From 294c4f73b38c761497295685ff3fe8c42cdc0008 Mon Sep 17 00:00:00 2001 From: GitHub Action Date: Wed, 13 Nov 2024 11:02:37 +0000 Subject: [PATCH] Update documentation --- .../grid_examples_jupyter.zip | Bin 22864 -> 22864 bytes .../drive_examples_jupyter.zip | Bin 113444 -> 113444 bytes .../plot_flux_vector_pmsyrm_5kw.zip | Bin 17249 -> 17249 bytes .../plot_vector_ctrl_im_2kw.zip | Bin 9634 -> 9634 bytes .../plot_gfm_obs_13kva.zip | Bin 7248 -> 7248 bytes .../plot_vector_ctrl_im_2kw_tq_mode.zip | Bin 6829 -> 6829 bytes .../plot_gfl_10kva.zip | Bin 6889 -> 6889 bytes .../plot_obs_vhz_ctrl_pmsm_2kw_two_mass.zip | Bin 11021 -> 11021 bytes .../plot_gfl_dc_bus_10kva.zip | Bin 6773 -> 6773 bytes .../plot_vector_ctrl_pmsm_2kw_diode.zip | Bin 5996 -> 5996 bytes .../plot_vhz_ctrl_6step_im_2kw.zip | Bin 7377 -> 7377 bytes .../plot_vector_ctrl_pmsyrm_thor.zip | Bin 7278 -> 7278 bytes .../plot_obs_vhz_ctrl_im_2kw.zip | Bin 7037 -> 7037 bytes .../plot_flux_vector_pmsm_2kw.zip | Bin 5614 -> 5614 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\mathrm{j}\omega_\mathrm{s}\boldsymbol{k}_\mathrm{t} )\left(\boldsymbol{\psi}_\mathrm{s,ref} - \hat{\boldsymbol{\psi}}_\mathrm{s}\right) \\ \boldsymbol{u}_\mathrm{s,ref} &= \boldsymbol{k}_\mathrm{t}\boldsymbol{\psi}_\mathrm{s,ref} - \boldsymbol{k}_\mathrm{p}\hat{\boldsymbol{\psi}}_\mathrm{s} + \boldsymbol{u}_\mathrm{i}\end{split}\]

where the angular speed of the coordinate system equals typically the measured rotor speed, \(\omega_\mathrm{s} = \omega_\mathrm{m}\), or the estimated rotor speed \(\omega_\mathrm{s} = \hat{\omega}_\mathrm{m}\). If the magnetic saturation is not considered, this flux-linkage-based current controller is equivalent to a regular 2DOF PI current controller (even if inductance estimates are inaccurate). Notice that \(\boldsymbol{i}_\mathrm{s,ref} = \boldsymbol{i}_\mathrm{s}\) holds in the steady state even with inductance estimate inaccuracies, since the same inductances are used to map both the reference current and the actual current to the corresponding flux linkages.

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Note

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The control law (8) omits the effect of the stator resistance for simplicity, i.e., \(\hat R_\mathrm{s} = 0\) is assumed. This is a common and practical assumption. However, if needed, the resistive voltage drop term \(\hat R_\mathrm{s}\boldsymbol{i}_\mathrm{s}\) could be simply added to \(\boldsymbol{u}_\mathrm{s,ref}\) in (8).

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The gain selection analogous to (5) becomes

-\[\boldsymbol{k}_\mathrm{p} = 2\alpha_\mathrm{c} - \hat R_\mathrm{s} \qquad\qquad +\[\boldsymbol{k}_\mathrm{p} = 2\alpha_\mathrm{c} \qquad\qquad \boldsymbol{k}_\mathrm{i} = \alpha_\mathrm{c}^2 \qquad \qquad \boldsymbol{k}_\mathrm{t} = \alpha_\mathrm{c}\]
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where \(\hat R_\mathrm{s} = 0\) can be used in practice. Assume accurate parameter estimates and perfect alignment of the controller coordinate system with the rotor coordinate system. Then, using (6), (7), and (8), the closed-loop system can be shown to be analogous to the induction machine case. This control design corresponds to the implementation in the motulator.drive.control.sm.CurrentController class.

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Assume accurate parameter estimates and perfect alignment of the controller coordinate system with the rotor coordinate system. Then, using (6), (7), and (8), the closed-loop system can be shown to be analogous to the induction machine case. This control design corresponds to the implementation in the motulator.drive.control.sm.CurrentController class.

References

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