Linear Simulation Tool

Specify input signals and initial conditions for simulating linear models with arbitrary input signals and initial conditions

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Description

Use the Linear Simulation Tool to specify input signals and initial conditions for simulating linear models with arbitrary input signals and initial conditions.

The Linear Simulation Tool lets you do the following:

  • Import input signals from the MATLAB® workspace.

  • Import input signals from a MAT file, Microsoft® Excel® spreadsheet, ASCII flat-file, comma-separated variable file (CSV), or text file.

  • Generate arbitrary input signals in the form of a sine wave, square wave, step function, or white noise.

  • Specify initial states for state-space models. Default initial states are zero.

Open the Linear Simulation Tool

  • MATLAB command prompt: Use the lsimplot or lsim function without specifying input and time arguments.

  • MATLAB command prompt: Use the linearSystemAnalyzer function with an "lsim" plot type without specifying input and time arguments.

  • In the Linear System Analyzer app: Right-click the plot area and select Plot Types > Linear Simulation.

  • In a linear simulation plot: Right-click the plot area and select Input Data or Initial Condition.

Examples

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On the Input Signals tab, in the Timing section, specify the time vector for your signal.

To do so, you can:

  • Specify the start time, end time, and sampling interval.

  • Import the time vector from the MATLAB workspace.

To manually specify the time vector, enter the following values in seconds.

  • Start Time — Simulation start time, specified as a numeric value.

  • End Time — Simulation end time, specified as a numeric value greater than the sum of the start time and sampling interval.

  • Interval — Sampling interval, specified as a positive numeric value.

When you modify any of these values, the software automatically adjusts the end time such that it is equal to the start time plus a multiple of the sampling interval.

To import a time vector, click Import Time.

In the Import Time dialog box, the table shows any variables in the MATLAB workspace that are row or column vectors.

In the table, select a vector to import. The vector must be uniformly sampled with a positive sampling interval.

Click Import.

Once you define a time vector, the Number of Samples field shows how many samples it contains. This value must match the length of any input signals that you define.

Also, the System Inputs table shows the specified time vector in the first column. The remaining columns correspond to the input signals for your dynamic system model.

To import signal data from a file, first import the data to the MATLAB workspace. For more information on importing data from files, see Supported File Formats for Import and Export.

Specify a time vector. For more information, see Specify Time Vector.

On the Input Signals tab, the System Inputs table shows the specified time vector in the first column. The remaining columns contain the input signals for your dynamic system model.

Click the input column for which you want to import signal data.

Click Import Signal.

In the Data Import dialog box, the table shows any variables in the MATLAB workspace that are row or column vectors and that have a length equal to the number of samples in your specified time vector.

Select a variable from the table and click Import.

In the System Inputs table, the selected data column updates to show the imported signal values. You can manually edit the values in the System Inputs table.

For multi-input systems, select columns and import signal data for each input channel separately.

To import the same input signal into multiple input channels, you can select multiple signals in the System Inputs table by holding Ctrl while clicking signals. When you do so, the software copies the imported input signal to all selected inputs channels.

You can generate arbitrary input signals in the form of a sine wave, square wave, step function, or white noise.

Specify a time vector. For more information, see Specify Time Vector.

On the Input Signals tab, the System Inputs table shows the specified time vector in the first column. The remaining columns contain the input signals for your dynamic system model. The number of columns equals the number of model inputs.

Click one or more input columns for the channel for which you want to design an input signal. To select multiple signals, hold Ctrl while clicking signals. If you select multiple columns, each signal is set to the same designed signal.

Click Design Signal.

In the Signal Designer dialog box, select the type of signal to create and specify the signal parameters.

To create a sine wave, under Signal type, select Sine wave and specify these signal parameters:

  • Frequency — Signal frequency in rad/TimeUnit, where TimeUnit is the is the time unit of the specified dynamic system model

  • Amplitude — Signal amplitude

  • Duration — Signal duration in the time unit of the specified dynamic system model

To create a square wave, under Signal type, select Square wave and specify these signal parameters:

  • Frequency — Signal frequency in rad/TimeUnit, where TimeUnit is the is the time unit of the specified dynamic system model

  • Amplitude — Signal amplitude

  • Duration — Signal duration in the time unit of the specified dynamic system model

To create a step function, under Signal type, select Step function wave and specify these signal parameters:

  • Starting level — Initial signal value

  • Step size — Amplitude of the step size

  • Transition time — Time of the step transition in seconds

  • Duration — Signal duration in the time unit of the specified dynamic system model

To create a white noise signal, under Signal type, select White noise and specify these signal parameters:

  • Mean — Average signal value

  • Standard deviation — Standard deviation of the signal

  • Probability density — Select whether to generate Gaussian or uniform white noise.

  • Duration — Signal duration in the time unit of the specified dynamic system model

For all signals, if you specify a duration that is less than the length of your time vector, the software pads the input signal with zeros.

Click Insert.

In the System Inputs table, the selected data columns update to show the designed signal values. You can manually edit the values in the System Inputs table.

If your system is a state-space model, you can specify initial state values for the simulation.

On the Initial States tab, in the Specify Initial States table, you can manually specify initial values for each state in your system.

To do so, specify the state value in the Initial Value column.

You can also import initial conditions by clicking Import State Vector.

In the State Import dialog box, the table lists any variables in the MATLAB workspace that are vectors with length equal to the number of states in your system.

Select a variable from the table and click Import.

Parameters

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Discretization interpolation method for sampling continuous-time models, specified as one of these values:

  • Automatic — Automatically select the interpolation method based on the smoothness of the input signal.

  • Zero order hold — Zero order hold

  • First order hold — First order hold

Dependencies

This parameter applies only when simulating continuous-time models.

Programmatic Use

lsimplot(sys) opens the Linear Simulation Tool for simulating dynamic system model sys and plots the simulation results with default plotting options. 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.)

lsimplot(sys1,sys2,...,sysN) opens the Linear Simulation Tool for simulating multiple dynamic system models.

lsimplot(sys1,LineSpec1,...,sysN,LineSpecN) specifies line styles for plotting simulation results.

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

lsimplot(___,plotoptions) specifies additional plotting options as a timeoptions object.

lsimplot(___,Name=Value) specifies response properties using one or more name-value arguments. For more information, see the name-value arguments for the lsimplot function. (since R2026a)

lp = lsimplot(___) returns a chart object for the simulation results. To customize the appearance and behavior of the response plot, modify the chart object properties using dot notation. For more information, see LSimPlot Properties.

lsim(sys) opens the Linear Simulation Tool for dynamic system model sys and plots the simulation results with default plotting options.

linearSystemAnalyzer("lsim",sys) opens the Linear Simulation Tool and opens the simulation results in a Linear System Analyzer app session showing a linear simulation plot.

Version History

Introduced before R2006a

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See Also

Apps

Functions