generate a root-contour plot - Maple Help

Online Help

All Products    Maple    MapleSim

Home : Support : Online Help : Science and Engineering : Dynamic Systems : Plotting and Graphical Tools : DynamicSystems/RootContourPlot

DynamicSystems[RootContourPlot] - generate a root-contour plot

Calling Sequence

RootContourPlot(sys, range, opts)




System; system object



realcons .. realcons; range over which parameter is swept



(optional) equation(s) of the form option = value; specify options for the RootContourPlot command



The RootContourPlot command plots the root-contour of a subsystem of sys, a System object.


The transfer function of the selected subsystem must be a univariate rational polynomial in s (z for discrete systems), with one symbolic parameter. For example, s+1gs+s2+1 has symbolic parameter g.


The root-contour consists of the roots of 1+HK, where H is the transfer function of the selected subsystem of sys and K is the symbolic parameter. K is swept over range.


To plot the root-contour, the numerator of 1+HK is transformed to the equivalent expression GK+1; if it cannot be so transformed, an error is generated. A new system with transfer function G is then generated and its root-locus plotted with a call to DynamicSystems[RootLocusPlot].


The info option can be used to get information about the subsystem with transformed transfer function G. This is the same record returned by DynamicSystems[RootLocusPlot].

Info Record Details

If the value of the keyword parameter info is a name, then that name is assigned a record containing information about the root-locus. The following paragraphs describe each of the fields of the record.


charpoly = polynom

The characteristic polynomial of the system, with parameter K. This is the polynomial whose roots make up the root-locus as K varies.


deq = equation

The differential equation passed to dsolve. If algorithm = fsolve, the value is NULL.


G = ratpoly

The transfer-function of the selected subsystem of sys.


Kbranches = list( realcons )

A list of the values of K at which the root-locus branches.


Kcrit = realcons

The critical value of K, that is, the value at which charpoly acquires a degree less than its maximum (there can be at most one such value). If no critical value exists, the value is NULL.


poles = list( complexcons )

A list of the roots of the denominator of G.


zeros = list( complexcons )

A list of the roots of the numerator of G.


The RootContourPlot command takes all standard plot,options.






The command to create the plot from the Plotting Guide is


See Also

DynamicSystems, DynamicSystems[RootLocusPlot], DynamicSystems[SystemObject], DynamicSystems[ZeroPolePlot]

Download Help Document

Was this information helpful?

Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam