I wonder what's the difference between having a integral action or correction factor when it comes to disturbances?
Ofc I know how to apply then, the reason for this question is: What's suits best for disturbances?
Assume that we got a system discribed as a transer function $G(s)$ LTV system and we have a controller $K(s)$.
The feedback loop will then be:
$$G_f (s) = \frac{K(s)G(s)}{1+K(s)G(s)}$$
Assume that our reference value $r(t)$ should be the same as output value $y(t)$, but it isin't! There is a error between $r(t)$ and $y(t)$.
$$y(t) = G_f(s)r(t)$$
To solve this I just add a constant after reference $r(t)$.
$$y(t) = G_f(s)\frac{1}{G_f(0)}r(t)$$
$\frac{1}{G_f(0)}$ is called the low gain frequency. A correction factor for $r(t)$ so $r(t) = y(t)$
Question:
What do you recomend: Correction factor for $r(t)$ if we can estimate the system $G(s)$ over time, or integral action when it comes to small disturbances?