[primis]

"PID (Proportional, Integral, Derivative) works by continuously monitoring the boiler’s temperature and making small adjustments to maintain an exact and stable target temperature."

So basically a smart thermostat that accounts for ramp up and cool down times when adjusting the temperatures.

[throwaway9870]

Yes and no. PID loops are linear systems and don't understand ramp-up and ramp-down times. They understand poles and zeros. So normally you would speak of time constants and bandwidths rather than ramp (slew) rates. This is not just semantics, they function differently. However is not unusual to add non-linear constraints on top of of linear control loop so you end up with a hybrid control system.