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Gain and phase margins of linear system approximated from nonlinear Simulink model
This block is same as the Check Gain and Phase Margins block except for different default parameter settings in the Bounds tab.
Compute a linear system from a nonlinear Simulink model and view the gain and phase margins on a Bode, Nichols or Nyquist plot. Alternatively, you can view the margins in a table. By default, the margins are computed using negative feedback for the closedloop system.
During simulation, the software linearizes the portion of the model between specified linearization inputs and outputs, and plots the linear system on the specified plot type.
The Simulink model can be continuous or discretetime or multirate and can have time delays. Because you can specify only one linearization input/output pair in this block, the linear system is SingleInput SingleOutput (SISO).
You can specify only one gain and phase margin bound each and view them on the selected plot or table. The block does not support multiple gain and phase margin bounds. You can also check that the bounds are satisfied during simulation:
If all bounds are satisfied, the block does nothing.
If a bound is not satisfied, the block asserts, and a warning message appears at the MATLAB^{®} prompt. You can also specify that the block:
Evaluate a MATLAB expression.
Stop the simulation and bring that block into focus.
During simulation, the block can also output a logical assertion signal:
If all bounds are satisfied, the signal is true (1).
If a bound is not satisfied, the signal is false (0).
You can add multiple Gain and Phase Margin Plot blocks to compute and plot the gain and phase margins of various portions of the model.
You can save the linear system as a variable in the MATLAB workspace.
The block does not support code generation and can be used only in Normal simulation mode.
The following table summarizes the Gain and Phase Margin Plot block parameters, accessible via the block parameter dialog box.
Task  Parameters  

Configure linearization.  Specify inputs and outputs (I/Os).  In Linearizations tab: 
Specify settings.  In Linearizations tab:  
Specify algorithm options.  In Algorithm Options of Linearizations tab:  
Specify labels for linear system I/Os and state names.  In Labels of Linearizations tab:  
Specify plot type for viewing gain and phase margins.  
Plot the linear system.  Show Plot  
Specify the feedback sign for closedloop gain and phase margins.  Feedback sign in Bounds tab.  
(Optional) Specify bounds on gain and phase margins of the linear system for assertion.  Include gain and phase margins in assertion in Bounds tab.  
Specify assertion options (only when you specify bounds on the linear system).  In Assertion tab:  
Save linear system to MATLAB workspace.  Save data to workspace in Logging tab.  
Display plot window instead of block parameters dialog box on doubleclicking the block.  Show plot on block open. 
Linearization inputs and outputs that define the portion of a nonlinear Simulink model to linearize.
Click .
The dialog box expands to display a Click a signal in the model to select it area and a new button.
Select a signal in the Simulink Editor.
The selected signal appears as a Model signal in the Click a signal in the model to select it area.
(Optional) For buses, expand the bus signal to select an individual element.
Tip For large buses, you can enter search text for filtering element names in the Filter by name edit box. The name match is casesensitive. Additionally, you can enter MATLAB regular expression. To modify the filtering options, click . 
Click to add the signal to the Linearization inputs/outputs table.
The table displays the following information about the selected signal:
Block : Port : Bus Element  Name of the block associated with the input/output. The number adjacent to the block name is the port number where the selected bus signal is located. The last entry is the selected bus element name. 
Configuration  Type of linearization point:

Note: If you simulate the model without specifying an input or output, the software does not compute a linear system. Instead, you see a warning message at the MATLAB prompt. 
No default
Use getlinio and setlinio to specify linearization inputs and outputs.
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Enables signal selection in the Simulink model. Appears only when you click .
When this option appears, you also see the following changes:
A new button.
Use to add a selected signal as a linearization input or output in the Linearization inputs/outputs table. For more information, see Linearization inputs/outputs.
changes to .
Use to collapse the Click a signal in the model to select it area.
No default
Use the getlinio and setlinio commands to select signals as linearization inputs and outputs.
