precision rectifier in thermostat circuit / understanding Hakko 936 circuit

[JeanF]

Hello,
I try to learn by looking at simple circuits around me and spending some (usually large amount of) time figuring out how they work. Sometimes it gets a little bit tedious, I tend to get stuck! But I enjoy it, that's the main thing.

In the Hakko 936 thermostat circuit, I get the basic principle of operation but I have a hard time with a few specific questions ; could anybody please help me with these ? Let's say that the opamps are named U1, U2, etc from left to right.

- why are they using a precision rectifier (U3) to amplify the output voltage of U2 ? I can't see any situation where the output of U2 would go above 5.8 V. The input of the precision rectifier (left pin of R7) should be always less than the noninverting input of U3, so doesn't U3 behaves like an inverting amplifier at all times ? What am I missing here?
- if I understand correctly, R9 is used to substract a constant value from U3's output, by reducing the current in R6 by a constant amount. What's the point of doing that?
- I think R13 is here to give positive feedback/hysteresis for the internal comparator of the µPC1701 triac driver, is that correct ?

Thank you!

Credits (and thank you) to EEVBlog member "saturation" for the schematic.  

Notes:
- VR2 is 0 to 300 ohms
- Rsensor is around 40-50 ohms at room temperature (according to user manual) and can go up to around 140-150 ohms when hot (according to this post)
- µPC1701 datasheet is attached for anyone curious
- partial (about one half of it) LTSpice schematic attached if anyone wants to play with component values