The circadian system acts as your body’s internal clock and is part of the system that helps control when you sleep.
It creates a drive for the body to sleep, depending on how long it has been since you last slept.
Sleep pressure (Process S) builds up the longer you are awake and lessens during sleep; this pressure is stronger after being awake for a long time and drops after sleeping.
A sleep-regulating chemical that builds up in your brain fluid while you are awake adds to this drive.
People tend to sleep longer after long periods of wakefulness to make up for lost sleep.
A simple way to think about sleep pressure (conceptually) is given by:
Let S(t) be sleep pressure at time t.
$$ \frac{dS}{dt} = \begin{cases} \alpha, & \text{awake