Why this inverter is used in the PWM circuit?
Let's call the input of the delay line D. The inputs of the NAND A (upper one) and B (lower one). The output of the NAND is called Q.

Start: D=1, A=1, B=0, Q=1

Then we change: D->0 then B->1 and therefore Q->0
After D propagates through the delay line: B->0 and therefore Q->1.

So we get a short zero pulse, having the length of the delay given by the delay line.

It's basically this circuit, the important thing is the delay: