clear all
clc
close all

% define the plant to be controlled
s=tf('s');
P=1/s/(s+1);

% or using tf function
P1=tf(1,[1 1 0]);

%% requirments
% - error null in the case of step disturbance -->  open loop function 
%  with one integrator (pole in the origin) 
% - s% <= 15% (phase_margin >= 50°)
% - ta5% <= 300 ms (w_c >= 20 rad/s)
% - Ts = 30 ms (delay at w_c, in terms of phase, about  -wc*Ts/2=-17°)

% define the sampling time
Ts=0.03;

% the sampling angular frequency
w_s=2*pi/Ts;

% define the open-loop function
C=1;
F=C*P; 

% evaluate the margins
figure,
margin(F)
grid on

% define C1 in order to get w_c=20 rad/s: need an increase of the magnitude
% of F1 in w_c of about 50dB and of the phase of F1 in w_c equal to 50+17 degrees (the latter taking 
% into account the delay introduced by ZOH)
C1=20*(s+1)/(s/50+1); % add a zero in -1 and a pole at high frequency (-50) for realizable devise
F1=C1*P;

figure
margin(F1)
grid on

% discret equivalent tf by using Tustin
D1=c2d(C1,Ts,'tustin');

% anti-aliasing filter - a pole at frequency w_f such that w_f<w_s/2 and
% w_f>>w_c
w_f=w_s/2.1;
Fa=1/(s/w_f+1);

% open the schemes (analog, digital and digital with anti-aliasing filter) implemented in Simulink 
feedback_control_scheme_analog_vs_digital