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Helicopter Pitch Model

Source Notebook

Model of a helicopter's pitch dynamics

Examples

Basic Examples (3) 

Retrieve the model:

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

The icon:

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

The annotation:

In[3]:=
ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\), "Annotation"]
Out[3]=

Scope & Additional Elements (4) 

Available content elements:

In[4]:=
\!\(\* TagBox[ RowBox[{"ResourceObject", "[", "\"\<Helicopter Pitch Model\>\"", "]"}], #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\)["ContentElements"]
Out[4]=

The available model types:

In[5]:=
ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\), "AvailableModelTypes"]
Out[5]=

The operating point:

In[6]:=
ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\), "OperatingPoint"]
Out[6]=

The parameters:

In[7]:=
ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\), "Parameters"]
Out[7]=

Analysis (5) 

The numerical model:

In[8]:=
helicopter = ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\)] /. ResourceData[\!\(\* TagBox["\"\<Helicopter Pitch Model\>\"", #& , BoxID -> "ResourceTag-Helicopter Pitch Model-Input", AutoDelete->True]\), "Parameters"]
Out[8]=

It's unstable:

In[9]:=
StateResponse[{helicopter, {0, 0, 0.02}}, 0, {t, 0, 2}]; Table[Plot[\[ScriptS]\[ScriptR][[1]], {t, 0, 2}, Sequence[ PlotLabel -> Part[\[ScriptS]\[ScriptR], 2], PlotRange -> All, ImageSize -> Small]], {\[ScriptS]\[ScriptR], ({%, {x, x', \[Theta], \[Theta]'}}\[Transpose])}]
Out[10]=

An LQ regulator controller that stabilizes the helicopter:

In[11]:=
cd = LQRegulatorGains[helicopter, {({ {10^4, 0, 0, 0}, {0, 10, 0, 0}, {0, 0, 10^4, 0}, {0, 0, 0, 1} }), {{10^3}}}, "Data"]
Out[11]=

The closed-loop system is stable:

In[12]:=
sr = StateResponse[{cd["ClosedLoopSystem"], {0, 0, 0.02}}, 0, {t, 0, 10}]; Table[Plot[\[ScriptS]\[ScriptR][[1]], {t, 0, 10}, Sequence[ PlotLabel -> Part[\[ScriptS]\[ScriptR], 2], PlotRange -> All, ImageSize -> Small]], {\[ScriptS]\[ScriptR], ({%, {x, x', \[Theta], \[Theta]'}}\[Transpose])}]
Out[13]=

The control effort:

In[14]:=
OutputResponse[cd["ControllerModel"], Join[{0}, sr], {t, 0, 10}]; Plot[%, {t, 0, 6}, PlotRange -> All]
Out[15]=

Suba Thomas, "Helicopter Pitch Model" from the Wolfram Data Repository (2025)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation: R. C. Dorf and R. H. Bishop, "Modern Control Systems, 13th ed.", Pearson, 2017.

Publisher Information

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