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Root locus plot of dynamic system


[r,k] = rlocus(sys)
r = rlocus(sys,k)


rlocus computes the root locus of a SISO open-loop model. The root locus gives the closed-loop pole trajectories as a function of the feedback gain k (assuming negative feedback). Root loci are used to study the effects of varying feedback gains on closed-loop pole locations. In turn, these locations provide indirect information on the time and frequency responses.

rlocus(sys) calculates and plots the root locus of the open-loop SISO model sys. This function can be applied to any of the following negative feedback loops by setting sys appropriately.

If sys has transfer function


the closed-loop poles are the roots of


rlocus adaptively selects a set of positive gains k to produce a smooth plot. Alternatively,


uses the user-specified vector k of gains to plot the root locus.

rlocus(sys1,sys2,...) draws the root loci of multiple LTI models sys1, sys2,... on a single plot. You can specify a color, line style, and marker for each model, as in


[r,k] = rlocus(sys) and r = rlocus(sys,k) return the vector k of selected gains and the complex root locations r for these gains. The matrix r has length(k) columns and its jth column lists the closed-loop roots for the gain k(j).


collapse all

Plot the root-locus of the following system.

h = tf([2 5 1],[1 2 3]);

You can use the right-click menu for rlocus to add grid lines, zoom in or out, and invoke the Property Editor to customize the plot. Also, click anywhere on the curve to activate a data marker that displays the gain value, pole, damping, overshoot, and frequency at the selected point.


You can change the properties of your plot, for example the units. For information on the ways to change properties of your plots, see Ways to Customize Plots.

See Also


Introduced before R2006a