Hello again,
It is hard to tell what is the output and what is the input in that 'scope' drawing because the waves are superimposed on each other. It would also be a good idea to show what the input is, and what the output voltages are and times.
Also, even if it does appear to work that doesnt mean that will work using real op amps anyway. That's because many op amps do not like to be driven from open loop back into closed loop again without a significant delay. This is one of those op amp aspects that you NEVER see talked about on web sites. What this means is that it may not work at all or it just might introduce some distortion. In any case, real life testing would be mandatory before settling on a particular design.
But assuming it does work or it can be modified slightly to get it to work, how does he intend to filter the output? With the op amp driving the output directly an inductor and capacitor would probably be needed to filter it into DC, rather than just the usual capacitor.
Just for reference, here is some scaled time data assuming the op amps were perfectly compliant:
[Vin is 1 volt peak]
-- Results with first op amp gain adjusted:
-- ...time..........Vo1.........Vout...
-- 0.050000 0.370820 0.463525
-- 0.100000 0.705342 0.881677
-- 0.150000 0.970820 1.213525
-- 0.200000 1.141267 1.426584
-- 0.250000 1.200000 1.500000 (first peak output)
-- 0.300000 1.141268 1.426586
-- 0.350000 0.970822 1.213527
-- 0.400000 0.705344 0.881680
-- 0.450000 0.370823 0.463529
-- 0.500000 0.000003 0.000004 (zero output)
-- 0.550000 0.000000 0.463521
-- 0.600000 0.000000 0.881674
-- 0.650000 0.000000 1.213522
-- 0.700000 0.000000 1.426583
-- 0.750000 0.000000 1.500000 (second peak output)
-- 0.800000 0.000000 1.426587
-- 0.850000 0.000000 1.213529
-- 0.900000 0.000000 0.881684
-- 0.950000 0.000000 0.463533
-- 1.000000 0.000000 0.000008 (zero output)
-- 1.050000 0.370814 0.463518