docs(i18n): PX4 guide translations (Crowdin) - uk (#26850)

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docs/uk/flight_stack/controller_diagrams.md

@@ -164,6 +164,42 @@ $$\dot{B} = \gamma - \frac{\dot{V_T}}{g}$$
 
 ## Контролер положення фіксованого крила
 
+### Setpoint modificaiton
+
+Most fixed-wing aircraft cannot generate a sustained yaw rate using the rudder alone. As a result, the yaw component of the quaternion attitude error should be removed before computing the control action.
+
+This is achieved by premultiplying the setpoint quaternion with a rotation about the global down axis. The additional rotation cancels the yaw component of the attitude error while preserving the roll and pitch components.
+
+The yaw offset is
+
+$$
+\psi =-2\frac{\hat{q}_0 q_3 - \hat{q}_1 q_2 + \hat{q}_2 q_1 -\hat{q}_3 q_0}
+{\hat{q}_0 q_0 - \hat{q}_1 q_1 - \hat{q}_2 q_2 + \hat{q}_3 q_3}
+$$
+
+The quaternion representing the yaw offset is
+
+$$
+ℚ_{\text{yaw}} =
+\operatorname{normalize}
+\left(
+\begin{bmatrix}
+1 \
+0 \
+0 \
+\frac{\psi}{2}
+\end{bmatrix}
+\right)
+$$
+
+The corrected setpoint quaternion is then obtained by applying the rotation
+
+$$
+ℚ_{\text{sp, corrected}} = ℚ_{\text{yaw}} \otimes ℚ_{sp}
+$$
+
+### Quaternion based attitude controller
+
 ![FW Attitude Controller Diagram](../../assets/diagrams/px4_fw_attitude_controller_diagram.png)
 
 <!-- The drawing is on draw.io: https://drive.google.com/file/d/1ibxekmtc6Ljq60DvNMplgnnU-JOvKYLQ/view?usp=sharing
@@ -186,12 +222,16 @@ The feedforward gain is used to compensate for aerodynamic damping.
 
 ### Поворотна координація
 
-Контролери крену та тангажу мають однакову структуру, і довжинна та поперечна динаміка вважаються достатньо роз'єднаними, щоб працювати незалежно один від одного.
-Контролер курсу, однак, генерує встановлення швидкості курсу, використовуючи обмеження координації повороту для мінімізації бокового прискорення, що виникає, коли літак слідкує. Алгоритм узгодження повороту базується виключно на узгодженому розрахунку геометрії повороту.
+The yaw rate setpoint is generated using the turn coordination constraint in order to minimize lateral acceleration, generated when the aircraft is slipping.
 
-$$\dot{\Psi}_{sp} = \frac{g}{V_T} \tan{\phi_{sp}} \cos{\theta_{sp}}$$
+$$r_{sp} = \frac{2g}{V_T}\left(q_0 q_1 + q_2 q_3\right)$$
 
-The yaw rate controller also helps to counteract [adverse yaw effects](https://youtu.be/sNV_SDDxuWk) and to damp the [Dutch roll mode](https://en.wikipedia.org/wiki/Dutch_roll) by providing extra directional damping.
+This also helps to counteract [adverse yaw effects](https://youtu.be/sNV_SDDxuWk) and to damp the [Dutch roll mode](https://en.wikipedia.org/wiki/Dutch_roll) by providing extra directional damping.
+
+To compensate for the non-zero pitch rate that naturally occurs during coordinated turns, a geometry-based feedforward term is added to the pitch-rate command.
+This feedforward term accounts for the aircraft's current attitude and airspeed so that the controller does not need to generate this motion purely through feedback.
+
+$$q_{sp}^{ff} = \frac{4g(q_0 q_1 + q_2 q_3)^2}{V(1 - 2q_1^2 - 2q_2^2)}$$
 
 ## Диспетчер польотів VTOL