F-15 Active Lateral Directional Model

This is a linearized model for the lateral/directional dynamics of the F-15 Active aircraft. The F-15 Active used four control effectors in its dynamic simulation model: aileron, rudder, differential canard, and differential stabilator.

The state vector \(x\) is:
$$x=\begin{bmatrix}
\beta \\ p \\ r\\ \phi
\end{bmatrix}$$
The input vector $u$ is
$$u =\begin{bmatrix}
\delta_a \\ \delta_r \\ \delta_{dc}\\ \delta_{ds}
\end{bmatrix}$$

The state-space system matrices are as follows:
$$A=\begin{bmatrix}
Y_\beta & \sin\alpha_0 & -\cos\alpha_0 & g\cos(\theta)0/v_0 \\ L\beta & L_p & L_r & 0 \\
N_\beta & N_p & N_r & 0 \\
0 & 1 & tan\theta_0 & 0\end{bmatrix}$$


$$B=\begin{bmatrix}
0 & Y_{\delta_r} & Y_{\delta_{dc}} & Y_{\delta_{ds}} \\
L_{\delta_\alpha} & L_{\delta_r} & L_{\delta_{dc}} & L_{\delta_{ds}} \\
0 & N_{\delta_r} & N_{\delta_{dc}} & N_{\delta_{ds}} \\
0 & 0 & 0 & 0
\end{bmatrix}$$
$$C=\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\frac{V_0}{g}Y_\beta & 0 & 0 & 0 \
\end{bmatrix}$$
$$D=\begin{bmatrix}
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & Y_{\delta_r} & Y_{\delta_{dc}} & Y_{\delta_{ds}}\
\end{bmatrix}$$

The original design for the lateral-directional system had conventional dutch-roll damping of 0.7 with a frequency that was identical to the original F-15. The roll mode constant was 0.3s.

[[F-15 Flight Control System]] – improves lateral-directional stability with an aileron-rudder interconnect

  • morelliMultipleInputDesign2003
  • RTO-TR-029

Backlinks

4DoF Dynamic Lateral Aircraft Model
[[Aerodynamic Models]]
[[Dutch Roll]]
[[F-15 Active]]
F-15 Active Flight Control System
[[F-15 Active Flight Test]]
State-Space Model