BUILT-IN WOLFRAM LANGUAGE SYMBOL
RootLocusPlot
RootLocusPlot[lsys,{k,kmin,kmax}]
generates a root locus plot of a linear time-invariant system lsys as the parameter k ranges from kmin to kmax.
Details and Options
- RootLocusPlot plots the location of poles for the closed-loop system for a range of k values.
- RootLocusPlot treats the parameter k as local, effectively using Block.
- The systems model lsys can be a StateSpaceModel or a TransferFunctionModel.
- RootLocusPlot has the same options as Graphics, with the following additions and changes:
-
Axes True whether to draw axes ColorFunction Automatic how to apply coloring to the loci ColorFunctionScaling True whether to scale arguments to ColorFunction EvaluationMonitor None expression to evaluate at every parameter evaluation Exclusions Automatic parameter values to exclude ExclusionsStyle None what to draw at excluded points FeedbackType "Negative" feedback type MaxRecursion Automatic the maximum number of recursive subdivisions allowed Mesh Automatic how many mesh divisions to draw MeshFunctions Automatic how to determine the placement of the mesh divisions MeshShading None how to shade regions between mesh points MeshStyle None the style for mesh divisions Method Automatic the method to determine the loci PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotPoints Automatic initial number of sample parameter points PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to specify the style for the loci PlotTheme $PlotTheme overall theme for the plot PoleZeroMarkers Automatic markers for poles and zeros RegionFunction (True&) how to determine whether a point should be included PlotLegends None legends for root loci WorkingPrecision MachinePrecision the precision used in internal computations - RootLocusPlot takes a Method option that specifies the method used for computing the root loci.
- With the setting Method->"GenericSolve", the loci are determined by computing the roots at the sample points and then sorting them.
- With Method->"NDSolve", RootLocusPlot uses NDSolve to solve the differential equation
, where 
is the characteristic equation of the closed-loop system and 
is the complex variable. - Method->{"NDSolve",opt1->val1,opt2->val2,…} uses the specified NDSolve options.
- The closed-loop poles for specific values of k can be plotted with appropriate settings for Mesh, MeshFunctions, and MeshStyle.
- Markers for open-loop poles and zeros, as well as closed-loop poles, can be specified by setting the PoleZeroMarkers option.
- The arguments to RegionFunction are x, y, and k.
Introduced in 2010
(8.0)
| Updated in 2014 (10.0)