Reference Feed-Forward

We want ${\lim }_{t\to \infty }y(t)=r$, giving us

$$\begin{array}{r}u=K_{r}r-Kx\end{array}$$

Where $K_{r}r$ is the reference feedforward, and $-Kx$ is the state feedback.

Calculation for a system with State Space Representation and $D=0$ gives us $K_r=[C(BK-A{)}^{-1}B{]}^{-1}$

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The reference feed-forward moves the equilibrium point of the closed-loop system so $y=r$ in the equilibrium point.