.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/plot_3kw_bsyrm_dfc.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_dfc.py: 2.6-kW bearingless SyRM, direct force control ============================================= 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. .. GENERATED FROM PYTHON SOURCE LINES 15-21 .. code-block:: Python from math import pi import numpy as np from motulator_bearingless import control, model, utils .. GENERATED FROM PYTHON SOURCE LINES 22-23 Compute base values based on the nominal values (just for figures). .. GENERATED FROM PYTHON SOURCE LINES 23-27 .. 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 28-32 Configure the system model. The stator resistance is from [#Das2026]_. The inductances and the radial force constants are scaled from the finite-element results of the same machine with separate windings [#Saa2016]_ such that the rated torque is reached at about the rated current. The values are illustrative. .. GENERATED FROM PYTHON SOURCE LINES 32-49 .. 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 ) 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)) converter = model.MultiThreePhaseConverter(u_dc=540) # Rotor held at a fixed position, e.g., by active magnetic bearings. A static # eccentricity of 30 µm and -20 µm could be set as follows: radial = model.ExternalRotorPosition() # radial.set_external_displacement(30e-6 - 20e-6j) mdl = model.BearinglessDrive(machine, mechanics, radial, converter) .. GENERATED FROM PYTHON SOURCE LINES 50-51 Configure the control system. The controller uses the same parameters as the model. .. GENERATED FROM PYTHON SOURCE LINES 51-67 .. code-block:: Python cfg = control.DirectForceControllerCfg( i_s_max=1.5 * base.i, psi_s_min=0.3, alpha_f=2 * pi * 300, alpha_i=2 * pi * 30, alpha_psi=2 * pi * 200, alpha_tau=2 * pi * 200, zeta=0.45, sensorless=True, T_s=125e-6, ) force_ctrl = control.DirectForceController(par, cfg) speed_ctrl = control.SpeedController(J=0.05, alpha_s=2 * pi * 4) ctrl = control.DirectForceControlSystem(force_ctrl, speed_ctrl) .. GENERATED FROM PYTHON SOURCE LINES 68-72 Set the speed and force references. 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 radial force references of 100 N and 150 N are applied during the acceleration at t = 0.4 s and t = 0.6 s. .. GENERATED FROM PYTHON SOURCE LINES 72-76 .. code-block:: Python ctrl.set_speed_ref(lambda t: min(max(t - 0.2, 0) / 0.6, 1) * w_M_rated) ctrl.set_force_ref(lambda t: (t > 0.4) * 100 + 1j * (t > 0.6) * 150) .. GENERATED FROM PYTHON SOURCE LINES 77-78 Create the simulation object, simulate, and plot the results. .. GENERATED FROM PYTHON SOURCE LINES 78-84 .. code-block:: Python sim = model.Simulation(mdl, ctrl) res = sim.simulate(t_stop=1.2) i_lims = (-1.0, 0.95) # Room for the legends utils.plot(res, base, y_lims=[None, None, None, None, i_lims]) .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_dfc_001.png :alt: plot 3kw bsyrm dfc :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_dfc_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 85-86 Plot the phase currents around the force step. .. GENERATED FROM PYTHON SOURCE LINES 86-93 .. code-block:: Python t_lims = (0.35, 0.45) mask = (res.mdl.t > t_lims[0]) & (res.mdl.t < t_lims[1]) i_abc = utils.sixphase_currents(res.mdl.machine.i_c_ab[:, mask]) utils.plot_phase_currents(res.mdl.t[mask], i_abc, y_lims=(-17.0, 24.0)) print("Force at the end (N):", np.round(res.mdl.machine.f_M_ab[-1], 1)) .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_dfc_002.png :alt: plot 3kw bsyrm dfc :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_dfc_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Force at the end (N): (100+149.8j) .. GENERATED FROM PYTHON SOURCE LINES 94-103 .. 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 .. [#Saa2016] Saarakkala, Sokolov, Mukherjee, Pippuri, Tammi, Belahcen, Hinkkanen, "Flux-linkage model including cross-saturation for a bearingless synchronous reluctance motor," Proc. ISMB15, 2016. .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 21.631 seconds) .. _sphx_glr_download_examples_plot_3kw_bsyrm_dfc.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_dfc.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_3kw_bsyrm_dfc.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_3kw_bsyrm_dfc.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_