Transfer Function of a boost converter

Hello everyone,

I designed a boost converter, which allows a user to set his desired output voltage and PID gains. The circuit was finished already, and from an oscilloscope, I can see how well-set PID gains eliminate output's steady state error, oscillation and provide a quicker response.

However, the only thing that I don't know is the converter transfer function (an output voltage to switching device's duty cycle). The reason is that the second way of Ziegler-Nichols methods doesn't require a transfer function. It says that we have to set Ki and Kd to zero, then , increase a proportional gain til the output oscillates, lastly, obtain the value of the proportional gain and a period of oscillating output to calculate the best fit PID gains. Lacking the knowledge of its transfer function, I won't be able to show how my circuit works on MATLAB Simulink. (I need the TRF to tell the simulink that I'm working on a boost converter).

Later on, I've found this paper on IEEE: https://www.mediafire.com/?p5a6cyjng6fgk1d. However, it shows me only the TRF in low frequencies (<10kHz).

My question is "Is there any paper presenting a transfer function (Vout/DutyCycle) of a boost converter in high frequency (125kHz)?"

Thank you

PS. I looked in IEEE for many times, but found nothing that match what I want exactly. Perhaps, I don't know some keywords to get it.