:orphan:

Examples
========

These examples demonstrate radial force control of six-phase bearingless synchronous machine drives. The two three-phase sets of the symmetrical six-phase winding produce both the torque and the radial force. In direct force control [#Das2026]_, the torque and the force are controlled directly by means of feedback linearization. For comparison, in current-based force control, the four-pole plane is controlled by a vector controller of motulator, and the force reference is converted to the current reference of the two-pole plane. In both cases, the rotor displacement can be controlled by an outer levitation controller. The magnetic model of the machine and of the controller is either linear or a gradient network trained on finite-element data [#Li2026]_, with or without the spatial harmonics. The examples with the gradient networks load the networks and the dataset from the folders ``trained_models`` and ``datasets`` of ``examples/``, so they are run in a clone of the repository.

.. rubric:: References

.. [#Das2026] Das, Martin, Kontodinas, Hinkkanen, "Direct force control of six-phase bearingless synchronous machines," Proc. ICEM, 2026, https://doi.org/10.1109/ICEM68283.2026.11757980

.. [#Li2026] Li, Foissner, Martin, Piippo, Hinkkanen, "Gradient networks for universal magnetic modeling of synchronous machines," 2026, https://arxiv.org/abs/2602.14947


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    <div class="sphx-glr-thumbcontainer" tooltip="This example simulates current-based radial force control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM) drive, in the same operating sequence as in the direct force control example. The four-pole plane is controlled by the sensorless current-vector controller of motulator, configured with the parameters of the equivalent three-phase machine. The radial force reference is converted to the current reference of the two-pole plane using the linear force model [#Sok2019]_, and the current is controlled in the coordinates of the vector controller. This is the classical approach to bearingless control [#Chi2005]_, in which the force is controlled via the currents instead of directly. The machine and the controller use the same constant parameters.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_current_based_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_current_based`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, current-based force control</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example simulates levitation control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM) drive. The rotor is a point mass, whose radial position is controlled by means of state feedback with a disturbance observer. The levitation controller gives the radial force reference to the direct force controller [#Das2026]_. The machine and the controller use the same constant parameters, i.e., magnetic saturation and the unbalanced magnetic pull are omitted, while the inductances depend linearly on the displacement.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_levitation_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_levitation`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, levitation control</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example simulates direct radial force control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM) drive. The rotor is held at a fixed radial position by external bearings. The radial force references are those of [#Das2026]_, but the rotor angle and the rotor speed are estimated instead of measured. The machine and the controller use the same constant parameters, i.e., magnetic saturation and the unbalanced magnetic pull are omitted.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_dfc_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_dfc`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, direct force control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example simulates levitation control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM) drive. The machine model is a GradNet current map trained on finite-element data, including magnetic saturation, the spatial harmonics, and the unbalanced magnetic pull. The force is controlled by the direct force controller [#Das2026]_, parametrized by a GradNet flux map with the spatial harmonics averaged. Its radial force estimate includes the unbalanced magnetic pull, since the force map depends on the measured displacement.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_levitation_gradnet_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_levitation_gradnet`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, GradNet from FEM data, levitation control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example simulates direct radial force control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM) drive, as in [#Das2026]_. The machine model is a GradNet current map trained on finite-element data, including magnetic saturation, the rotor displacement, and the spatial harmonics. The control system uses a GradNet flux map trained on the same data, the spatial harmonics being averaged over the rotor angle. The rotor speed and the rotor angle are measured, and the rotor is held at a fixed radial position by external bearings.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_dfc_gradnet_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_dfc_gradnet`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, GradNet from FEM data, direct force control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares two parametrizations of the direct force controller [#Das2026]_ of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM). The machine model is a GradNet current map with the spatial harmonics. The controller uses either constant parameters, computed at the rated peak current, or a GradNet flux map, which includes saturation and the unbalanced magnetic pull. The rotor runs at the rated speed, driven externally, and it is held at a fixed radial position. After magnetization, the radial force references are applied, followed by a torque reference step.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_dfc_comparison_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_dfc_comparison`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, comparison of control models in force control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares two parametrizations of the direct force controller [#Das2026]_ in the levitation control of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM). The machine model is a GradNet current map with the spatial harmonics. The controller uses either constant parameters, computed at the rated peak current, or a GradNet flux map. The rotor runs at the rated speed, driven externally.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_levitation_comparison_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_levitation_comparison`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, comparison of control models in levitation control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example visualizes the GradNet magnetic maps [#Li2026]_ of a 2.6-kW six-phase bearingless synchronous reluctance machine (SyRM), trained on finite-element data. As in motulator, the machine model uses the energy-based current map, with or without the spatial harmonics, and the control system uses the co-energy-based flux map without the rotor angle, which approximates the average over the angle [#Das2026]_. In the figures, the markers show the finite-element results, averaged over the rotor angle unless otherwise noted, and the lines show the networks. The markers are not used in the training.">

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  .. image:: /examples/images/thumb/sphx_glr_plot_3kw_bsyrm_gradnet_maps_thumb.png
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  :doc:`/examples/plot_3kw_bsyrm_gradnet_maps`

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      <div class="sphx-glr-thumbnail-title">2.6-kW bearingless SyRM, GradNet magnetic maps</div>
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.. toctree::
   :hidden:

   /examples/plot_3kw_bsyrm_current_based
   /examples/plot_3kw_bsyrm_levitation
   /examples/plot_3kw_bsyrm_dfc
   /examples/plot_3kw_bsyrm_levitation_gradnet
   /examples/plot_3kw_bsyrm_dfc_gradnet
   /examples/plot_3kw_bsyrm_dfc_comparison
   /examples/plot_3kw_bsyrm_levitation_comparison
   /examples/plot_3kw_bsyrm_gradnet_maps


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    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: examples_python.zip </examples/examples_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: examples_jupyter.zip </examples/examples_jupyter.zip>`


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    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_