I'm building my own hobbyist microprocessor-controlled reflow oven. I'm using (mechanical) relays to turn the heaters (i.e. quartz tubes) on or off. I've noticed heating lags a couple of seconds before the temperature starts to rise.
For now I'm managing the temperature profile manually with the assistance of an Arduino, which just turns the heaters off when the set temperature is reached. For instance when I set the temperature to, say 120° Celsius and the heaters stop, the temperature still climbs 10-20 degrees so there is quite a bit of overshoot then some ringing, which decreases slowly.
I've read and watched many examples that make use of a PID for a better temperature control. Without that I would just stop the heaters, like 10-20 degrees below the set value and turn them on/off in short periods afterwards until the temperature stabilizes around the set value. I just know the delta varies with the temperature so it might not be as straightforward — I know about the exponential nature of temperature rise with a fixed set value.
So can anybody explain in layman's terms how a PID accounts for the inertia, e.g. what role the integral part and what the derivative part play in simple terms, as well as how/if I can figure out rather intuitively an estimation of the derivative and integral quantities without resorting to complex calculations.