.. _sphx_glr_api_gallery_control_systems_time_response:

Time response
-------------

Transient specifications of second-order servomechanisms.


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    <div class="sphx-glr-thumbcontainer" tooltip="Harold Hazen at MIT (1934) coined servomechanism and analysed position-following systems as second-order dynamics, \omega_n^2/(s^2 + 2\zeta\omega_n s + \omega_n^2). The damping ratio \zeta alone fixes the overshoot, and \zeta with the natural frequency \omega_n sets peak and settling times (~engineeringkit.control_systems.second_order_metrics). The simulated step and impulse responses (~engineeringkit.control_systems.step_response, impulse_response) confirm the formulas.">

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  :doc:`/api/gallery/control_systems/time_response/plot_01_hazen_servomechanism`

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      <div class="sphx-glr-thumbnail-title">Hazen's theory of servomechanisms</div>
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   /api/gallery/control_systems/time_response/plot_01_hazen_servomechanism