Type 3 Error Compensator design adaptation from Type 2

My professor has given the following code for designing a Type 2 controller

Vs = 10;
fsw = 100e3;%switching frequency
L = 100e-6;
C = 100e-6;
R = 5;
Vp = 3;%PWM peak voltage
rC = 0.5;
%% given crossover frequency, fc
fco = 10e3;
wco = 2*pi*fco;
%% PWM TF
Gpwm = 1/Vp;
Gpwm_gain_in_dB = 20*log10(Gpwm)
%% Buck TF
[num,den] = tfdata(((1/(L*C))*(1+s*rC*C)) / (s^2+(1/(R*C) + (rC/L))*s+1/(L*C)))
Gf = tf(num,den);
figure()
bode(Gf)
[mag_Gf,phase_Gf,wout] = bode(Gf,wco)
mag_Gf_in_dB = 20*log10(mag_Gf)
phase_Gf
%% Finding the open Loop gain w/o controller, GM, PM
Gsw = Vs;
Gol = Gpwm * Gsw * Gf;
figure()
bode(Gol)
title('Gol')
[mag_Gol,phase_Gol] = bode(Gol,wco);
mag_Gol_in_dB = 20*log10(mag_Gol)
phase_Gol
%% Finding required gain and phase of Controller to satisfy PM of between 45 and 60
degree.
% The required gain of the compensated error amplifier = mag_Gol_in_dB + 20log(1/Vp)
CombinedGain = mag_Gol_in_dB 
% The phase angle of the compensated error amplifier at the crossover frequency to 
% satisfy given PM of 60 degree:
% = PM - (phase_Gol)
PM = 60;
ContPhase = PM - phase_Gf
%% Type 2 controller
R1 = 1e3
R2 = 10^(-CombinedGain/20)*R1
K = tand(ContPhase/2)
C1 = K / (2*pi*fco*R2)
C2 = 1 / (K*2*pi*fco*R2)
%% Error Amplifier Bode plot: PPT7, p43
TF_Vc_over_Vo = (1+(s*R2*C1)) / ((s^2*C1*C2*R2)+(s*(C1+C2))) / R1
wz = 1/(R2*C1)
wp = (C1+C2) / (C1*C2*R2)
figure()
bode(TF_Vc_over_Vo)
[mag_wz,phase_wz] = bode(TF_Vc_over_Vo,wz)
mag_wz_in_dB = 20*log10(mag_wz)
phase_wz
[mag_wp,phase_wp] = bode(TF_Vc_over_Vo,wp)
mag_wp_in_dB = 20*log10(mag_wp)
phase_wp
%% TF of Type 2 controller
[num,den] = tfdata((s+(1/(R2*C1)))/(R1*C2*s*(s+(1/(R2*C2))))); %(7-71)
ContTF = tf(num,den);
figure()
bode(ContTF)
[mag_ContTF,phase_ContTF] = bode(ContTF,wco);
mag_ContTF_in_dB = 20*log10(mag_ContTF)
phase_ContTF
[mag_ContTF_wz,phase_ContTF_wz] = bode(ContTF,wz)
mag_ContTF_wz_in_dB = 20*log10(mag_ContTF_wz)
phase_ContTF_wz 

[mag_ContTF_wp,phase_ContTF_wp] = bode(ContTF,wp)
mag_ContTF_wp_in_dB = 20*log10(mag_ContTF_wp)
phase_ContTF_wp
figure()
bode(Gol*ContTF)
[GM,PM] = margin(Gol*ContTF)
%% Verification: Input is Vref, Output is Vout
step(5*Gol*ContTF / (1+Gol*ContTF)

I need to adapt it to a Type 3 controller, using the equations for the R and C values from the textbook

How would i change the code that i have to design a Type 3 error compensator