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Fix duplicate references in docs/source/control/grid/current_ctrl.rst #166

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Sep 7, 2024
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Fix duplicate references in docs/source/control/grid/current_ctrl.rst #166

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6 changes: 3 additions & 3 deletions docs/source/control/grid/current_ctrl.rst
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Expand Up @@ -35,13 +35,13 @@ The disturbance rejection depends on the closed-loop admittance

.. math::
\boldsymbol{Y}_\mathrm{c}(s) = \frac{s}{L s^2 + (\boldsymbol{k}_\mathrm{p} + \mathrm{j}\omega_\mathrm{c} L) s + \boldsymbol{k}_\mathrm{i} + \mathrm{j}\omega_\mathrm{c} \boldsymbol{k}_\mathrm{t}}
:label: Yc
:label: Yc_grid

The closed-loop poles can be arbitrarily placed by means of the gains. The reference-tracking transfer function is

.. math::
\boldsymbol{G}_\mathrm{c}(s) = \frac{(s + \mathrm{j}\omega_\mathrm{c}) \boldsymbol{k}_\mathrm{t} + \boldsymbol{k}_\mathrm{i} }{L s^2 + (\boldsymbol{k}_\mathrm{p} + \mathrm{j}\omega_\mathrm{c} L) s + \boldsymbol{k}_\mathrm{i} + \mathrm{j}\omega_\mathrm{c} \boldsymbol{k}_\mathrm{t}}
:label: Gc
:label: Gc_grid

whose zero can be placed by means of the reference-feedforward gain :math:`\boldsymbol{k}_\mathrm{t}`.

Expand All @@ -55,7 +55,7 @@ Consider the gains
\boldsymbol{k}_\mathrm{i} = \alpha_\mathrm{c}^2\hat L \qquad \qquad
\boldsymbol{k}_\mathrm{t} = \alpha_\mathrm{c} \hat L

where :math:`\hat L` is the inductance estimate. Assuming accurate parameter estimates, the closed-loop transfer functions :eq:`Yc` and :eq:`Gc` reduce to
where :math:`\hat L` is the inductance estimate. Assuming accurate parameter estimates, the closed-loop transfer functions :eq:`Yc_grid` and :eq:`Gc_grid` reduce to

.. math::
\boldsymbol{Y}_\mathrm{c}(s) = \frac{s}{L (s + \alpha_\mathrm{c})(s + \alpha_\mathrm{c} + \mathrm{j}\omega_\mathrm{c})}
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