The rate saturation equations are based on an equivalent scheme of the rate limiter. Rate saturation occurs when the error signal exceeds the saturation value$$e_L=\frac{V_L}{\omega_B}$$ and is forced to move at the maximum rate \(V_L\)
We can take the equivalent scheme and add it to a state-space model
$$x_s=
\begin{bmatrix}
x \\ \delta_{ns} \\ \delta
\end{bmatrix}$$
$$A_s=\begin{bmatrix}
A & B & 0 \\
0 & -\omega_B & \omega_B \\
0 & 0 & -1/\tau_\eta
\end{bmatrix}$$
$$B=
\begin{bmatrix}
0 \\ 0 \\ 1/\tau_\eta
\end{bmatrix}$$
$$C=
\begin{bmatrix}
C & 0 & 0
\end{bmatrix}$$
[[Eurofighter Control Law Control Surface and Integration Location]] – deals with decoupling control surface saturation
[[MPU-9250 Gyroscope Model]] – saturation limits must be applied to keep the output in the range of the ADC
[[X-29 Lateral Directional Control System]] – forward-loop integrator would saturate in a pro-spin condition
[[Integral Windup]] – saturated actuators can cause an integrator to wind up
- incasnationalinstituteforaerospaceresearcheliecarafolib
[[Control Surface Rate Limits]]
[[State-Space Model]]