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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, 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.

Examples

withDynamicSystems:

sys:=NewSystem1s2+γs+1:

RootContourPlotsys,0..1

RootContourPlotsys,0..100

The command to create the plot from the Plotting Guide is

RootContourPlotsys

See Also

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


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