SystemModelUncertaintyPlot

SystemModelUncertaintyPlot[sys,spec]

plots the uncertainty in outputs in the system model sys from uncertainty in inputs according to spec.

Details and Options

Examples

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Basic Examples  (1)

Plot the uncertainty in the voltage of a capacitor in an RC circuit when the resistance takes values in a given interval:

Scope  (19)

Models  (4)

Plot uncertainty in two variables of a SystemModel:

Plot the uncertainty in the output of an AffineStateSpaceModel:

Plot the uncertainty in the output of a NonlinearStateSpaceModel:

Plot the uncertainty in the output of a DiscreteInputOutputModel:

Use a SquareWave input:

Specification  (3)

Plot the uncertainty for a specific output:

Plot the uncertainty in a model using a custom number of simulations:

Plot the uncertainty for a specific output using a custom simulation interval:

Uncertainty in Values  (5)

Plot the uncertainty generated from giving a list of values for a parameter:

Plot the uncertainty generated from sampling an interval for a parameter value:

Plot the uncertainty generated from sampling a distribution for a parameter value:

Plot the uncertainty generated from sampling a geometric region for a parameter value:

Plot the uncertainty generated from sampling a Circle for two initial values:

Uncertainty in Inputs  (3)

Plot the uncertainty generated when an ARIMAProcess is used for an input:

Plot the uncertainty generated when several functions are used as input:

Use these profiles for the input flow rate in a continuous stirred tank reactor:

Plot the uncertainty generated when using a two-dimensional process for two inputs:

Slice Function  (4)

Plot the range between the minimum and maximum of the temporal data:

Plot custom quantiles of the temporal data:

Plot confidence bands for the temporal data with custom confidence levels:

Plot a custom slice function:

Options  (15)

AxesLabel  (2)

AxesLabel is set to None by default in the default PlotLayout:

Set custom labels:

Filling  (2)

Known slice functions use a customized Filling by default:

Set a custom filling:

FrameLabel  (2)

The units of the plotted variables are used as the FrameLabel by default:

Set custom labels:

Method  (1)

Set a custom simulation method with Method:

PlotLabel  (1)

Set a custom plot label:

PlotLayout  (2)

Obtain an Association with individual plots for each output:

Merge individual plots:

PlotLegends  (2)

Known slice functions use customized PlotLegends by default:

Set a custom plot legend:

ProgressReporting  (1)

Control progress reporting with ProgressReporting:

SamplingPeriod  (1)

Set a custom sampling period when sampling a random process:

TargetUnits  (1)

Set custom units with TargetUnits:

Applications  (4)

Trajectories Near Equilibrium  (1)

Plot the uncertainty in the angle and angular velocity of a simple damped pendulum when the initial conditions take values near equilibrium points:

When the system starts at rest at small angles, it evolves toward the stable ground position:

When the system starts near the unstable fully inverted position, it also evolves toward the ground position:

Plot a few randomly chosen trajectories:

System Tolerance  (1)

The performance of a circuit depends heavily on its components and parameter tolerances. When the resistance of one of the components in this model of a speaker follows a truncated normal distribution, the variation in the current going through the speaker can be measurable:

External disturbances can also affect the performance of a circuit. For instance, the input voltage of the speaker can be affected by high-frequency signals:

Plot the uncertainty in the current of the speaker when affected by these high-frequency disturbances:

Validation of Controlled Systems  (1)

Validate a controlled ball and beam system by placing the ball away from the stable position:

The system model:

The farther away the ball starts from the equilibrium point, the more the system will struggle bringing it back to the stable position:

The control effort peaks at the start and then later a few more times to stop the ball from overshooting the stable position:

Controlled systems should also be validated against external disturbances. Stress the controlled ball and beam system with a white noise torque disturbance and plot the control effort as the system experiences various sampling periods of the noise:

Orbital Maneuver  (1)

Study the effect of a short-time tangential boost on a toy spacecraft in a circular orbit:

Boosts of large magnitude can lead to unbounded trajectories:

Bounded or unbounded trajectories can unfold if the magnitude of the boost follows a normal distribution. Plot the uncertainty in the distance to the center of force:

Properties & Relations  (2)

Use SystemModelPlot to plot individual curves:

Use SystemModelPlot to plot individual curves when doing a parameter sweep:

Use SystemModelPlot to plot sensitivity bands computed with SystemModelSimulateSensitivity:

Use SystemModelUncertaintyPlot to plot uncertainty:

Interval and CenteredInterval are sampled as regions:

Around and VectorAround are sampled as their corresponding distributions:

Neat Examples  (1)

Visualize the sensitivity of a chaotic system with respect to small changes in initial conditions:

Wolfram Research (2024), SystemModelUncertaintyPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html.

Text

Wolfram Research (2024), SystemModelUncertaintyPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html.

CMS

Wolfram Language. 2024. "SystemModelUncertaintyPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html.

APA

Wolfram Language. (2024). SystemModelUncertaintyPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html

BibTeX

@misc{reference.wolfram_2024_systemmodeluncertaintyplot, author="Wolfram Research", title="{SystemModelUncertaintyPlot}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html}", note=[Accessed: 05-October-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_systemmodeluncertaintyplot, organization={Wolfram Research}, title={SystemModelUncertaintyPlot}, year={2024}, url={https://reference.wolfram.com/language/ref/SystemModelUncertaintyPlot.html}, note=[Accessed: 05-October-2024 ]}