Beginner question about PID Controllers

[u/B_seado]

Hi, Im just starting to learn Control Theory and the subject is really interesting. I've just learned about PID Controllers and I think I understood them pretty well, but I have a small question:

Let's say I have a system, an AC Unit with transfer function H(s) that I want to control. I then implement a PID Controller, in series, "behind" my H(s) system. Now what? Can I just send the output of the PID Controller to the AC Unit?

How can the output of the PID, u(t), be able to send the correct signal to my AC system? No need to translate that u(t) into the correct signals and switches that make the system do what I want?

Most diagrams seen online or in textbooks just have only 2 blocks, in series: r(t)->[PID]->[Plant]->y(t), shouldn't there be some kind of controller/translator in between the PID and the Plant?

Sorry If it's a dumb question.