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Enable the use of MATLAB regular expressions for filtering signal names. For example, entering t$ in the Filter by name edit box displays all signals whose names end with a lowercase t (and their immediate parents). For details, see Regular Expressions.
Default: On
Allow use of MATLAB regular expressions for filtering signal names.
Disable use of MATLAB regular expressions for filtering signal names. Filtering treats the text you enter in the Filter by name edit box as a literal string.
Selecting the Options button on the righthand side of the Filter by name edit box ( ) enables this parameter.
Uses a flat list format to display the list of filtered signals, based on the search text in the Filter by name edit box. The flat list format uses dot notation to reflect the hierarchy of bus signals. The following is an example of a flat list format for a filtered set of nested bus signals.
Default: Off
Display the filtered list of signals using a flat list format, indicating bus hierarchies with dot notation instead of using a tree format.
Display filtered bus hierarchies using a tree format.
Selecting the Options button on the righthand side of the Filter by name edit box ( ) enables this parameter.
When to compute the linear system during simulation.
Default: Simulation snapshots
Specific simulation time, specified in Snapshot times.
Use when you:
Know one or more times when the model is at steadystate operating point
Want to compute the linear systems at specific times
Triggerbased simulation event. Specify the trigger type in Trigger type.
Use when a signal generated during simulation indicates steadystate operating point.
Selecting this option adds a trigger port to the block. Use this port to connect the block to the trigger signal.
For example, for an aircraft model, you might want to compute the linear system whenever the fuel mass is a fraction of the maximum fuel mass. In this case, model this condition as an external trigger.
Setting this parameter to Simulation snapshots enables Snapshot times.
Setting this parameter to External trigger enables Trigger type.
Parameter: LinearizeAt 
Type: string 
Value: 'SnapshotTimes'  'ExternalTrigger' 
Default: 'SnapshotTimes' 
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One or more simulation times. The linear system is computed at these times.
Default: 0
For a different simulation time, enter the time. Use when you:
Want to plot the linear system at a specific time
Know the approximate time when the model reaches steadystate operating point
For multiple simulation times, enter a vector. Use when you want to compute and plot linear systems at multiple times.
Snapshot times must be less than or equal to the simulation time specified in the Simulink model.
Selecting Simulation snapshots in Linearize on enables this parameter.
Parameter: SnapshotTimes 
Type: string 
Value: 0  positive real number  vector of positive real numbers 
Default: 0 
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Trigger type of an external trigger for computing linear system.
Default: Rising edge
Rising edge of the external trigger signal.
Falling edge of the external trigger signal.
Selecting External trigger in Linearize on enables this parameter.
Parameter: TriggerType 
Type: string 
Value: 'rising'  'falling' 
Default: 'rising' 
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Enable zerocrossing detection to ensure that the software computes the linear system characteristics at the following simulation times:
The exact snapshot times, specified in Snapshot times.
As shown in the following figure, when zerocrossing detection is enabled, the variablestep Simulink solver simulates the model at the snapshot time T_{snap}. T_{snap} may lie between the simulation time steps T_{n1} and T_{n} which are automatically chosen by the solver.
The exact times when an external trigger is detected, specified in Trigger type.
As shown in the following figure, when zerocrossing detection is enabled, the variablestep Simulink solver simulates the model at the time, T_{trig}, when the trigger signal is detected. T_{trig} may lie between the simulation time steps T_{n1} and T_{n} which are automatically chosen by the solver.
For more information on zerocrossing detection, see ZeroCrossing Detection in the Simulink User Guide.
Default: On
Compute linear system characteristics at the exact snapshot time or exact time when a trigger signal is detected.
This setting is ignored if the Simulink solver is fixed step.
Compute linear system characteristics at the simulation time steps that the variablestep solver chooses. The software may not compute the linear system at the exact snapshot time or exact time when a trigger signal is detected.
Parameter: ZeroCross 
Type: string 
Value: 'on'  'off' 
Default: 'on' 
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How to represent time delays in your linear model.
Use this option if you have blocks in your model that have time delays.
