Assume that we have a estimated system:
$$\hat G(s)$$
And we want the system $\hat G(s)$ follow the reference $r(t)$. If we add an input $u(t)$ to $\hat G(s)$ we will get a output response:
$$y(t) = \hat G(s) u(t)$$
Now define our control law like this if we want $y(t)$ to follow the reference $r(t)$
$$u(t) = \frac{1}{\hat {G}(0)}[r(t) - y(t)]$$
This $\frac{1}{\hat {G}(0)}$ is a reference gain. At time $t = 0$, then $y(0) = 0$, the system will become.
$$y(t) = \hat G(s) u(t) = \hat G(s)\frac{1}{\hat {G}(0)}[r(t) - y(t)] = \hat G(s)\frac{1}{\hat {G}(0)}r(0) = r(0)$$
At steady state $s -> 0$
For state feedback, the control law would look like this:
$$ u(t) = \frac{1}{\hat {G}(0)}[r(t) - \hat C\hat x(t)]$$
Where $\hat x(t)$ is estimated state from an observer and $\hat C$ is the estimated output matrix. If case if filtering is needed.
Question:
Is this a good control strategy? I'm mean, it's simple and it based on real time estimation and also it have some kind of "I know what input you need"-prediction. It does not follows dead beat control and it takes account on how the model can perform. There is no tuning parameter, not even for the Kalman gain filter if it's estimated by Recursive Least Squares which also can estimate a Kalman filter.
Or what can be it for drawbacks about this control strategy?
This control law will most likely not work well. The inverse of the DC gain of the system multiplied by the reference can be seen as a feed-forward term, however the feed-back term as a function of the (filtered) output perturbs this. Namely if $\hat{G}(0)$ exactly matches the DC gain of the system then just applying the term proportional to the reference should shift the equilibrium of the system to the reference (assuming that it is constant or sufficiently slowly changing in time), but the added feedback in the output "pulls" the system away from this desired equilibrium. Only if the DC gain of the system is zero it would work, but in that case the inverse of $\hat{G}(0)$ is not well defined.
It can also be noted that the term in the output might or might not be sufficient to stabilize the system if it is unstable or marginally stable, or might even make a stable system unstable.