The roll stick position is scaled from -1 to 1 to represent maximum left roll and maximum right roll. This represents -240 deg/s to 240 deg/s wind-axis roll rates. The control surface power is modulated so that as much as possible is used for steady-state roll rates while maintaining a margin for stabilization and departure prevention. The wind axis roll command is the scaled stick position multiplied by the maximum roll rate. The maximum rudder deflection \(\beta_{c_{max}}\) is a function of AOA and airspeed. It is limited up to 12 degrees at low speeds. The maximum command is the scaled rudder pedal (-1 to 1) multiplied by the maximum deflection angle. During rapid rolls the sideslip command is blended down to 0.
The gain matrix are a table of 3×5 matrix of combined feedback and feedforward matrices. The output of this is the differential flap and rudder commands. These gains are interpolated based on the flight condition(AOA, Mach Number, altitude). The direct link yaw moment is blended into the thrust vectoring, as the rudder becomes ineffective at AOAs above 30 deg. The yaw rate command is calculated from a lateral acceleration lookup table by aircraft estimated weight and dynamic pressure. Rudder and differential flaps are precomputed into the gain matrices and scheduled to provide a pure yaw moment. Thrust vectoring can give an almost pure yaw moment as well. The state and control vectors for the lateral-directional state-space models are
$$x^T=\Big [\beta, p_w, r_w, \Phi\Big ]$$
$$u^T=\Big[ \delta_{DF}, \delta_r, \delta_{TV}\Big]$$
The Weighting matrices are
$$Q=\begin{bmatrix}
q_\beta & q_{\beta_p} & q_{\beta_r} & 0 \\
q_{\beta_p} & q_{p} & q_{p_r} & 0 \\
q_{\beta_r} & q_{p_r} & q_{r} & 0 \\
0 & 0 & 0 & 0
\end{bmatrix}$$
$$R=\begin{bmatrix}
r_{\delta_{DF}} & 0 & 0 \\
0 & r_{\delta_r} & 0 \\
0 & 0 & r_{\delta_{TV}}
\end{bmatrix}$$
Where the \(\Phi\) rows and columns are set to 0 and the \(\Phi\) feedbacks are ignored as they only have a marginal effect on the dutch-roll modes. Because of this omission there is no spiral mode stabilization. The diagonal elements of the Q matrix define the eigenvalues of the lateral/directional aircraft motion. The command shaping functions are shown below.[^2]
F-22 Lateral Directional Flight Control System – completely removes some control surfaces at some AOAs
Sources
- ControlLawDesignExperimentalAircraftX-31A[^1]
Backlinks
[[Angle of Attack]]
[[Dutch Roll]]
[[Dynamic Pressure]]
Eigenvalue
[[Interpolation]]
[[Mode-Blending]]
[[Spiral Mode]]
[[Velocity]]
[[X-31A Flight Control Laws]]
[[X-38 Airframe]]