Transfer function for six-pulse controlled rectifier
Assuming when you say transfer function you are not referring to an S-domain "transfer function" for the behaviour (as this is actually really hard and relies on alot of heaviside functions) but more of a relationship of input to output.

ASUMMUMING the supply is an ideal supply with each voltage sources being 120degree's separated and their amplitudes &amp; freq are all the same and that there is no supply feeder impedance

With the firing angle = 0 and thus the SCR's act like diodes, we know that:

Vd = \$\frac{3\sqrt{2}}{\pi}V_L\$

Where Vd = DClink voltage and \$V_L\$ = the Line-Line (rms) voltage from the supply

We want to know what Vd is with regards to some arbitary firing angle \$\alpha\$

\$V_\alpha = Vd - \frac{A_\alpha}{\pi/3} \$

\$A_\alpha\$ is the volts-second area that occurs every 60degrees which reduces the average DClink.

We know that:
\$V_a = \sqrt{2} V_L Sin(\omega t)\$

Thus

\$A_\alpha = \int\limits_0^\alpha \sqrt{2}V_LSin(\omega t) d(\omega t) \$

\$ = \sqrt{2}V_L(1-cos\alpha)\$

Thus 

\$ V_\alpha = \frac{3\sqrt{2}}{\pi} V_Lcos\alpha \$