SystemModelMeasurements [sspec]
computes measurement properties for the system specification sspec.
SystemModelMeasurements [sspec,prop]
computes the property prop.
SystemModelMeasurements [sim,…]
computes properties for the SystemModelSimulationData object sim.
SystemModelMeasurements
SystemModelMeasurements [sspec]
computes measurement properties for the system specification sspec.
SystemModelMeasurements [sspec,prop]
computes the property prop.
SystemModelMeasurements [sim,…]
computes properties for the SystemModelSimulationData object sim.
Details and Options
- SystemModelMeasurements is typically used to quantify system performance and quality by measuring how it responds to a step input.
- The measurements only make sense for stable systems, i.e. systems for which bounded inputs result in bounded outputs.
- The system sys can have the following forms:
-
- The system specification sspec can have the following keys:
-
"Model" sys any one of the models with inputs"SimulationInterval" Automatic simulation interval {tinit,tfinal}"Inputs" All inputs to turn on {u1,…}"Outputs" Automatic variables to measure {y1,…}
- For a system with multiple inputs, measurements are performed with each input turned on one at a time.
- Measurement properties typically depend on the initial value, yinit, and final value, yfinal, of the measured output y.
- Time properties prop include:
-
"RiseTime" time for output to change from 10% to 90% of the final value"DelayTime" time for output to reach 50% of the final value"TransientTime" time for output transients to subside, i.e. TemplateBox[{{{y, (, t, )}, -, {y, _, {(, final, )}}}}, Abs]/max_t TemplateBox[{{{y, (, t, )}, -, {y, _, {(, final, )}}}}, Abs]<=0.02 for"SettlingTime" time for output to settle, i.e. for"MinValueTime" time tmin for output to reach the minimum ymin, i.e."MaxValueTime" time tmax for output to reach the maximum ymax, i.e.
- Value properties prop include:
-
"InitialValue" initial value yinit, i.e."FinalValue" final value yfinal, i.e."MaxOvershootPercent" maximum percent of signal excess beyond yfinal, i.e."MaxUndershootPercent" maximum percent of signal excess beyond yinit, i.e."MinValue" minimum value"MaxValue" maximum value"SettlingMinValue"
- minimum value
ysmin once the output has risen, i.e. for"SettlingMaxValue"- minimum value
ysmax once the output has risen, i.e. for - Response properties prop include:
-
"Plot" response plot
- The following options can be given:
-
- Method settings take the form Method {"sub1"val1,…}.
- Method suboptions "subi" include:
-
"RiseTimeLowerThreshold" 0.1 fraction of signal change at start of rise time"RiseTimeUpperThreshold" 0.9 fraction of signal change at end of rise time"DelayTimeThreshold" 0.5
- fraction of signal change at end of delay time
"SettlingTimeThreshold" 0.02 settling time threshold - The option TargetUnits controls the units of quantities in measurement properties:
-
None no unit (default)"Unit" unit defined in model"DisplayUnit" display unit defined in modelunit explicit unit{unitt,unit} units for time and data
Examples
open all close allBasic Examples (3)
Compute measurement properties for a model:
Compute the settling time for a single-output model:
Compute measurement properties for simulation data:
Compute the rise time for the simulated variable:
Scope (13)
Basic Uses (4)
Compute measurements for a SystemModel :
Compute measurements for an AffineStateSpaceModel :
Compute measurements for a discrete multiple-input multiple-output StateSpaceModel :
Compute measurements for SystemModelSimulationData :
Properties (5)
Compute the maximum overshoot for a single-output model:
Compute the settling time for a model:
Compute the maximum and minimum values for a model:
Compute the response for a single-output model:
Plot the response for a single-output model:
System Specification (4)
Specify a custom simulation interval:
Specify a custom set of inputs to turn on:
Specify a custom set of variables to measure:
Specify both a custom set of inputs to turn on and a custom set of variables to measure:
Options (7)
Method (3)
Set custom rise time thresholds:
Set a custom settling time threshold:
Set a custom delay time threshold:
ProgressReporting (1)
Control progress reporting with ProgressReporting :
TargetUnits (3)
Compute measurements with the output units defined in the model:
Compute measurements with the time and output units defined in the model:
Compute measurements with custom time and output units:
Applications (7)
Basic Applications (4)
Study how the settling time varies with the location of poles for a discrete-time system:
Compute the closed-loop system for several different designs based on pole locations:
Compute the setting times for the resulting systems:
Show the pole location and the corresponding settling time:
Or look at the actual step responses:
Study how overshoot varies with the location of poles for a discrete-time system:
Compute the closed-loop system for several different designs based on pole locations:
Compute the maximum overshoot for the resulting systems:
Show the pole location and the corresponding maximum overshoot:
Or look at the actual step responses:
Study how the settling time varies with the location of poles for a continuous-time system:
Compute the closed-loop system for several different designs based on pole locations:
Compute the setting times for the resulting systems:
Show the pole location and the corresponding settling time:
Or look at the actual step responses:
Study how the overshoot varies with the location of poles for a continuous-time system:
Compute the closed-loop system for several different designs based on pole locations:
Compute the maximum overshoot for the resulting systems:
Show the pole location and the corresponding maximum overshoot:
Or look at the actual step responses:
Ball and Beam (1)
Study a controlled system of a ball placed at the top of a beam:
When passing an input torque, the controller responds by moving the ball to a position off-center that cancels it:
With all torques cancelled, the angle of the beam goes back to 0:
Compute the time it takes the system to settle:
Camera Stabilizer (1)
Start with a model of a camera attached to the top of a moving vehicle:
Simulate the model with a vertical force perturbation:
Compute the extremes for the position of the camera and plot the full response:
Linearize the model around the equilibrium point:
Design a controller:
Generate a closed-loop system for the controlled model:
Simulate the closed-loop system with the same perturbation:
The camera oscillations are now 10 times smaller:
The magnitude of the control effort is within reason:
Quadcopter Drone (1)
Start with a model of a quadcopter drone:
Design a controller that tracks the altitude of the drone:
Introduce an observer with EstimatorRegulator and produce the closed-loop system:
When a unit step input is provided as reference, the drone elevates in a few seconds to the desired height:
Properties & Relations (2)
The "Response" measurement property is computed with SystemModelSimulate :
Simulate with UnitStep as input and extract the response:
The "Plot" measurement property is computed with SystemModelPlot :
SystemModelPlot has multiple options to customize plots as desired:
Related Guides
Related Links
History
Text
Wolfram Research (2022), SystemModelMeasurements, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelMeasurements.html.
CMS
Wolfram Language. 2022. "SystemModelMeasurements." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SystemModelMeasurements.html.
APA
Wolfram Language. (2022). SystemModelMeasurements. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemModelMeasurements.html
BibTeX
@misc{reference.wolfram_2025_systemmodelmeasurements, author="Wolfram Research", title="{SystemModelMeasurements}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/SystemModelMeasurements.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_systemmodelmeasurements, organization={Wolfram Research}, title={SystemModelMeasurements}, year={2022}, url={https://reference.wolfram.com/language/ref/SystemModelMeasurements.html}, note=[Accessed: 16-November-2025]}