:orphan:

.. _general_examples:

Examples
========

Below are examples demonstrating the usage of `tdcpy` package.

Examples are divided thematically into groups and we recommend to start from top.
If you are coming from MATLAB package ``tds-control``, we recommend starting
with the :ref:`these <tds_control_manual_examples>` examples.

Attention deserves also :ref:`section with applications <applications_examples>`
that demonstrates real-world usecases for the package.

At the end, you find :ref:`tutorials <tutorials>` - more in-depth
examples that cover specific topics step by step.


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Stability
=========



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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we create an animation of the right-most part of the spectrum obtained via method proposed in jarlebring2010krylov. The considered  system is the following retarded delay differential equation (RDDE) from verheyden2008efficient Section 6.1:">

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  .. image:: /auto_examples/02_stability/images/thumb/sphx_glr_example_05_animation_thumb.png
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  :doc:`/auto_examples/02_stability/example_05_animation`

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      <div class="sphx-glr-thumbnail-title">Discretization Animation</div>
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Stabilization via Optimization
==============================



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    <div class="sphx-glr-thumbcontainer" tooltip="We consider the system described by the following delay-differential equation from michielsStability2007 and  Example 3.2 of appeltans2023analysis     ">

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  .. image:: /auto_examples/03_stabopt/images/thumb/sphx_glr_example_strong_sa_02_thumb.png
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  :doc:`/auto_examples/03_stabopt/example_strong_sa_02`

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      <div class="sphx-glr-thumbnail-title">Example - strong stabilization</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="First, we consider Example 13 from michiels2011spectrum">

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  .. image:: /auto_examples/03_stabopt/images/thumb/sphx_glr_example_strong_sa_thumb.png
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  :doc:`/auto_examples/03_stabopt/example_strong_sa`

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      <div class="sphx-glr-thumbnail-title">Prelude to strong stability - gradient of c_D</div>
    </div>


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Examples from tds-control manual
================================



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    <div class="sphx-glr-thumbcontainer" tooltip="We consider the following retarded delay differential equation (RDDE) from verheyden2008efficient Section 6.1:">

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  .. image:: /auto_examples/09_tds_control_manual/images/thumb/sphx_glr_example_2_01_thumb.png
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  :doc:`/auto_examples/09_tds_control_manual/example_2_01`

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      <div class="sphx-glr-thumbnail-title">Example 2.1 - Stability analysis of retarded DDE</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example 2.6 from appeltans2023analysis Section 2.3.2 demonstrates that the exponential stability of neutral systems might be fragile with respect to small delay perturbations.">

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  .. image:: /auto_examples/09_tds_control_manual/images/thumb/sphx_glr_example_2_06_thumb.png
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  :doc:`/auto_examples/09_tds_control_manual/example_2_06`

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      <div class="sphx-glr-thumbnail-title">Example 2.6 - Stability analysis of neutral DDE with multiple delays</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We will follow example 2.12 from appeltans2023analysis Section 2.6.2. In there, for given plant and controller">

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  .. image:: /auto_examples/09_tds_control_manual/images/thumb/sphx_glr_example_2_12_thumb.png
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  :doc:`/auto_examples/09_tds_control_manual/example_2_12`

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      <div class="sphx-glr-thumbnail-title">Example 2.12 - Stability analysis of a Smith predictor with delay mismatch</div>
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Applications
============



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    <div class="sphx-glr-thumbcontainer" tooltip="Spectrum of zero-vibration (ZV) input shaper">

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  .. image:: /auto_examples/10_aplications/images/thumb/sphx_glr_zv_shaper_thumb.png
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  :doc:`/auto_examples/10_aplications/zv_shaper`

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      <div class="sphx-glr-thumbnail-title">Spectrum of zero-vibration (ZV) input shaper</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this peichl2025integrated authors considered chain of 3 flexibly linked masses (first and last also connected to rigid frame). Harmonic disturbance d(t) = \text{cos}(\omega t) acts on last mass, absorber m_a, k_a, c_a together with voice coil u(t) is mounted on the first mass to supress harmonic disturbance.">

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  .. image:: /auto_examples/10_aplications/images/thumb/sphx_glr_peichl2025integrated_thumb.png
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  :doc:`/auto_examples/10_aplications/peichl2025integrated`

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      <div class="sphx-glr-thumbnail-title">Non-collocated vibration absorbtion via delayed resonator</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Let us consider the following example, retrieved from  Appeltans et al. The system is described as follows:">

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  .. image:: /auto_examples/10_aplications/images/thumb/sphx_glr_filter_opt_thumb.png
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  :doc:`/auto_examples/10_aplications/filter_opt`

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      <div class="sphx-glr-thumbnail-title">Co-design of PD controllers and low-pass filter for TDS</div>
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Tutorials
=========


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    <div class="sphx-glr-thumbcontainer" tooltip="TODO - work in progress">

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  .. image:: /auto_examples/20_tutorials/images/thumb/sphx_glr_tutorial02_discretization5_thumb.png
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  :doc:`/auto_examples/20_tutorials/tutorial02_discretization5`

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      <div class="sphx-glr-thumbnail-title">Tutorial - Discretization Heuristic II</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this tutorial we will dive into the discretization heuristic,  an algorithm proposed in wu2012reliably designed for automatic selection of the number of discretization points such that the approximation of roots obtained via solving the discretized eigenvalue problem is good enough to be corrected by local method.">

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  .. image:: /auto_examples/20_tutorials/images/thumb/sphx_glr_tutorial01_discretization1_thumb.png
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  :doc:`/auto_examples/20_tutorials/tutorial01_discretization1`

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      <div class="sphx-glr-thumbnail-title">Tutorial - Discretization Heuristic I</div>
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.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/02_stability/index.rst
   /auto_examples/03_stabopt/index.rst
   /auto_examples/09_tds_control_manual/index.rst
   /auto_examples/10_aplications/index.rst
   /auto_examples/20_tutorials/index.rst



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