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Analyze time and frequency responses of linear time-invariant (LTI) systems

The **Linear System Analyzer** app lets
you analyze time and frequency responses of LTI
systems. Using this app, you can:

View and compare the response plots of SISO and MIMO systems, or of several linear models at the same time.

Generate time response plots such as step, impulse, and time response to arbitrary inputs.

Generate frequency response plots such as Bode, Nyquist, Nichols, singular-value, and pole-zero plots.

Inspect key response characteristics, such as rise time, maximum overshoot, and stability margins.

**Linear System Analyzer** can
generate the following response plots:

Step response

Impulse response

Simulated time response to specified input signal

Simulated time response from specified initial conditions (state-space models only)

Bode diagram (magnitude and phase, or magnitude alone)

Nyquist plot

Nichols plot

Singular value plot

Pole/zero map and I/O pole/zero map

MATLAB

^{®}Toolstrip: On the**Apps**tab, under**Control System Design and Analysis**, click the app icon.MATLAB command prompt: Enter

`linearSystemAnalyzer`

.

`linearSystemAnalyzer`

`linearSystemAnalyzer`

opens the **Linear System Analyzer** app
with no LTI systems to analyze. To specify a
system to analyze, select **File** > **Import**.

`linearSystemAnalyzer(sys1,sys2,...,sysn)`

`linearSystemAnalyzer(sys1,sys2,...,sysn)`

opens **Linear System Analyzer** and displays the
step response of one or more dynamic system
models, `sys1`

,
`sys2`

, ...,
`sysn`

. Such models include:

Numeric LTI models such as

`tf`

,`zpk`

, or`ss`

models.Identified models such as

`idtf`

,`idss`

, or`idproc`

(requires System Identification Toolbox™ software).Generalized LTI models such as

`genss`

or`uss`

models. For generalized LTI models without uncertainty,**Linear System Analyzer**plots the response of the nominal value of the model. For generalized models with uncertainty, the app plots the responses of 20 random samples of the uncertain system. (Uncertain models require Robust Control Toolbox™ software.)

`linearSystemAnalyzer(sys1,LineSpec1,sys2,LineSpec2...,sysn,LineSpecn)`

`linearSystemAnalyzer(sys1,LineSpec1,sys2,LineSpec2...,sysn,LineSpecn)`

specifies the line style, marker, and color of each response
plot. Specify plot styles using one, two, or three
characters. For example, the following code uses red
asterisks for the response of `sys1`

, and a
magenta dotted line for the response of
`sys2`

.

linearSystemAnalyzer(sys1,'r-*',sys2,'m--');

For more information about configuring this
argument, see the `LineSpec`

input argument
of the `plot`

function.

`linearSystemAnalyzer(plottype,___)`

`linearSystemAnalyzer(plottype,___)`

opens **Linear System Analyzer** and
displays the response types specified by
`plottype`

. You can use this
syntax with any of the previous input argument
combinations. The `plottype`

argument can be any one of the following:

`'step'`

— Step response.`'impulse'`

— Impulse response.`'lsim'`

— Linear simulation plot. When you use this plot type, the Linear Simulation Tool dialog box prompts you to specify an input signal for the simulation.`'initial'`

— Initial condition plot (state-space models only). You can use the`extras`

argument to specify the initial state. If you do not, the Linear Simulation Tool dialog box opens and prompts you to specify an initial state for the simulation.`'bode'`

— Bode diagram.`'bodemag'`

— Bode magnitude diagram.`'nyquist'`

— Nyquist plot.`'nichols'`

— Nichols plot.`'sigma'`

— Singular value plot. (See`sigma`

).`'pzmap'`

— Pole/zero map.`'iopzmap'`

— Pole/zero map of each input/output pair of the LTI system.

To open **Linear System Analyzer**
with multiple response plots, use a cell array of
up to six of these plot types for the
`plottype`

input argument. For
example, the following command opens the app with
a step response plot and a Nyquist plot for the
system
`sys`

.

linearSystemAnalyzer({'step';'nyquist'},sys)

`linearSystemAnalyzer(plottype,sys1,sys2,...,sysn,extras)`

`linearSystemAnalyzer(plottype,sys1,sys2,...,sysn,extras)`

specifies additional input arguments specific to
the type of response plot.
`extras`

can be one or more of
the input arguments available for the function
corresponding to the plot type. For example,
suppose `plottype`

is
`'step'`

. Then,
`extras`

enables you to use the
additional arguments that you could use with the
`step`

command, such as the desired final time,
`Tfinal`

. Thus, the following
command opens the app with a step response plot of
`sys`

, with a final time of
`Tfinal`

.

```
linearSystemAnalyzer('step',sys,Tfinal)
```

If `plottype`

is
`'initial'`

, you can use
`extras`

to supply the initial
conditions `x0`

, and other
arguments such as `Tfinal`

. For
example:

```
linearSystemAnalyzer('initial',sys,x0,Tfinal)
```

To determine appropriate arguments for
`extras`

, see the reference pages
of the functions corresponding to each plot type,
such as `step`

, `bode`

, or `initial`

.

`h = linearSystemAnalyzer(___)`

`h = linearSystemAnalyzer(___)`

returns a handle to the **Linear System
Analyzer** figure. You can use this syntax
with any of the previous combinations of input
arguments. Use the handle to modify previously
opened **Linear System Analyzer**
instances, as described in the next two
syntaxes.

`linearSystemAnalyzer('clear',h)`

`linearSystemAnalyzer('clear',h)`

clears the plots and data from the **Linear
System Analyzer** corresponding to handle
`h`

. To clear multiple app
instances at once, set `h`

to a
vector of handles.

`linearSystemAnalyzer('current',sys1,sys2,...,sysn,h)`

`linearSystemAnalyzer('current',sys1,sys2,...,sysn,h)`

adds the responses of the systems
`sys1`

, `sys2`

,
..., `sysn`

to the **Linear
System Analyzer** corresponding to handle
`h`

. To update multiple app
instances at once, set `h`

to a
vector of handles. If the new systems have
different I/O dimensions from the currently
displayed systems, the app clears the existing
responses and displays only the new ones.

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