Root locus for a controller class that yields cubic gain parameterization

We present rules for constructing the root locus for a class of linear feedback systems, where the closed-loop denominator polynomial is cubic in the root-locus parameter k. Cubic root-locus rules apply to a class of controllers that are rational functions of k and result in closed-loop denominator polynomials that are cubic in k. We provide a controller design example to demonstrate the cubic root locus.