The LQR-PI controller generates an optimal control law that assumes a MIMO system in state-space form. Optimal control with state feedback is the best that you can do. You should not push the system too far, be wary of actuator limits and time delays. It assumes a MIMO in state-space form. The equation for the dynamic controller is:
$$\dot{x_c} = A_cx_c+B_c(r-y)$$
This makes the equation for the open-loop augmented system:
$$\begin{bmatrix}\dot{x} \\
\dot{x_c}
\end{bmatrix}
= \begin{bmatrix}
A & 0 \\
-B_CC & A_c\end{bmatrix}
\begin{bmatrix}
x \\
x_c\end{bmatrix}
+
\begin{bmatrix}B \\ -B_cD\end{bmatrix}U
$$
If this system has a stable closed-loop, then there is an optimal control law. Be very careful when tracking a rate with the LQR-PI controller.
[[MIMO model with disturbances]]
State Feedback
[[JDAM Baseline Guidance System]]
- LearningLookingFuture
Backlinks:
[[Actuator Limits]]
[[First-Order Continuous System with Time-Delay]]
LQR Controller
[[Proportional Control]]
[[Second-Order Continuous System with Time Delay]]
[[State-Space Model