Default: Off
Return a linear model with exact delay representations.
Return a linear model with Padé approximations of delays, as specified in your Transport Delay and Variable Transport Delay blocks.
Parameter: UseExactDelayModel 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Sample time of the linear system computed during simulation.
Use this parameter to:
Compute a discretetime system with a specific sample time from a continuoustime system
Resample a discretetime system with a different sample time
Compute a continuoustime system from a discretetime system
When computing discretetime systems from continuoustime systems and viceversa, the software uses the conversion method specified in Sample time rate conversion method.
Default: auto
0, for continuoustime models.
For models that have blocks with different sample times (multirate models), least common multiple of the sample times. For example, if you have a mix of continuoustime and discretetime blocks with sample times of 0, 0.2 and 0.3, the sample time of the linear model is 0.6.
A discretetime linear system from a continuoustime system.
A discretetime linear system from another discretetime system with a different sample time
Use to compute a continuoustime linear system from a discretetime model.
Parameter: SampleTime 
Type: string 
Value: auto  Positive finite value  0 
Default: auto 
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Method for converting the sample time of single or multirate models.
This parameter is used only when the value of Linear system sample time is not auto.
Default: ZeroOrder Hold
Zeroorder hold, where the control inputs are assumed piecewise constant over the sampling time Ts. For more information, see ZeroOrder Hold in Control System Toolbox™ User's Guide.
This method usually performs better in time domain.
Bilinear (Tustin) approximation without frequency prewarping. The software rounds off fractional time delays to the nearest multiple of the sampling time. For more information, see Tustin Approximation in Control System Toolbox User's Guide.
This method usually perform better in the frequency domain.
Bilinear (Tustin) approximation with frequency prewarping. Also specify the prewarp frequency in Prewarp frequency (rad/s). For more information, see Tustin Approximation in Control System Toolbox User's Guide.
This method usually perform better in the frequency domain. Use this method to ensure matching at frequency region of interest.
Upsample a discretetime system when possible and use ZeroOrder Hold otherwise.
You can upsample only when you convert discretetime system to a new sample time that is an integervaluetimes faster than the sampling time of the original system.
Upsample a discretetime system when possible and use Tustin (bilinear) otherwise.
You can upsample only when you convert discretetime system to a new sample time that is an integervaluetimes faster than the sampling time of the original system.
Upsample a discretetime system when possible and use Tustin with Prewarping otherwise. Also, specify the prewarp frequency in Prewarp frequency (rad/s).
You can upsample only when you convert discretetime system to a new sample time that is an integervaluetimes faster than the sampling time of the original system.
Selecting either:
Tustin with Prewarping
Upsampling when possible, Tustin with Prewarping otherwise
enables Prewarp frequency (rad/s).
Parameter: RateConversionMethod 
Type: string 
Value: 'zoh'  'tustin'  'prewarp' 'upsampling_zoh' 'upsampling_tustin' 'upsampling_prewarp' 
Default: 'zoh' 
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Prewarp frequency for Tustin method, specified in radians/second.
Default: 10
Positive scalar value, smaller than the Nyquist frequency before and after resampling. A value of 0 corresponds to the standard Tustin method without frequency prewarping.
Selecting either
Tustin with Prewarping
Upsampling when possible, Tustin with Prewarping otherwise
in Sample time rate conversion method enables this parameter.
Parameter: PreWarpFreq 
Type: string 
Value: 10  positive scalar value 
Default: 10 
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How the state, input and output names appear in the linear system computed during simulation.
The linear system is a statespace object and system states and input/output names appear in following statespace object properties:
Input, Output or State Name  Appears in Which StateSpace Object Property 

Linearization input name  InputName 
Linearization output name  OutputName 
State names  StateName 
Default: Off
Show state and input/output names with their path through the model hierarchy. For example, in the chemical reactor modelchemical reactor model, a state in the Integrator1 block of the CSTR subsystem appears with full path as scdcstr/CSTR/Integrator1.
