Analog Multiplier with MOSFET – Implementation not working

The Vth of a NMOS is the Vgs at which it operate until (ie. so long as Vgs > Vth it will continue to conduct).

As you have stated this Vth is 1.0V. Initially when the switch is closed the NMOSes will turn on as the voltage at their respective sources will be zero and the voltage at the gates will be 2.5 - this is well above the Vth that you mentioned of 1.0V. As the capacitor charges through these NMOSes which are now more or less making short circuit the voltage at the source is increasing and it will continue to do this until it reaches 1.5V at which point the Vgs will start to go below 1.0V thus making the NMOS transistors turn off.

The fact that there are two of them doesn't really make any difference, there could be 1 or 10 and it would have the same result.

The mistake you made by thinking it will only charge to 0.5V is that the voltage drop is not from the drain - source so there would not be two drops, it si only to do with the potential between the gate and source and as explained once this goes below 1.0V the transistor turns off.

As others have said you may get an unstable situation so, temporarily forget about the multiplier and check to see that you can control the voltage output of the power supply based on voltage feedback directly to the op-amp. Use your pot to check that you can control it across the levels you might need with the load resistances you might use.

For a simple and fairly accurate multiplier you could turn the current feedback signal into a PWM signal - duty cycle proportional to output current. Then, use the PWM signal and a couple of analogue switches to chop up the voltage feedback signal. Use a filter on the output to give you a dc value proportional to power. Try and use a fairly high PWM frequency so that the extra low pass filter can run at tens of kHz.

Linear tech make the LTC6992 that would suit your needs: -

It takes a dc input voltage (aka current reference) and converts it to a duty cycle of up to 1 MHz frequency. Here's the idea applied to a triangle wave and note that this is a 4 quadrant multiplier but who cares - it operates in the first quadrant just as well as the other three: -

If the duty cycle were more like 99% the resulting red triangle wave would be much fuller in amplitude and just fractionally less than the original triangle wave.

Finally the block diagram would look like this: -