.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/plot_3kw_bsyrm_levitation_comparison.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_comparison.py: 2.6-kW bearingless SyRM, comparison of control models in levitation control =========================================================================== 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. The unbalanced magnetic pull is a negative stiffness in the radial dynamics. The force estimate of the flux map includes it, while that of the constant-parameter model omits it, leaving the pull for the disturbance observer of the levitation controller. .. GENERATED FROM PYTHON SOURCE LINES 18-26 .. code-block:: Python from math import pi from pathlib import Path import numpy as np import motulator_bearingless.gradnet as gn from motulator_bearingless import control, model, utils .. GENERATED FROM PYTHON SOURCE LINES 27-28 Compute base values based on the nominal values (just for figures). .. GENERATED FROM PYTHON SOURCE LINES 28-32 .. 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 33-36 Load the magnetic models and compute the stiffness of the unbalanced magnetic pull from the force map at constant currents. The rotor mass is that of the levitation examples. .. GENERATED FROM PYTHON SOURCE LINES 36-54 .. code-block:: Python p = Path(__file__).resolve().parent if "__file__" in globals() else Path.cwd() R_s = 0.215 # Stator resistance from [#Das2026]_ path = "trained_models/bsyrm_fem_curr_map_harm_softmax_d128.npz" current_map = gn.CurrentMapWithHarmonics(gn.load_gradnet(p / path)) par = model.SpatialSaturatedBearinglessSynchronousMachinePars(R_s, current_map) path = "trained_models/bsyrm_fem_flux_map_softmax_d128.npz" est_flux_map = gn.FluxMap(gn.load_gradnet(p / path)) est_par = control.SaturatedBearinglessSynchronousMachinePars( R_s, psi_s_fcn=est_flux_map ) est_par_lin = est_par.linearized(12 + 12j) m = 20.0 for i_s2 in (13.5 + 0j, 12 + 12j): k_u = np.real(est_par.f_M(0j, i_s2, 1e-6)) # Force (N) at the displacement of 1 µm print(f"Stiffness of the pull at i_s2 = {i_s2} A: {k_u:.1f} N/µm") .. rst-class:: sphx-glr-script-out .. code-block:: none Stiffness of the pull at i_s2 = (13.5+0j) A: 6.1 N/µm Stiffness of the pull at i_s2 = (12+12j) A: 4.2 N/µm .. GENERATED FROM PYTHON SOURCE LINES 55-61 Configure the simulation. Without the pull in the force estimate, the stability of the displacement control is limited. For one axis in continuous time, an ideal inner force control loop, and `alpha_o = 3*alpha_q`, the closed-loop poles stay in the left half-plane only if the stiffness is below `1.39*m*alpha_q**2`. The limit is 2.75 N/µm at the bandwidth of 50 Hz and 11 N/µm at the bandwidth of 100 Hz used here. The constant-parameter controller would hence be unstable at 50 Hz, unlike the flux map. .. GENERATED FROM PYTHON SOURCE LINES 61-95 .. code-block:: Python alpha_q = 2 * pi * 100 w_M_rated = 2 * pi * 1700 / 60 t_stop = 0.6 def simulate(par_c: control.BearinglessMagneticModel): """Simulate the drive with the given control model.""" machine = model.BearinglessSynchronousMachine(par) mechanics = model.ExternalRotorSpeed() mechanics.set_external_rotor_speed(w_M_rated) radial = model.RadialMechanics(m=m) radial.set_external_force(lambda t: (t > 0.1) * -9.81j * 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) cfg = control.DirectForceControllerCfg(i_s_max=25.5, psi_s_min=0.4) force_ctrl = control.DirectForceController(par_c, cfg) levitation_ctrl = control.LevitationController(m=m, alpha_q=alpha_q) ctrl = control.DirectForceControlSystem(force_ctrl, None, levitation_ctrl) ctrl.set_torque_ref(lambda t: (t > 0.45) * 0.7 * nom.tau) ctrl.set_displacement_ref(lambda t: (t > 0.3) * 50e-6) return model.Simulation(mdl, ctrl).simulate(t_stop=t_stop) res_lin = simulate(est_par_lin) res_map = simulate(est_par) for name, res in (("Constant parameters", res_lin), ("Flux map", res_map)): q_M_ab = res.mdl.machine.q_M_ab print( f"{name}: peak displacement {1e6 * np.max(np.abs(q_M_ab)):.1f} µm, " f"final displacement {1e6 * np.mean(q_M_ab[res.mdl.t > 0.55]):.1f} µm" ) .. rst-class:: sphx-glr-script-out .. code-block:: none Constant parameters: peak displacement 63.8 µm, final displacement 50.0-0.0j µm Flux map: peak displacement 51.3 µm, final displacement 50.0-0.0j µm .. GENERATED FROM PYTHON SOURCE LINES 96-99 Plot the results of the constant-parameter controller. Gravity is applied at t = 0.1 s, the displacement reference step at t = 0.3 s, and the torque reference step at t = 0.45 s. .. GENERATED FROM PYTHON SOURCE LINES 99-103 .. code-block:: Python y_lims = [(-800.0, 600.0), (-30.0, 70.0)] # Same scales for both controllers utils.plot(res_lin, base, ["force", "displacement"], y_lims=y_lims) .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_comparison_001.png :alt: plot 3kw bsyrm levitation comparison :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_comparison_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 104-105 Plot the results of the flux-map controller. .. GENERATED FROM PYTHON SOURCE LINES 105-108 .. code-block:: Python utils.plot(res_map, base, ["force", "displacement"], y_lims=y_lims) .. image-sg:: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_comparison_002.png :alt: plot 3kw bsyrm levitation comparison :srcset: /examples/images/sphx_glr_plot_3kw_bsyrm_levitation_comparison_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 109-114 .. 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 25.782 seconds) .. _sphx_glr_download_examples_plot_3kw_bsyrm_levitation_comparison.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_comparison.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_3kw_bsyrm_levitation_comparison.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_3kw_bsyrm_levitation_comparison.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_