.. _sphx_glr_api_gallery_control_systems_root_locus:

Root locus
----------

Closed-loop poles as the loop gain varies.


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    <div class="sphx-glr-thumbcontainer" tooltip="Walter Evans at North American Aviation (1948) showed how to sketch the paths of the closed-loop poles as a single gain K rises from zero, without solving a polynomial for each gain (~engineeringkit.control_systems.root_locus). For K/(s(s+2)(s+4)) the branches leave the poles at 0, -2 and -4. Two of them meet and break away from the real axis where \tfrac{d}{ds}[s(s+2)(s+4)] = 0, at s = -2 + 2/\sqrt3. They cross the imaginary axis at \pm j\sqrt8 when K = 48.">

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  :doc:`/api/gallery/control_systems/root_locus/plot_01_evans_root_locus`

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      <div class="sphx-glr-thumbnail-title">Evans's root locus</div>
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   /api/gallery/control_systems/root_locus/plot_01_evans_root_locus