True RMS and Duty cycle calculation

[rrn]

Can someone help with calculating modified sine wave true RMS value and also how to Control PWM dutycycle to maintain fixed output.
Example: input volatge 100Vdc.
Need to maintain fixed Vrms 50VAC
Frequency = 50hz
Modified sine wave same as in the picture

[gcewing]

For PWM with duty cycle d,

Vrms = sqrt(d * Vin**2) = sqrt(d) * Vin

so

sqrt(d) = Vrms / Vin

or

d = (Vrms / Vin) ** 2

So for Vin = 100V and Vrms = 50V, you want d = 1/4.

The frequency doesn't come into it.