which reveals what features in the data the model can and cannot reproduce. Also a legend shows the fit between the signals, in terms of how much of the output variation is reproduced by the model(s).

Frequency Response

Three functions offer graphic display of the frequency functions and spectra: bode, ffplot, and nyquist.

• bode(G)
  

plots the Bode diagram of G (logarithmic scales and frequencies in rad/sec). If G is a spectrum, only an amplitude plot (the power spectrum) is given. Here G can be any idmodel or idfrd object.

The command ffplot has the same syntax as bode but works with linear frequency scales and Hertz as the unit. The command nyquist also has the same syntax, but produces Nyquist plots; i.e., graphs of the frequency function in the complex plane.

Transient Response

The impulse and step responses of the models are shown by

• impulse(Model) and step(Model)
  

impulse and step follow the general syntax, but can also accept iddata objects as arguments. For direct estimation of step and impulse responses from data, the procedure described in Estimating Impulse Responses is used.

Zeros and Poles

The zeros and poles are graphed by

• pzmap(Model)
  

This gives a plot with `x' marking poles and `o' marking zeros. Otherwise, pzmap follows the general syntax.

General

If you have the Control System Toolbox

• view(Model)
  

will open the LTI-viewer with access to a number of model displays. No uncertainty information can be shown, though.

Frequency Function Format: the idfrd model

Transformations to Other Model Representations