%{
ELEC-E8116 Model-based Control Systems
Exercise 6
%}

clearvars;
close all;
clc;

%% 2. 
k = [2, 2.5, 3];
tau = [2, 2.5, 3];
theta = [2, 2.5, 3];

T = 4;
dG1 = tf([T, 0.2],[(T/2.4) , 1])

dG2 = dG1 *  tf([1, 1.6, 1],[1, 1.4 , 1]);

figure(1);clf;
for ii = 1:3
    for jj = 1:3
        for kk = 1:3
       
            Gp = tf(k(ii),[tau(jj), 1], 'InputDelay', theta(kk));
            G = tf(k(ii),[tau(jj), 1]);
            lI = (Gp-G)/G;

            bodemag(lI, 'b:')
            hold on;
        end
    end
end

bodemag(dG1, 'k-');
bodemag(dG2, 'r--');
yline(1);
% ylim([-10, 10]);
legend('Gp: dotted', 'dG1: solid', 'dG2: dashed');
%% 3. 

% process
G = tf([-6, 3],[50, 15, 1]);
% G = 3*tf([-2 1],conv([5 1],[10 1]))

% controller 
s= tf('s');
% K = 1.136;
K = 0.31;
Ti=12.7;
Gc = K*(1+(1/(Ti*s)));

% loop transfer function
L=G*Gc; 

% sensitivity function
S=1/(1+L); 
% complementary sensitivity function T = ((1+L)^(-1))*L
T=1-S; 

dG = tf([10, 0.33],[(10/5.25), 1]);

w =  logspace(-2,1);

figure(2); clf;
bodemag(T,w,'b-');
hold on;
bodemag(1/dG, w, 'r--')
grid on;