Exactly - the ability to see process change is based on the resolution of the measuring instrument (GAGE R%R to %PV). Enough resolution will definitely see sawtooth...its physics. You would have to have a perfectly synced load to energy application to have it on...constantly...and not have it rise in temperature. Pretty rare, I would say.
Also, remember, ramp up and ramp down are special causes, and do not relate to the capability, only the steady state.
Also, remember, ramp up and ramp down are special causes, and do not relate to the capability, only the steady state.