Show only state and input/output names. Use this option when the signal name is unique and you know where the signal is location in your Simulink model. For example, a state in the Integrator1 block of the CSTR subsystem appears as Integrator1.
Parameter: UseFullBlockNameLabels 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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How to label signals associated with linearization inputs and outputs on buses, in the linear system computed during simulation (applies only when you select an entire bus as an I/O point).
Selecting an entire bus signal is not recommended. Instead, select individual bus elements.
You cannot use this parameter when your model has mux/bus mixtures.
Default: Off
Use the signal names of the individual bus elements.
Bus signal names appear when the input and output are at the output of the following blocks:
Rootlevel inport block containing a bus object
Bus creator block
Subsystem block whose source traces back to one of the following blocks:
Output of a bus creator block
Rootlevel inport block by passing through only virtual or nonvirtual subsystem boundaries
Use the bus signal channel number.
Parameter: UseBusSignalLabels 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Check that the gain and phase margins are greater than the values specified in Gain margin (dB) > and Phase margin (deg) >, during simulation. The software displays a warning if the gain or phase margin is less than or equals the specified value.
By default, negative feedback, specified in Feedback sign, is used to compute the margins.
This parameter is used for assertion only if Enable assertion in the Assertion tab is selected.
You can view the gain and phase margin bound on one of the following plot types:
Bode
Nichols
Nyquist
Table
If you clear Enable assertion, the bounds are not used for assertion but continue to appear on the plot.
Default:
Off for Gain and Phase Margin Plot block.
On for Check Gain and Phase Margins block.
Check that the gain and phase margins satisfy the specified values, during simulation.
Do not check that the gain and phase margins satisfy the specified values, during simulation.
Clearing this parameter disables the gain and phase margin bounds and the software stops checking that the gain and phase margins satisfy the bounds during simulation. The gain and phase margin bounds are also disabled on the plot.
To only view the gain and phase margin on the plot, clear Enable assertion.
Parameter: EnableMargins 
Type: string 
Value: 'on'  'off' 
Default: 'off' for Gain and Phase Margin Plot block, 'on' for Check Gain and Phase Margins block 
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Gain margin, specified in decibels.
By default, negative feedback, specified in Feedback sign, is used to compute the gain margin.
You can specify only one gain margin bound on the linear system in this block.
Default:
[] for Gain and Phase Margin Plot block. 
20 for Check Gain and Phase Margins block. 
Positive finite number.
To assert that the gain margin is satisfied, select both Include gain and phase margins in assertion and Enable assertion.
To modify the gain margin from the plot window, rightclick the plot, and select Bounds > Edit Bound. Specify the new gain margin in Gain margin >. You must click Update Block before simulating the model.
Parameter: GainMargin 
Type: string 
Value: []  20  positive finite number. Must be specified inside single quotes (''). 
Default: '[]' for Gain and Phase Margin Plot block, '20' for Check Gain and Phase Margins block. 
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Phase margin, specified in degrees.
By default, negative feedback, specified in Feedback sign, is used to compute the phase margin.
You can specify only one phase margin bound on the linear system in this block.
Default:
[] for Gain and Phase Margin Plot block. 
30 for Check Gain and Phase Margins block. 
Positive finite number.
To assert that the phase margin is satisfied, select both Include gain and phase margins in assertion and Enable assertion.
To modify the phase margin from the plot window, rightclick the plot, and select Bounds > Edit Bound. Specify the new phase margin in Phase margin >. You must click Update Block before simulating the model.
Parameter: PhaseMargin 
Type: string 
Value: []  30  positive finite number. Must be specified inside single quotes (''). 
Default: '[]' for Gain and Phase Margin Plot block, '30' for Check Gain and Phase Margins block. 
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Feedback sign to determine the gain and phase margins of the linear system, computed during simulation.
To determine the feedback sign, check if the path defined by the linearization inputs and outputs include the feedback Sum block:
If the path includes the Sum block, specify positive feedback.
If the path does not include the Sum block, specify the same feedback sign as the Sum block.
