Some sort of an inverter

Sooo, you made an inverter that is basically a class-D amplifier with a 60Hz signal to control the output and a 5kHz PWM frequency? From what little I’ve messed around with class-Ds I’m generally unable to make negative feedback due to the high delay between input and output unless I skip the sawtooth signal altogether and have the high/low of the peaks be controlled directly by whether the output is higher or lower than the desired signal, but it can be tricky making it limited to a stable frequency like 5kHz instead of it going higher and higher until the simulation stops doing PWM altogether and uses the H-bridge as an analog amplifier.

http://everycircuit.com/circuit/6190109595271168

I was thinking something along the line of rectifying and integrating the output and then comparing it to a reference voltage. After that we can use the error voltage to drive the PWM somehow. The major problem I'm facing is how to use the error voltage to gradually increase or decrease the amplitude of the 50Hz voltage source. That's how we can change the depth of the PWM and the output voltage respectively.

Hmm, that could work. But it has a slower response than my design and would be more complicated, but has the potential for an output with a lower amount of high frequency harmonics. You could also use an AM modulator style design for modifying the amplitude of the 60Hz signal, where the 60Hz is the carrier and the feedback modulates its amplitude.

Yes, it is too slow, already tried it. I got this - not the best solution, but it keeps the output somewhat stable between 50W and 100W loads. http://everycircuit.com/circuit/4737798616383488

Fact is - simple inverters with feedback don't exist. Especially if you want pure sinewave.

I messed around with your circuit, and I noticed that in your feedback section you added an op-amp that had a lot of negative feedback. This made it so that high loads still reduce the voltage significantly. If you reduce the negative feedback (instead of a 1:1 ratio of the two resistors, I made it 100:1 to still stabilize it but still remove most of the feedback) and decrease the 50Hz voltage source to 325mV (to aim for the inverter to get 325V) it seems to function much better in my opinion as heavy loading drops the voltage very little. In fact, you could make it something like 350mV so that unloaded, it produces a little too much voltage, and while loaded it produces just the right amount of voltage.

It's way better this way. Good tolerance up to maybe 250-300W, after which it goes outside the pwm range.

I see you changed the circuit you gave a link to to match my description of the changes, but it doesn’t behave the same way it did when I made the modifications originally and I can’t find the difference. I wonder why.

I changed the VCVS with a step down transformer. It still gives galvanic separation, and works with AC.