thank you,bradtherad and fvm,thanks for your replying
there is no schematic,i just model the converter with simulink,and i do both the bode plot and step response with simulink.the converter is synchronous with constant frequency clock turning on the power switch. the figures of the converter are: VI=12V;VO=5V;fs=100kHz;L=16uH;C=540uF;RO=0.5ohm;Vp=2V(Vp is the peak value of the sawtooth)
the following are my steps to derive the transfer function:
1,divide the converter into three part:LC filter,modulator and compensator
2,the transfer function of LC filter is (1/LC)/(s^2+s/RC+1/LC)
3,the transfer function of the modulator is VI/Vp;
4,use type3 compensator for the compensation(as figure"compen" shows)
5,i set a zero in the type3 compensator at the the crossover frequency of the converter to get a phrase margin higher than 45.
figure "loop gain" and "feedback loop" show how the bode plot is from and how the step response is from respectively.