Linear System Analyzer

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

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Description

The Linear System Analyzer app lets you analyze time-domain and frequency-domain 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

Linear System Analyzer app

Open the Linear System Analyzer App

  • MATLAB® Toolstrip: On the Apps tab, under Control System Design and Analysis, click the app icon.

  • MATLAB command prompt: Enter linearSystemAnalyzer.

Examples

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To import models into Linear System Analyzer, select File > Import. The Import System Data dialog box opens.

Under Import from, select whether to import a model from:

  • The MATLAB workspace by selecting Workspace

  • A MAT-file by selecting MAT-file

In the Import column of the table, select one or models to import.

Click the Import.

To export models from Linear System Analyzer, select File > Export. The Linear System Analyzer Export dialog box opens.

In the Export column of the table, select one or models to import.

To export models to the MATLAB workspace, click Export to Workspace.

To export models to a MAT-file, click Export to Disk.

In the Select File to Write dialog box, specify the name and location for saved MAT-file and click Save.

To remove models from Linear System Analyzer, select Edit > Delete Systems. The Linear System Analyzer Delete dialog box opens.

In the Select column, select one or models to delete.

Click Delete.

To interactively specify the types of responses to plot, in Linear System Analyzer, select Edit > Plot Configurations. The Plot Configurations dialog box opens.

In the Select a response plot configuration section, select how many plots to show.

In the Response type section, use the drop-down lists to select the response type for each plot.

To update the plot configuration and close the dialog box, click OK.

To update the plot configuration without closing the dialog box, click Apply.

To switch the response type for an existing plot, right click the plot and, under Plot Types, select the type of response.

To interactively specify the line styles for responses, in Linear System Analyzer, select Edit > Response Styles. The Response Styles dialog box opens.

In the Distinguish by section, you can select how to distinguish between system, inputs, and outputs using the corresponding drop-down lists.

The selections in these drop-down lists are mutually exclusive, that is, you must use a different type of ordering for systems, inputs, and outputs.

Linear System Analyzer assigns response color, marker style, and line style based on the order specified under Color Order, Marker Order, and Linestyle Order, respectively.

You can modify these orders by clicking an item in the list and adjusting its position using the corresponding arrows.

To update the response styles and close the dialog box, click OK.

To update the response styles without closing the dialog box, click Apply.

To display response characteristics in a response plot, right-click the plot area and, under Characteristics, select a characteristic to display. You can display multiple characteristics on the same plot.

The available characteristics depend on the type of response plot.

Response PlotAvailable Characteristics
Step plot

  • Peak response

  • Rise time

  • Settling time

  • Transient time

  • Steady state

Impulse plot

  • Peak response

  • Transient time

Initial condition plot
Linear simulation plot

Peak response

Singular-value plot
Bode plot

  • Peak response

  • All stability margins

  • Minimum stability margins

Nyquist plot
Nichols plot
Pole-zero plotNone
Pole/zero plot of each input/output pair

The plot shows each characteristic using a marker on the response. To view information about the characteristic, click the marker.

Related Examples

Programmatic Use

linearSystemAnalyzer opens the Linear System Analyzer app with no LTI systems to analyze. For information on how to import a system, see Import Models.

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,...,sysN,LineSpecN) specifies the line style, marker, and color of each response plot.

For more information about line style specifications, see the LineSpec input argument of the lsimplot function.

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. If you do not specify input and time vectors using the extras syntax, then the Linear Simulation Tool dialog box opens and prompts you to specify the input and time vectors.

  • "initial" — Initial condition plot (state-space models only). You must specify an initial condition using use the extras syntax.

  • "bode" — Bode diagram

  • "bodemag" — Bode magnitude diagram

  • "nyquist" — Nyquist plot

  • "nichols" — Nichols plot

  • "sigma" — Singular value plot

  • "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, specify string array of up to six plot types. For example, the following command opens the app with a step response and a Nyquist plot for system sys.

linearSystemAnalyzer(["step","nyquist"],sys)

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, except the plotoptions argument and name-value arguments.

To determine appropriate arguments for extras, see the reference pages of the functions corresponding to each plot type, such as stepplot, bodeplot, or initialplot.

For example, suppose plottype is "step". Then, extras enables you to use the additional arguments that you could use with the stepplot 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 must use extras to supply initial conditions IC. For example, the following command sets the initial condition to vector x0 of state values.

linearSystemAnalyzer("initial",sys,x0)

If plottype is "lsim", you can use extras to specify input vector u and time vector t.

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) clears the plots and data from the Linear System Analyzer session corresponding to handle h. To clear multiple app instances at once, set h to a vector of handles.

linearSystemAnalyzer("current",sys1,sys2,...,sysn,h) adds the responses of the systems sys1, sys2, ..., sysn to the Linear System Analyzer session 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.

Version History

Introduced in R2015a

See Also

Apps

Functions