Control to output transfer function

I am trying to derive control to output transfer function of phase shift full bridge converter.

Applying small signal analysis, I reach to the point/schematic as shown in the picture below:

Document calculated the control to output transfer fucntion as shown in the picture below. When I equate vin = 0 V, both sides of the transformer becomes short, so it turns out to point as shown in the picture below. But here there are 2 dependent and 2 independent source. I dont know how to deal with 4 source. Generally if I had 2 source, I was making superposition technique. How should I proceed with 4 source?

Source: https://www.researchgate.net/publication/3279135_Small-signal_analysis_of_the_phase-shifted_PWM_converter

Considering my above question, control to output transfer function given in the picture below. I think they both connected to each other. I think first I need to understand my above question, than I can derive the transfer function as stated in the picture below. But here I couldn't understand the Zf/ (Zf+Rd). How should I come to that point?

Source: https://www.researchgate.net/publication/3279135_Small-signal_analysis_of_the_phase-shifted_PWM_converter

By the way, dv and di are given as below. These are just equations derived for the small signal model. Ho is also given below I have no question about dv, di or Ho. I just put them to show what are they.

Source: https://www.researchgate.net/publication/3279135_Small-signal_analysis_of_the_phase-shifted_PWM_converter