motulator_impedance.drive

motulator_impedance.drive#

Mechanical impedance of machine drives.

The mechanical impedance Z_M = -Delta tau_M/Delta w_M describes the dynamics of the machine and its control system, as seen from the shaft [1]. It is measured from simulations by a frequency sweep: the rotor speed is imposed, and small-signal speed excitations are superimposed on it one frequency at a time.

References

Classes#

MeasurementCfg

Configuration of the mechanical impedance measurement.

MechanicalImpedance

Measured mechanical impedance.

Functions#

measure_mechanical_impedance(mdl, ctrl, cfg)

Measure the mechanical impedance.

plot_mechanical_impedance(res[, latex])

Plot the magnitude and phase of the mechanical impedance.

Module Contents#

class motulator_impedance.drive.MeasurementCfg[source]#

Configuration of the mechanical impedance measurement.

Parameters:

  • abs_w_e (float) – Magnitude of the rotor speed excitation (mechanical rad/s) at the first frequency.

  • freqs (ndarray, optional) – Excitation frequencies (Hz), defaults to 100 logarithmically spaced frequencies from 1 Hz to 1 kHz.

  • amplitude_multiplier (float, optional) – Excitation magnitude at the last frequency relative to the first one, defaults to 5. The magnitude changes linearly over the frequency array. Use 1 for a constant magnitude.

  • t0 (float, optional) – Simulation time (s) for reaching the operating point, defaults to 1.0.

  • t1 (float, optional) – Additional simulation time (s) for reaching the sinusoidal steady state during signal injection, defaults to 0.5.

  • N_eval (int, optional) – Number of evenly spaced data points the solver should return for each integration interval, i.e., for each sampling period or, if carrier comparison is used, for each switching interval, defaults to 10. More points are used at high excitation frequencies, so that each excitation period has at least 10 points.

  • n_periods_excitation (int, optional) – Number of excitation signal periods used in calculating the DFT, defaults to 4. At least 3 are needed if use_window is True.

  • multiprocess (bool, optional) – If True, the frequencies are simulated in parallel using all available CPU cores, defaults to True. The model and the control system are copied to the worker processes, which can require pickling them. Lambda functions and nested functions (e.g., as references) cannot be pickled, but module-level functions can. In a script, call the measurement under if __name__ == “__main__”:, as in the examples.

  • use_window (bool, optional) – Whether to use window function for calculating DFT, defaults to True.

class motulator_impedance.drive.MechanicalImpedance[source]#

Measured mechanical impedance.

Contains fields for the excitation frequency f_e, the mechanical impedance Z_M, and the operating-point rotor speed w_M0 and electromagnetic torque tau_M0. The results can be saved, e.g., by scipy.io.savemat(path, dataclasses.asdict(res)).

motulator_impedance.drive.measure_mechanical_impedance(mdl, ctrl, cfg)[source]#

Measure the mechanical impedance.

The rotor speed is imposed by the ExternalRotorSpeed model of mdl, i.e., no mechanical system is used. The system is first simulated to the operating point, given by the rotor speed and the references of the control system. Then, small-signal speed excitations are injected and the impedance is computed from the electromagnetic torque response at each excitation frequency.

Parameters:

  • mdl (Drive) – Continuous-time system model, whose mechanics is ExternalRotorSpeed.

  • ctrl (VectorControlSystem | VHzControlSystem) – Discrete-time control system.

  • cfg (MeasurementCfg) – Measurement configuration.

Returns:

Mechanical impedance and the operating point.

Return type:

MechanicalImpedance

Notes

The mechanical impedance is passive at the frequencies where its real part is nonnegative, i.e., its phase is within ±90°. Combined with any passive mechanical system, a drive whose mechanical impedance is passive at all frequencies is stable.

motulator_impedance.drive.plot_mechanical_impedance(res, latex=False)[source]#

Plot the magnitude and phase of the mechanical impedance.

The passivity limits of the phase, -90° and 90°, are shown as dashed lines on the side of the phase values.

Parameters:
Return type:

None