cflab6

close all
T1 = 3;
T2 = 0.5;
T3=2;
k = 3;
kr=4.86; %4.86 crit, 2.43 for P controller
kcrit=4.86;
kP=0.5*kr;
kPI=0.45*kr;
kPID=0.6*kr;
Tosc=34.18;
TiPI=0.85*Tosc;
TiPID=0.5*Tosc;
Td=0.125*Tosc;

Ti = [0.85*Tosc 0.5*Tosc];
Td = 0.125*Tosc;
kc = [0.5*kcrit 0.45*kcrit 0.6*kcrit];

s=tf('s');
K=(kr*k)/((1+3*s)*(1+0.5*s)*(1+2*s)); %plant
Kcl=K/(1+K); %cls plant
Kunc=(k)/((1+3*s)*(1+0.5*s)*(1+2*s)); %uncompensated system
Kucl=Kunc/(1+Kunc); %cls uncomp
KuAT=1/(1+Kunc);
Kr= [kc(1) kc(2)*(1 + 1/(s*Ti(1))) kc(3)*(1 + Td*s + 1/(s*Ti(2)) )];
Kcont = k*Kr/((1+s*T1)*(1+s*T2)*(1+s*T3));
for i = 1:3
    Kcontcl(i) = Kcont(i)/(1 + Kcont(i));
    KcontAT(i)=1/(1 + Kcont(i));
end

P = bodeoptions('cstprefs');
P.FreqScale = 'linear';
P.MagUnits = 'abs';
P.MagScale = 'linear';

N = nyquistoptions('cstprefs');
N.ShowFullContour = 'off';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% PART A %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%TASK 2
figure(1)
nyquist(Kcont(1),N);
title('Nyquist diagram for system with P controller')
%TASK 3
[Gm1,Pm1,Wgm1,Wpm1] = margin(Kcontcl(1))
%TASK 4
figure(2)
bodemag(KcontAT(1),P)
hold on
bodemag(Kucl,P)
axis([0 6 0 3.5])
title('attenuation index for system with P controller')
legend('with P controller','without controller','Location','northeast');
%TASK 5
figure(3)
bodemag(Kcontcl(1),P)
hold on
bodemag(KuAT,P)
axis([0 6 0 3])
title('tracking index for system with P controller')
legend('with P controller','without controller','Location','northeast');
%TASK 6
figure(4)
step(Kcontcl(1))
hold on
step(Kucl)
title('step responses of system with and without P controller')
legend('with P controller','without controller','Location','northeast');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% PART B %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%TASK 2
figure(5)
nyquist(Kcont(2),N);
title('Nyquist diagram for system with PI controller')
%TASK 3
[Gm2,Pm2,Wgm2,Wpm2] = margin(Kcontcl(1))
%TASK 4
figure(6)
bodemag(KcontAT(2),P)
hold on
bodemag(Kucl,P)
axis([0 6 0 3.5])
title('attenuation index for system with PI controller')
legend('with PI controller','without controller','Location','northeast');
%TASK 5
figure(7)
bodemag(Kcontcl(2),P)
hold on
bodemag(KuAT,P)
axis([0 6 0 3])
title('tracking index for system with PI controller')
legend('with PI controller','without controller','Location','northeast');
%TASK 6
figure(8)
step(Kcontcl(2))
hold on
step(Kucl)
axis([0 60 0 1.45])
title('step responses of system with and without PI controller')
legend('with PI controller','without controller','Location','northeast');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% PART C %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%TASK 2
figure(9)
nyquist(Kcont(3),N);
title('Nyquist diagram for system with PID controller')
%TASK 3
[Gm3,Pm3,Wgm3,Wpm3] = margin(Kcontcl(3))
%TASK 4
figure(10)
bodemag(KcontAT(3),P)
hold on
bodemag(Kucl,P)
axis([0 20 0 2])
title('attenuation index for system with PID controller')
legend('with PID controller','without controller','Location','northeast');
%TASK 5
figure(11)
bodemag(Kcontcl(3),P)
hold on
bodemag(KuAT,P)
axis([0 20 0 2])
title('tracking index for system with PID controller')
legend('with PID controller','without controller','Location','northeast');
%TASK 6
figure(12)
step(Kcontcl(3))
hold on
step(Kucl)
axis([0 30 0 1.2])
title('step responses of system with and without PID controller')
legend('with PID controller','without controller','Location','northeast');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% PART D %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(13)
nyquist(Kcont(1),N);
hold on
nyquist(Kcont(2),N);
nyquist(Kcont(3),N);
nyquist(Kunc,N);
axis([-1.63 7.44 -13.4 10])
title('Nyquist diagrams')
legend('with P controller','with PI controller','with PID controller','without controller','Location','northeast');

figure(14)
bodemag(KcontAT(1),P)
hold on
bodemag(KcontAT(2),P)
bodemag(KcontAT(3),P)
bodemag(KuAT,P)
axis([0 20 0 3.5])
title('Attenuation indices')
legend('with P controller','with PI controller','with PID controller','without controller','Location','northeast');


figure(15)
bodemag(Kcontcl(1),P)
hold on
bodemag(Kcontcl(2),P)
bodemag(Kcontcl(3),P)
bodemag(Kucl,P)
axis([0 10 0 3])
title('Tracking indices')
legend('with P controller','with PI controller','with PID controller','without controller','Location','northeast');

figure(16)
step(Kcontcl(1))
hold on
step(Kcontcl(2))
step(Kcontcl(3))
step(Kucl)
axis([0 30 0 1.45])
title('Step responses')
legend('with P controller','with PI controller','with PID controller','without controller','Location','northeast');