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Quarter-Car Suspension Model

Model of a quarter-car suspension

Examples

Basic Examples (2) 

Retrieve the model:

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\)]
Out[1]=

The icon:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "Icon"]
Out[2]=

Scope & Additional Elements (4) 

Available content elements:

In[3]:=
\!\(\* TagBox[ RowBox[{"ResourceObject", "[", "\"\<Quarter-Car Suspension Model\>\"", "]"}], #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\)["ContentElements"]
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The available model types:

In[4]:=
ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "AvailableModelTypes"]
Out[4]=

The operating point:

In[5]:=
ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "OperatingPoint"]
Out[5]=

The parameters:

In[6]:=
ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "Parameters"]
Out[6]=

Visualizations (3) 

The numerical model:

In[7]:=
sys = ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\)] /. ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "Parameters"]
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Extract the subsystem from input s to output x2:

In[8]:=
tfm = SystemsModelExtract[sys, 1]
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Its Bode plot:

In[9]:=
BodePlot[%, ImageSize -> 300]
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Analysis (7) 

The numerical model:

In[10]:=
ssm = ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\)] /. ResourceData[\!\(\* TagBox["\"\<Quarter-Car Suspension Model\>\"", #& , BoxID -> "ResourceTag-Quarter-Car Suspension Model-Input", AutoDelete->True]\), "Parameters"] // N
Out[10]=

Simulate the suspension on a bumpy surface:

In[11]:=
surf = 0.1 (SquareWave[t/3 - 1] + 1);
In[12]:=
olor = OutputResponse[ssm, {surf, 0}, {t, 0, 10}]; Plot[{surf, olor}, {t, 0, 10}, Sequence[ PlotRange -> All, Exclusions -> None, PlotLegends -> {"input", "output"}]]
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A system specification for a controller design that attenuates the oscillations:

In[14]:=
sspec = <|"InputModel" -> ssm, "FeedbackInputs" -> 2|>
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An LQ-regulator:

In[15]:=
cd = LQRegulatorGains[ sspec, {DiagonalMatrix[{10^2, 10^2, 10^8, 10^2}], {{10^-3}}}, "Data"]
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Simulate the closed-loop system:

In[16]:=
ior = InputOutputResponse[ cd[{"ClosedLoopSystem", <|"Merge" -> False|>}], {surf, 0}, {t, 0, 10}, "Data"]
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The oscillations are attenuated by the controller:

In[17]:=
Plot[{surf, olor, ior["OutputResponse"]}, {t, 0, 10}, Sequence[ PlotRange -> All, PlotLegends -> {"input", "open-loop", "closed-loop"}, Exclusions -> None, PlotStyle -> { Dashing[{Small, Small}], Automatic, Automatic}]]
Out[17]=

The control effort:

In[18]:=
Plot[ior["SubsystemOutputResponse"][[5]], {t, 0, 10}, PlotRange -> All]
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Suba Thomas, "Quarter-Car Suspension Model" from the Wolfram Data Repository (2025)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • G. F. Franklin, J. D. Powell, and A. Emami-Naeini, "Feedback Control of Dynamic Systems", 8th ed. Harlow, England: Pearson Education Limited, 2019.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Maher Kuzbari, Suba Thomas
  • Publisher of Record: Suba Thomas