Feedback system

Feedback systems are closed-loop systems (especially control systems) meant to make unstable systems more stable. As a result, they’re used anywhere control systems are (including aircraft and vehicle systems). Take this example: The parameter $E(s)$ is the tracking error, defined as $E(s)=R(s)-Y(s)$, where $Y(s)$ is the output that is fed back into the input.

Why aren’t open loop systems useful?

• Systems often aren’t robust with respect to uncertainties in the system. Open-loop systems can’t get rid of uncertainty terms as $t\to \infty$.
• The system also won’t be robust with respect to external disturbances. We similarly can’t get rid of these terms.
• And our controller won’t have any influence on the speed of convergence.

In contrast, feedback systems are invariant to the presence of uncertainty, external disturbances, and we can control for the convergence rate.