SystemModelDelay
SystemModelDelay[texpr,δ]
delays the temporal expression texpr by δ units of time, i.e. texpr[t-δ].
SystemModelDelay[texpr,{δmin,δmax}]
delays texpr by a minimum delay δmin and a maximum delay δmax.
Details
- SystemModelDelay is typically used to validate requirements that have uncertain start times and may be used to consider relaxed time constraints or to quantify inertia in the system response times.
- SystemModelDelay[texpr,δ][t] is True for
if texpr[t] is True for 
. - SystemModelDelay[texpr,{δmin,δmax}][t] is True for
if texpr[t] is True for 
. - SystemModelDelay can be used to specify system behaviors in functions like SystemModelValidate.
Examples
open all close allBasic Examples (1)
Use SystemModelDelay to delay phenomena in validation:
model = [image];Validate the requirement, "Whenever the controller is turned on, and for an extra period of at least 300 seconds, the room temperature must be between 19.5 °C and 20.6 °C.":
req = SystemModelAlways[t, SystemModelDelay["thermostat.onOffController.y"[t], 300]19.5 < "temperatureSensor1.T"[t] < 20.6];spec = <|"SimulationInterval" -> 2000|>;The model fails the requirement:
SystemModelValidate[model, req, spec]Scope (2)
Basic Uses (1)
Validate requirements in a model of a pendulum:
model = CreateSystemModel["MyPendulum", {θ'[t] == ω[t], ω'[t] == -θ[t], right[t] == (θ[t] ≥ 0), θ[0] == 1}, t, {right∈ Booleans}, <|"SimulationSettings" -> <|"StopTime" -> 13|>|>];
SystemModelPlot[model, {θ, right}]Validate the requirement, "Whenever the angle is non-negative, with a delay of 
seconds, the angular velocity is positive.":
smv = SystemModelValidate[model, SystemModelAlways[t, SystemModelDelay[θ[t] ≥ 0, π / 2](ω[t] > 0)]]smv["FailurePlot", 1]Validate the requirement, "Whenever the angle is non-negative, with a delay between 
and 
seconds, the angular velocity is positive.":
smv2 = SystemModelValidate[model, SystemModelAlways[t, SystemModelDelay[θ[t] ≥ 0, {π / 2, 3π / 4}](ω[t] > 0)]]smv2["FailurePlot", 1]Delay (1)
Validate requirements using temporal delays in a model of a pendulum:
model = CreateSystemModel["MyPendulum", {θ'[t] == ω[t], ω'[t] == -θ[t], right[t] == (θ[t] ≥ 0), θ[0] == 1}, t, {right∈ Booleans}, <|"SimulationSettings" -> <|"StopTime" -> 13|>|>];
SystemModelPlot[model, {θ, right}]Validate the requirement, "Whenever the angle is non-negative, with a delay of 
seconds, the angular velocity is less than or equal to 0.01.":
SystemModelValidate[model, SystemModelAlways[t, SystemModelDelay[θ[t] ≥ 0, π / 2](ω[t] ≤ 0.01)]]Use time quantities to specify delays:
SystemModelValidate[model, SystemModelAlways[t, SystemModelDelay[θ[t] ≥ 0, Quantity[Pi/2, "Seconds"]](ω[t] ≤ 0.01)]]Validate the requirement, "Whenever the angle is non-negative, with a delay between 
and 
seconds, the angular velocity is less than or equal to 0.":
SystemModelValidate[model, SystemModelAlways[t, SystemModelDelay[θ[t] ≥ 0, {π / 2 + 0.1, π / 2 - 0.1}](ω[t] ≤ 0)]]Applications (1)
Start with a simple model of an electrical vehicle following the US EPA Highway Fuel Economy Driving Schedule (HWFET):
model = \!\(\*GraphicsBox[«8»]\);Validate the stricter requirement, "Whenever the velocity of the vehicle is less than or equal to 11 m/s, and for an extra period of at least 20 seconds, the temperature in the battery must remain below 28 ºC.":
sim = SystemModelSimulate[model]val = SystemModelValidate[sim, SystemModelAlways[t, SystemModelDelay[11 ≤ "mass.v", {0, 20}]"T"[t] < 28 + 273.15]]val["FailurePlot", 1]Find the earliest and latest failure times:
plotInterval = MinMax[val["FailureIntervals", 1]]Plot the velocity with the bound:
SystemModelPlot[sim, {"mass.v", 11}, plotInterval]Plot the temperature with the bound:
SystemModelPlot[sim, {"T", 28 + 273.15}, plotInterval]Related Links
Wolfram System Modeler DocumentationText
Wolfram Research (2025), SystemModelDelay, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemModelDelay.html.
CMS
Wolfram Language. 2025. "SystemModelDelay." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SystemModelDelay.html.
APA
Wolfram Language. (2025). SystemModelDelay. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemModelDelay.html