%{
ELEC-E8116 Model-based Control Systems
Exercise 5
%}

clearvars;
close all;
clc;

%% 1.

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

% controller 
Gc = tf([14.427, 1], [12.7 0]);

% loop transfer function
L=G*Gc; 

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

w =  logspace(-2,1);
figure(1); clf;
bode(L,S,T,w) 
grid on;
legend;

[Gm, Pm, wcg, wcp] = margin(L)

%{
Bandwidth can be defined in several ways: 
- heuristically it means the frequency range, in which control is efficient.

- Sometimes the gain crossover frequency is used as the 
bandwidth, sometimes it is the frequency, at which the sensitivity function S first time 
crosses (1/sqrt(2)) = 0.707 (-3 dB) from below. 

- Perhaps the most common definition is that frequency, for 
which the complementary sensitivity function T crosses first time 
that value –3dB from above. 
%}
[mag,phase]=bode(T,w);
figure(2); clf;
bode(T,w);
grid on;

%% 3. 
Qmax = 2000; % [W]
Tmax = 1; % [K]
T0max = 10; % [K]
a = 100; % [W/K]
Cv = 100e3; % [J/K]
tau = Cv/a; % [s]

G = (Qmax/Tmax)*(1/a)*tf(1,[tau, 1]) 

Gd = (T0max/Tmax)*tf(1,[tau, 1]) 

figure(3);clf;
bode(G, Gd)
grid on;
legend;