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DynamicSystems[RootLocusPlot] - generate a root-locus plot

Calling Sequence

RootLocusPlot(sys, Krange, opts)

Parameters

sys

-

System; system object

Krange

-

(optional) realcons .. realcons; range over which K is swept

opts

-

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

Description

• 

The RootLocusPlot command plots the root-locus of a subsystem of sys, a System object. The subsystem must be numeric.

• 

The root-locus consists of the roots of 1+KGs, where Gs is the transfer function of the selected subsystem of sys, s is the frequency variable (z for discrete systems), and K is a parameter.

• 

The optional parameter Krange assigns the range over which K is swept. It is a range of type realcons; the left hand side must be less than the right hand side. The default is 0..10.

• 

The zeros and poles of G are plotted as the circles and crosses, respectively. At K=0 the poles of G lie on the root-locus. At K= the zeros of G lie on the root-locus.

• 

The option info can be used to get information about the root-locus.

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 RootLocusPlot command takes all standard plot,options.

Examples

withDynamicSystems:

sys:=NewSystems+12s3+s+1:

RootLocusPlotsys

Using fsolve is considerably faster than dsolve on the following system (this is not always the case).  These are the commands to create the plot from the Plotting Guide.

sys:=NewSystem9.505s2+16.81s+8.225s4+5.862s3+4.823s2:

RootLocusPlotsys,algorithm=fsolve,view=3..0,5..5

Inspect the values of K at which the locus branches.

RootLocusPlotsys,algorithm=fsolve,info='data':

data:-Kbranches

0.5836509958,0.,0.9213053493

(1)

sys:=NewSystem1s2,s+1.10-82s1.10-82:

RootLocusPlotsys,0..1000,subsystem=2,1

See Also

DynamicSystems, DynamicSystems[RootContourPlot], DynamicSystems[SystemObject], DynamicSystems[ZeroPolePlot]


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