Let's say my setup is something simple: I'm trying to heat some liquid to a temperature $T$. I can influence the temperature of the liquid by applying some potential difference $V$ across the liquid. This means that if I were to try to hold the temperature at some setpoint $T_{set}$ using a PID controller, then I would output some control variable $u(t)$.
Clearly all the terms used in calculating $u(t)$ would be in terms of the measured temperature $T$. The question is, what exactly is the output $u(t)$? Is this in units of temperature or voltage?
I don't think this is in temperature because I actually control the voltage. In that case, should I be setting the new voltage to u(t)
? Or is u(t)
more like a feedback such that I actually set $V_{new} \leftarrow V_{curr} + u(t)$?