.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/plot_3kw_bsyrm_levitation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_plot_3kw_bsyrm_levitation.py: 2.6-kW bearingless SyRM, levitation control =========================================== 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. .. GENERATED FROM PYTHON SOURCE LINES 16-20 .. code-block:: Python from math import pi from motulator_bearingless import control, model, utils .. GENERATED FROM PYTHON SOURCE LINES 21-22 Compute base values based on the nominal values (just for figures). .. GENERATED FROM PYTHON SOURCE LINES 22-26 .. code-block:: Python nom = utils.NominalValues(U=220, I=12, f=50, P=2.6e3, tau=14.5) base = utils.BaseValues.from_nominal(nom, n_p=2) .. GENERATED FROM PYTHON SOURCE LINES 27-30 Configure the system model. The machine parameters are those of the direct force control example. The rotor mass roughly corresponds to the rotor lamination and the shaft inside it. .. GENERATED FROM PYTHON SOURCE LINES 30-44 .. code-block:: Python par = model.BearinglessSynchronousMachinePars( R_s=0.215, L_1=0.03, L_d=0.03, L_q=0.01, m_d=10.0, m_q=0.2 ) m = 20.0 machine = model.BearinglessSynchronousMachine(par) w_M_rated = 2 * pi * 1700 / 60 k = nom.tau / w_M_rated**2 # Quadratic load torque, rated torque at the rated speed mechanics = model.MechanicalSystem(J=0.05, B_L=lambda w_M: k * abs(w_M)) radial = model.RadialMechanics(m=m) converter = model.MultiThreePhaseConverter(u_dc=540) sensors = model.BearinglessDriveSensors(w_M=model.Sensor(), theta_M=model.Sensor()) mdl = model.BearinglessDrive(machine, mechanics, radial, converter, sensors) .. GENERATED FROM PYTHON SOURCE LINES 45-48 Configure the control system. The observer of the levitation controller is driven by the radial force estimate, so its poles can be placed above the displacement-control bandwidth without considering the dynamics of the inner force control loop. .. GENERATED FROM PYTHON SOURCE LINES 48-57 .. code-block:: Python cfg = control.DirectForceControllerCfg(i_s_max=1.5 * base.i, psi_s_min=0.3) force_ctrl = control.DirectForceController(par, cfg) speed_ctrl = control.SpeedController(J=0.05, alpha_s=2 * pi * 4) levitation_ctrl = control.LevitationController( m=m, alpha_q=2 * pi * 50, alpha_o=2 * pi * 150 ) ctrl = control.DirectForceControlSystem(force_ctrl, speed_ctrl, levitation_ctrl) .. GENERATED FROM PYTHON SOURCE LINES 58-63 Set the references and the external force. The machine is magnetized during the first 0.2 s, after which the rotor is accelerated to the rated speed of 1700 r/min in 0.6 s against the quadratic load torque. The gravity is applied as a step at t = 0.1 s in the negative direction of the j axis, and a displacement reference step of 50 µm at t = 1 s. .. GENERATED FROM PYTHON SOURCE LINES 63-68 .. code-block:: Python ctrl.set_speed_ref(lambda t: min(max(t - 0.2, 0) / 0.6, 1) * w_M_rated) ctrl.set_displacement_ref(lambda t: (t > 1) * 50e-6) radial.set_external_force(lambda t: (t > 0.1) * -9.81j * radial.m) .. GENERATED FROM PYTHON SOURCE LINES 69-70 Create the simulation object, simulate, and plot the results. .. GENERATED FROM PYTHON SOURCE LINES 70-79 .. code-block:: Python sim = model.Simulation(mdl, ctrl) res = sim.simulate(t_stop=1.2) subplots = ["speed", "torque", "force", "displacement", "current"] f_lims = (-40.0, 450.0) # Room for the legends utils.plot( res, base, subplots, y_lims=[None, (-0.05, 1.625), f_lims, None, (-1.3, 0.95)] ) .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_001.png :alt: plot 3kw bsyrm levitation :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 80-81 Plot the response to the gravity step and to the displacement reference step. .. GENERATED FROM PYTHON SOURCE LINES 81-85 .. code-block:: Python utils.plot(res, base, ["force", "displacement"], t_lims=(0.08, 0.2), y_lims=[f_lims]) utils.plot(res, base, ["force", "displacement"], t_lims=(0.98, 1.1), y_lims=[f_lims]) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_002.png :alt: plot 3kw bsyrm levitation :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_002.png :class: sphx-glr-multi-img * .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_003.png :alt: plot 3kw bsyrm levitation :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_003.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 86-91 .. 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 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 22.607 seconds) .. _sphx_glr_download_examples_plot_3kw_bsyrm_levitation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_3kw_bsyrm_levitation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_3kw_bsyrm_levitation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_3kw_bsyrm_levitation.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_