"I tried driving the iron using 24 battery DC voltage, the comparator circuit shown above and an N-channeled mosfet with much success. The tricky part is the AC."
AC, I thought you were using DC???
Did you carefully check with a scope/DVM for ground loops or noise pickup adding noise/offset to your control loop?
Was your PID code oscillating?
The idea of my using PWM is to have just proportional control, not full PID, once the tip temp error output was near the correct value, a slow integral term was fine to keep the temp to a small delta degree C value, but otherwise from questimating the temperature of the tip from determining the exact point that a small wire sample of solder melts and then my visual estimation of viscosity of the fluid solder once melted, and experiencing it work great in actual use, I have no way to actually measure the instantaneous soldering iron tip temp when used in situ, say on a 4-layer circuit board, just my MCU's idea of the temperature on my digital LED panel readout based on the thermistor's resistance.
However it works much better than the orig controller built into the soldering station, esp. because of the faster response time. I had (with the orig. 40W AC- triac-transformer circuit) great difficulty to unsolder components from a 4 or 6-layer PC motherboard, it took ages! Not enough power.
Why two supplies, someone asked, ans: to make sure I have enough current when the iron is cold plus a little reserve and they were both free and on hand.
I don't have an accurate schematic on my PC of my breadboarded control circuit tried using a just a 339 comparator and lm358 op-amp by themselves, but it worked well although there was no way to calibrate the temperature adj. so I always had to guess what temperature I was dialing in with the pot.
So I switched over to develop a MCU circuit soon into this endeavor because it gave the use of PWM, A2D to use as temperature input directly from the thermistor, ability to have accurate thermistor temperature by resistance because of imbedded known thermistor resistance values to interpolate with(from thermistor mfg's accurate resistance v. temp charts), and also the ability to add a digital readout not originally on the cheap soldering station, plus the software approach replaces the comparator and allows me to create a proportional control PWM scheme to reach the temperature and a dithering integral PWM term to control the tip temp around the goal temperature.
As far as the switching regulator's ability to limit the mV's of noise to 2 mV an the tip, I could would not give a solder whisker's damn about that. The switcher output is very clean, anyway. There is some myth that SMPS power supplies always have to be noisey at their output. The truth is that it is so easy to filter their output noise which is high frequency stuff, so only small valued choke and a small valued cap at the output creates a very quiet output.
Because of PWM, there are no fast on/off surges of power that can create noise, just a MCU's casual drift towards applying the right power to get the right temperature.