How to find the closed loop transfer function of the LT1619 current mode controller
What you want is the open-loop transfer function of this boost converter to think about a possible compensation strategy. The closed-loop transfer function is really when the converter operates with the loop physically closed and you can't measure it with a switching converter (you can reconstruct it). Why? Because this is a control system fighting perturbation like \$I_{out}\$ or \$V_{in}\$ while the setpoint (or the input) is \$V_{ref}\$ but is fixed inside the IC. So the true closed-loop transfer function would be that linking \$V_{out}\$ to \$V_{ref}\$ but nobody does that. See the small sketch below:



The plant is your boost converter power stage and the left-side triangle is the error amplifier. You clearly see how the perturbations via their open-loop coefficients affect the output. By closing the loop, you will reduced their contribution by \$\frac{1}{1+T(s)}\$ in which \$T(s)\$ is the loop gain: \$T(s)=G(s)H(s)\$. \$G(s)\$ represents the compensator transfer function (that you shape via the elements connected to your pin 3) while \$H(s)\$ represents the power stage dynamic response you need to determine before attempting to compensate.

How can you determine that power stage response? This is good because it is the subject of my next APEC 2018 seminar : )


Use a small-signal transfer function obtained from the literature. Capture it in a mathematical solver and get the Bode plot. A good source for the transfer function is here.
Build you hardware prototype using the LT part and extract the power stage response. It can be tricky here but as pin 3 is an OTA output, I believe (to be confirmed) that you can override it with a dc+ac source and plot \$V_{out}\$ to \$V_c\$. If not:
Use a SPICE model to extract the dynamic response of the boost converter. You can use LTspice and apply the PWM-CM model to obtain the power stage and then further enrich the schematic with an OTA to compensate your loop:




You will find the model in my page and all the calculations around the OTA compensation in a seminar I gave in 2010. You must add parasitics such as the output capacitor ESR \$r_C\$ and the inductor ESR \$r_L\$ to show their effect on the response. Basically, you're all set!