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rootlocus

  

create a rootlocus plot

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

rootlocus(f, s, r, options)

Parameters

f

-

rational function in s

s

-

variable

r

-

(real) range

options

-

(optional) arguments; see Description

Description

• 

The rootlocus command plots the complex roots of the equation

1+kfs=0

  

as k runs over the range r=a..b . Since fs=nsds is a rational function in s, this is equivalent to tracing the paths of the complex roots of the polynomial

  

 

ds+knsforkina..b

  

Maple's fsolve command is used to compute the roots of the polynomials.  Remaining arguments are interpreted as options which are specified as equations of the form option = value. Standard plot options are supported.

• 

The polynomial is initially solved for n equally spaced points k in the range r=a..b. The optional argument numpoints=n specifies the number of points. The default is 49.

• 

Next, the code tries to pair up the roots for adjacent values of k by choosing those closest to each other. If two sets of roots for k=k1 and k=k2 are not sufficiently distinguishable from one another, the algorithm will compute a new set of roots for k=k12+k22. The optional argument adaptive = false will turn this off.

• 

Finally, the code tries to trace out the different curves. It tries to join up adjacent points with line segments. Sometimes this code can be fooled and the result is a messy plot. The optional argument style=point will turn this off by just displaying the roots as points.

• 

The command with(plots,rootlocus) allows the use of the abbreviated form of this command.

Examples

withplots,rootlocus:

rootlocuss31s,s,5..5

rootlocuss51s2+1,s,5..5,style=point,adaptive=false

The command to create the plot from the Plotting Guide is

rootlocuss51s2+1,s,5..5,style=point

See Also

DynamicSystems[RootLocusPlot]

fsolve

plot