Open Loop and Closed Loop Systems

• Open loop — e.g. a toaster timer or a stepper motor without encoder. Simple, cheap, but cannot correct disturbances.
• Closed loop — e.g. an air conditioner with a thermostat. Feedback corrects disturbances and component variation, but adds complexity and can become unstable.

Closed-loop transfer function with forward path $G(s)$ and feedback $H(s)$:

$T(s) = \frac{G(s)}{1 + G(s)H(s)}$

The term $1 + G(s)H(s) = 0$ is the characteristic equation — its roots decide stability.