Is there a way to compensate for the drop of voltage?
What is your desired AC range ?
The simplest passive circuit is a bridge, or even a single diode.
You can correct for the diode using a offset table, or custom scale, or just do a best-fit for your range.
You can buy a better diode, to help a little. eg Schottky diodes have lower drops.
You need to consider your DC voltmeter input impedance, and your AC source impedance.
Schottky diodes have lower drops, but somewhat trade off VR,VF, IR and vary with temperature.
A bridge design means there is a path for leakage currents, so you could experiment with varying diodes and graph VDC vs your AC range.
Higher current diodes have lower VF, but also higher leakage currents.
I would like to ask if the Vdc resulted from the precision rectifier would be the exact same as Vrms, and is it ok if the DC output was pulsating or does it need smoothing.
No.
VRMS means what the letters say - it is the
root of the mean of the squares.That matters if the waveform is not sine.
Who has specified RMS and why ?
Voltage waveforms are usually close to sine than current waveforms, so you may get away with a 'best guess' ratio.
How about using precision rectifier?
I have -15V and 15V power sources on the panel, perhaps I can use opamp like AD822, by summing these supplies to get 30V supply.
Yes, if you have addition power and parts, then you can add smarts to reduce errors.
You can even use better RMS to DC ICs, if that RMS matters.