The problem is, that we have only little information from you!
Let me tell you my thoughts:

1. Using a separate winding to gain information for controlling is not a good idea, because non ideal characteristics of transformer will give you different results for the two windings. Think of different saturation effects and different magnetic couplings, different source impedances and different loads at the two windings. If you want to control the duty cycle by looking at an output voltage of transfomer, then you must do this at the secondary winding for the main load.

2. In order to keep a lamp constantly bright you need to control for equal drawn energy per 50Hz period. Means you need contant W = Integral(P x dt) = Integral(U x I x dt) = 1/R x Integral(U^2 x dt), where each integral is over a 50Hz period.

But again there are some problems:

a. Lamp loads are non linear, means R depends on actual voltage dropping across them and depends on duration of being applied. So, you cannot expect R to be constant in this equation.

b. Human eye isn't linear with W. How bright a lamp appears also depends on maximum voltage dropping across it and duty cycle.

3. It makes no sense to provide a fast controlling, in order to derive a feedback value for each 50Hz period. Time constant of controlling must at least be greater than the thermal time constant of your lamp, which is many many 50Hz periods. If you control faster, then due to the non linear characteristic of lamp and transformer you will result in very fast fluctuations and oscillations of brightness of lamp, with the consequence of repeatedly exceeding the rated maximum power of lamp and resulting in early damage of lamp.

4. Life time of lamp is mainly influenced by peak power than average power. Using a duty cycle control means that lamp will experience unsane peak power, which will heavily shorten life time of lamp!

Kai