motulator-bearingless

Six-phase bearingless machine drives for motulator

Documentation: https://aalto-electric-drives.github.io/motulator-bearingless/

This package extends motulator with the continuous-time model of a symmetrical six-phase bearingless synchronous machine drive, a direct radial force controller based on feedback linearization, and a levitation controller [1]. The two three-phase sets of the winding produce both the torque and the radial force. The winding is described by means of the vector-space decomposition, and the magnetic model is a gradient of a magnetic energy function, which represents magnetic saturation and rotor eccentricity in a consistent manner. The six-phase converter model comes from motulator-multiphase.

The magnetic models follow motulator: constant parameters, or gradient networks [2] trained on the finite-element data of a 2.6-kW machine. The machine model uses an energy-based current map, with or without the spatial harmonics, and the controller a co-energy-based flux map without the rotor angle.

For comparison, a current-based force controller is included as well: 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 the manner of the common and differential modes of motulator-multiphase, see the relation between the packages.

Installation

Install the package in a virtual environment (motulator and motulator-multiphase are installed as dependencies). On Linux and macOS:

python3 -m venv .venv
source .venv/bin/activate
pip install motulator-bearingless

On Windows, the environment is created and activated with py -m venv .venv and .venv\Scripts\activate.

For development, and for the examples with the gradient networks, which load the networks and the dataset from examples/, clone the repository and install the package with pip install -e ".[dev]".

Usage

A sensorless direct-force-controlled 2.6-kW bearingless SyRM drive, whose rotor is held at a fixed radial position by external bearings:

from math import pi

from motulator_bearingless import control, model, utils

# System model: L_1 is the two-pole inductance, and m_d and m_q are the radial force
# constants of the d and q axes
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)
radial = model.ExternalRotorPosition()  # Fixed radial position
converter = model.MultiThreePhaseConverter(u_dc=540)  # Two sets by default
mdl = model.BearinglessDrive(machine, model.MechanicalSystem(J=0.15), radial, converter)

# Control system: the direct force controller and the speed controller
cfg = control.DirectForceControllerCfg(i_s_max=25, psi_s_min=0.3, sensorless=True)
force_ctrl = control.DirectForceController(par, cfg)
speed_ctrl = control.SpeedController(J=0.15, alpha_s=2 * pi * 8)
ctrl = control.DirectForceControlSystem(force_ctrl, speed_ctrl)

# Speed and force references and the load torque
ctrl.set_speed_ref(lambda t: min(t / 1.2, 1) * 2 * pi * 1700 / 60)
ctrl.set_force_ref(lambda t: (t > 1.6) * 100 + 1j * (t > 1.9) * 150)
mdl.mechanics.set_external_load_torque(lambda t: (t > 2) * 10)

res = model.Simulation(mdl, ctrl).simulate(t_stop=3)
utils.plot(res)

The gradient-network maps replace the constant parameters in the same manner as in motulator:

import motulator_bearingless.gradnet as gn

models = "examples/trained_models/"
current_map = gn.CurrentMapWithHarmonics(
    gn.load_gradnet(models + "bsyrm_fem_curr_map_harm_softmax_d128.npz")
)
par = model.SpatialSaturatedBearinglessSynchronousMachinePars(0.215, current_map)
machine = model.BearinglessSynchronousMachine(par)

flux_map = gn.FluxMap(gn.load_gradnet(models + "bsyrm_fem_flux_map_softmax_d128.npz"))
est_par = control.SaturatedBearinglessSynchronousMachinePars(0.215, psi_s_fcn=flux_map)
force_ctrl = control.DirectForceController(est_par, cfg)

Complete examples, including current-based force control, levitation control, and the magnetic maps, are in the example gallery.

Scope

• Symmetrical six-phase machines with two identical three-phase sets, without zero-sequence currents.
• The radial motion of the rotor is modeled as a point mass, or the rotor is held at a given radial position. The tilting and axial motion are not modeled.
• The constant machine parameters of the examples are illustrative.
• The trained networks describe a 2.6-kW bearingless synchronous reluctance machine, based on a finite-element model that has not been validated against measurements.
• The control methods do not use the spatial harmonics.

References

1. Das, Martin, Kontodinas, Hinkkanen, "Direct force control of six-phase bearingless synchronous machines," Proc. ICEM, 2026, https://doi.org/10.1109/ICEM68283.2026.11757980
2. Li, Foissner, Martin, Piippo, Hinkkanen, "Gradient networks for universal magnetic modeling of synchronous machines," 2026, https://arxiv.org/abs/2602.14947

Contributors

Nirangkush Das 🤔 🔬

Eleftherios Kontodinas 🤔 🔬

Floran Martin 🤔 🔬

jacopogertod 🤔 🔬

Junyi Li 🤔 🔬

Marko Hinkkanen 💻 💡