For example, in the aircraft modelaircraft model, the Check Gain and Phase Margins block includes the negative sign in the summation block. Therefore, the Feedback sign is positive.
Default: negative feedback
Use when the path defined by the linearization inputs/outputs does not include the Sum block and the Sum block feedback sign is .
Use when:
The path defined by the linearization inputs/outputs includes the Sum block.
The path defined by the linearization inputs/outputs does not include the Sum block and the Sum block feedback sign is +.
Parameter: FeedbackSign 
Type: string 
Value: '1'  '+1' 
Default: '1' 
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Save one or more linear systems to perform further linear analysis or control design.
The saved data is in a structure whose fields include:
time — Simulation times at which the linear systems are computed.
values — Statespace model representing the linear system. If the linear system is computed at multiple simulation times, values is an array of statespace objects.
operatingPoints — Operating points corresponding to each linear system in values. This field exists only if Save operating points for each linearization is checked.
The location of the saved data structure depends upon the configuration of the Simulink model:
If the Simulink model is not configured to save simulation output as a single object, the data structure is a variable in the MATLAB workspace.
If the Simulink model is configured to save simulation output as a single object, the data structure is a field in the Simulink.SimulationOutput object that contains the logged simulation data.
To configure your model to save simulation output in a single object, in the Simulink editor, select Simulation > Model Configuration Parameters. In the Configuration Parameters dialog box, in the Data Import/Export pane, check Save Simulation output as single object.
For more information about data logging in Simulink, see Export Simulation Data and the Simulink.SimulationOutput reference page.
Default: Off
This parameter enables Variable name.
Parameter: SaveToWorkspace 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Name of the data structure that stores one or more linear systems computed during simulation.
The location of the saved data structure depends upon the configuration of the Simulink model:
If the Simulink model is not configured to save simulation output as a single object, the data structure is a variable in the MATLAB workspace.
If the Simulink model is configured to save simulation output as a single object, the data structure is a field in the Simulink.SimulationOutput object that contains the logged simulation data. The
The name must be unique among the variable names used in all data logging model blocks, such as Linear Analysis Plot blocks, Model Verification blocks, Scope blocks, To Workspace blocks, and simulation return variables such as time, states, and outputs.
For more information about data logging in Simulink, see Export Simulation Data and the Simulink.SimulationOutput reference page.
Default: sys
String.
Save data to workspace enables this parameter.
Parameter: SaveName 
Type: string 
Value: sys  any string. Must be specified inside single quotes (''). 
Default: 'sys' 
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When saving linear systems to the workspace for further analysis or control design, also save the operating point corresponding to each linearization. Using this option adds a field named operatingPoints to the data structure that stores the saved linear systems.
Default: Off
Save data to workspace enables this parameter.
Parameter: SaveOperatingPoint 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Enable the block to check that bounds specified and included for assertion in the Bounds tab are satisfied during simulation. Assertion fails if a bound is not satisfied. A warning, reporting the assertion failure, appears at the MATLAB prompt.
If assertion fails, you can optionally specify that the block:
Execute a MATLAB expression, specified in Simulation callback when assertion fails (optional).
Stop the simulation and bring that block into focus, by selecting Stop simulation when assertion fails.
For the Linear Analysis Plots blocks, this parameter has no effect because no bounds are included by default. If you want to use the Linear Analysis Plots blocks for assertion, specify and include bounds in the Bounds tab.
Clearing this parameter disables assertion, i.e., the block no longer checks that specified bounds are satisfied. The block icon also updates to indicate that assertion is disabled.
In the Configuration Parameters dialog box of the Simulink model, the Model Verification block enabling option in the Debugging area of Data Validity node, lets you to enable or disable all model verification blocks in a model, regardless of the setting of this option.
Default: On
Check that bounds included for assertion in the Bounds tab are satisfied during simulation. A warning, reporting assertion failure, is displayed at the MATLAB prompt if bounds are violated.
Do not check that bounds included for assertion are satisfied during simulation.
