I have been tweaking the air-con even more.
The control I have, basically, is to set the target temperature. I can set higher than now, and lower than now, and so make it turn on or off. But sensibly the air-con has controls. It does not run the compressor exactly to match what I say, it turns on for a minimum time, and there are also sorts of laggy effects for the temperature to react. Once compressor was on it stays cool a while and then fan blows cool for a while.
But it is getting silly.
For the last hour or so, even more so. This is not like ±0.1℃, it is more like ±0.05℃.
It is really good. But I was thinking, is this just that it is a cold day in Wales and the temperature happens to be settling where I want? At 22℃?
Well no, it is not that, looking at the power usage I see that it is turning on and off the compressor to work the temperature.
What I did was make it predict on a trend the next 2 minutes and turn on/off (set high/low target) based on that. And it was surprisingly good. This is the power usage showing it is fine tuning it to manage that. It is controlling the temperature to well within ±0.1℃ with no problem.
P.S. Just to clarify (as someone asked), this is not switching between heating and cooling (which would use more power), this is turning cooling on and off. It will switch to heating, but only after quite a while of temperature not coming back within range when off - and that can happen on some days in spring/autumn, but usually only once (each way) in the day. It also does automatic fan control.