generate a root-contour plot - Maple Help

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DynamicSystems[RootContourPlot] - generate a root-contour plot

 Calling Sequence RootContourPlot(sys, range, opts)

Parameters

 sys - System; system object range - realcons .. realcons; range over which parameter is swept opts - (optional) equation(s) of the form option = value; specify options for the RootContourPlot command

Description

 • 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, $\frac{s+1}{gs+{s}^{2}+1}$ has symbolic parameter $g$.
 • The root-contour consists of the roots of $1+H\left(K\right)$, 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 $1+H\left(K\right)$ 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 $\mathrm{NULL}$.

 • 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 $\mathrm{NULL}$.

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sys}:=\mathrm{NewSystem}\left(\frac{1}{{s}^{2}+\mathrm{γ}s+1}\right):$
 > $\mathrm{RootContourPlot}\left(\mathrm{sys},0..1\right)$
 > $\mathrm{RootContourPlot}\left(\mathrm{sys},0..100\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{RootContourPlot}\left(\mathrm{sys}\right)$