This parameter enables:
Simulation callback when assertion fails (optional)
Stop simulation when assertion fails
Parameter: enabled 
Type: string 
Value: 'on'  'off' 
Default: 'on' 
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MATLAB expression to execute when assertion fails.
Because the expression is evaluated in the MATLAB workspace, define all variables used in the expression in that workspace.
No Default
A MATLAB expression.
Enable assertion enables this parameter.
Parameter: callback 
Type: string 
Value: ''  MATLAB expression 
Default: '' 
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Stop the simulation when a bound specified in the Bounds tab is violated during simulation, i.e., assertion fails.
If you run the simulation from the Simulink Editor, the Simulation Diagnostics window opens to display an error message. Also, the block where the bound violation occurs is highlighted in the model.
Default: Off
Stop simulation if a bound specified in the Bounds tab is violated.
Continue simulation if a bound is violated with a warning message at the MATLAB prompt.
Because selecting this option stops the simulation as soon as the assertion fails, assertion failures that might occur later during the simulation are not reported. If you want all assertion failures to be reported, do not select this option.
Enable assertion enables this parameter.
Parameter: stopWhenAssertionFail 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Output a Boolean signal that, at each time step, is:
True (1) if assertion succeeds, i.e., all bounds are satisfied
False (1) if assertion fails, i.e., a bound is violated.
The output signal data type is Boolean only if the Implement logic signals as Boolean data option in the Optimization pane of the Configuration Parameters dialog box of the Simulink model is selected. Otherwise, the data type of the output signal is double.
Selecting this parameter adds an output port to the block that you can connect to any block in the model.
Default:Off
Output a Boolean signal to indicate assertion status. Adds a port to the block.
Do not output a Boolean signal to indicate assertion status.
Use this parameter to design complex assertion logic. For an example, see Model Verification Using Simulink Control Design and Simulink Verification Blocks.
Parameter: export 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Plot to view gain and phase margins of the linear system computed during simulation.
Default: Bode
Rightclick the Bode , Nichols or Nyquist plot and select Characteristics > Minimum Stability Margins to view gain and phase margins. The table displays the computed margins automatically.
Parameter: PlotType 
Type: string 
Value: 'bode'  'nichols'  'nyquist'  'table' 
Default: 'bode' 
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Open the plot window instead of the Block Parameters dialog box when you doubleclick the block in the Simulink model.
Use this parameter if you prefer to open and perform tasks, such as adding or modifying bounds, in the plot window instead of the Block Parameters dialog box. If you want to access the block parameters from the plot window, select Edit or click .
For more information on the plot, see Show Plot.
Default: Off
Open the plot window when you doubleclick the block.
Open the Block Parameters dialog box when doubleclicking the block.
Parameter: LaunchViewOnOpen 
Type: string 
Value: 'on'  'off' 
Default: 'off' 
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Open the plot window.
Use the plot to view:
Linear system characteristics computed from the nonlinear Simulink model during simulation
You must click this button before you simulate the model to view the linear characteristics.
You can display additional characteristics, such as the peak response time and stability margins, of the linear system by rightclicking the plot and selecting Characteristics.
Bounds on the linear system characteristics
You can specify bounds in the Bounds tab of the Block Parameters dialog box or rightclick the plot and select Bounds > New Bound. For more information on the types of bounds you can specify on each plot, see Verifiable Linear System Characteristics in the User's Guide.
You can modify bounds by dragging the bound segment or by rightclicking the plot and selecting Bounds > Edit Bound. Before you simulate the model, click Update Block to update the bound value in the block parameters.
Typical tasks that you perform in the plot window include:
Opening the Block Parameters dialog box by clicking or selecting Edit.
Finding the block that the plot window corresponds to by clicking or selecting View > Highlight Simulink Block. This action makes the Simulink Editor active and highlights the block.
Simulating the model by clicking or selecting Simulation > Run. This action also linearizes the portion of the model between the specified linearization input and output.
Adding legend on the linear system characteristic plot by clicking .