rootlocus - Maple Help

plots

 rootlocus
 create a rootlocus plot

 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

$1+kf\left(s\right)=0$

 as k runs over the range $r=a..b$ . Since $f\left(s\right)=\frac{n\left(s\right)}{d\left(s\right)}$ is a rational function in s, this is equivalent to tracing the paths of the complex roots of the polynomial

$d\left(s\right)+kn\left(s\right)\mathrm{for}k\mathrm{in}a\mathrm{..}b$

 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 $\mathrm{numpoints}=n$ 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 $k=\mathrm{k1}$ and $k=\mathrm{k2}$ are not sufficiently distinguishable from one another, the algorithm will compute a new set of roots for $k=\frac{\mathrm{k1}}{2}+\frac{\mathrm{k2}}{2}$. 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

 > $\mathrm{with}\left(\mathrm{plots},\mathrm{rootlocus}\right):$
 > $\mathrm{rootlocus}\left(\frac{{s}^{3}-1}{s},s,-5..5\right)$
 > $\mathrm{rootlocus}\left(\frac{{s}^{5}-1}{{s}^{2}+1},s,-5..5,\mathrm{style}=\mathrm{point},\mathrm{adaptive}=\mathrm{false}\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{rootlocus}\left(\frac{{s}^{5}-1}{{s}^{2}+1},s,-5..5,\mathrm{style}=\mathrm{point}\right)$