Time delay and integration

Imagine you are playing a game with your friend where you have to toss a ball back and forth. Your friend has a rule that says they will only throw the ball after counting to three. This means that there will be a delay between when your friend catches the ball and when they throw it back. This delay is called time delay.

Now, if you keep playing this game for a while, you will get better at catching the ball and throwing it back. You might even start to anticipate when your friend will throw the ball and prepare your hands to catch it before the ball even reaches you. This is like integrating your actions with the time delay.

In other words, integration means taking into account a time delay and adjusting your actions to compensate for it. Just like you adjusted your actions in the game to catch the ball better, engineers and scientists use integration to help them design systems that take into account time delays. This can be especially important in things like controlling machines or sending signals over long distances.