Root locus plot of a transfer-function model:

Root loci of a state-space model:

The root locus plot for various pole-zero configurations:

Root locus plot of a TransferFunctionModel:

Root locus plot of a StateSpaceModel:

A root locus plot can be obtained from a transfer-function model or directly from its expression:

Explore and determine critical points such as break-away, break-in, and imaginary axis crossings:

Plot the roots of a polynomial as a parameter is varied:

Analyze the effect of the sensor gain on a system:

The root-locus consists of points with for negative feedback:

And points with for positive feedback:

The root locus plot does not depend on the sampling period:

For strictly proper systems, the root loci go to infinity with straight-line asymptotes:

For the strictly proper system, the number of poles is greater than the number of zeros:

The plot shows four loci going to infinity:

The slopes of the asymptotes for a negative feedback system:

Find where the asymptotes intercept the real axis:

Plot the root loci and the asymptotes:

The slopes of the asymptotes for a positive feedback system:

Plot the root loci and the asymptotes:

The break-away and break-in points on the real axis can be computed from the poles and zeros:

Select those points for which k∈Interval[{0,5}]:

Show the points on the root locus plot:

With the loci and closed-loop poles removed, it becomes a pole-zero plot of the open-loop system:

Compute the poles and zeros:

Use ListPlot to show the same pole-zero plot:

The complex-valued transfer function is a surface with "peaks" at the poles and "valleys" at the zeros:

The root locus plot travels from the "peaks" to the "valleys" along the lines of steepest descent:

The Bode magnitude plot is the intersection of the surface and the - plane: