On Friday, March 9, 2012 12:53:36 AM UTC, Andy Wade wrote:

'Modern digital thermostats',
you will find, implement the same 'anticipator' function in software.
As the sensed temperature gets close to the set point the heating power
input is turned down by controlling the on/off time ratio of the heater
(PWM control, in effect). That's exactly what the accelerator heater
does in a bi-metal 'stat - it creates a band of temperature over which
the heat input is proportional to the temperature error, greatly helping
to reduce overshoot.

You made that up. No-one is going to try to simulate the action of a heater with electronics.

They use PID feedback controls, the derivative constant reduces the output in proportion to the rate of change of the process variable in order to anticipate and reduce overshoot.

The derivative constant is often left at 0 on BMS controllers, since it is reckoned to be unnecessary and causes excessive hunting and premature wear of the control valves.