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Christos Choutouridis 2025-10-23 01:20:41 +03:00
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# Generic directories
Inbox/

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[submodule "Work 1/report/AUThReport"]
path = Work 1/report/AUThReport
url = ssh://git@git.hoo2.net:222/hoo2/AUThReport.git

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# LaTeX auxiliary files
*.aux
*.log
*.out
*.synctex.gz

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Subproject commit 74ec4b5f6c66382e5f1b6d2e6930897e4ed53ea6

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%
% !TEX TS-program = xelatex
% !TEX encoding = UTF-8 Unicode
% !TEX spellcheck = el-GR
%
% AUTH report template
%
% Requires compilation with pdfLaTeX or XeLaTeX
%
% authors:
% Χρήστος Χουτουρίδης ΑΕΜ 8997
% cchoutou@ece.auth.gr
% Options:
%
% 1) mainlang=<language>
% Default: english
% Set the default language of the document which affects hyphenations,
% localization (section, dates, etc...)
%
% example: \documentclass[mainlang=greek]{AUThReport}
%
% 2) <language>
% Add hyphenation and typesetting support for other languages
% Currently supports: english, greek, german, frenc
%
% example: \documentclass[english, greek]{AUThReport}
%
% 3) short: Requests a shorter title for the document
% Default: no short
%
% example: \documentclass[short]{AUThReport}
%
\documentclass[a4paper, 11pt, mainlang=greek, english]{AUThReport/AUThReport}
\CurrentDate{\today}
% Greek report document setup suggestions
%---------------------------------
% \WorkGroup{Ομάδα Χ}
\AuthorName{Χρήστος Χουτουρίδης}
\AuthorAEM{8997}
\AuthorMail{cchoutou@ece.auth.gr}
%\CoAuthorName{Όνομα Επίθετο}
%\CoAuthorAEM{1234}
%\CoAuthorMail{xxx@ece.auth.gr}
\DocTitle{Εργασία στα Ασαφή Συστήματα}
\DocSubTitle{Έλεγχος γωνίας προσανατολισμού δορυφόρου με ασαφείς ελεγκτές}
\Department{Τμήμα ΗΜΜΥ. Τομέας Ηλεκτρονικής}
\ClassName{Ασαφή Συστήματα (Υπολογιστική Νοημοσύνη)}
\InstructorName{Θεοχάρης Ιωάννης}
\InstructorMail{theochar@ece.auth.gr}
\CoInstructorName{Χαδουλός Χρήστος}
\CoInstructorMail{christgc@auth.gr}
\usepackage{float}
\usepackage{minted}
\usepackage{xcolor} %
\setminted[cpp]{
fontsize=\small,
breaklines,
autogobble,
baselinestretch=1.1,
tabsize=2,
numbersep=8pt,
gobble=0
}
\newcommand{\repo}{https://git.hoo2.net/hoo2/PDS/src/branch/master/homework_3}
\begin{document}
% Request a title page or header
\InsertTitle
%\InsertTitle[img/background.png][0.8\textwidth][2cm]
\section{Εισαγωγή}
Η παρούσα εργασία αποτελεί
\subsection{Παραδοτέα}
Τα παραδοτέα της εργασίας αποτελούνται από:
\begin{itemize}
\item Την παρούσα αναφορά.
\item Το \href{\hwThree}{σύνδεσμο με το αποθετήριο} που περιέχει τον κώδικα για την παραγωγή των εκτελέσιμων και της αναφοράς.
\end{itemize}
\end{document}

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function fis = mkFIS()
%mkFIS makes FIS
% FIS control
% R2025 compatibility:
% - newfis->mamfis
% - defuzzMethod='cos' -> AggregationMethod="sum", DefuzzificationMethod="centroid"
fis = mamfis( ...
AndMethod="min", ...
OrMethod="max", ...
ImplicationMethod="min", ...
AggregationMethod="sum", ...
DefuzzificationMethod="centroid" );
% Member functions
mf.Names = ["NV"; "NL"; "NM"; "NS"; "ZR"; "PS"; "PM"; "PL"; "PV"];
mf.Edges = [ ...
[-1.25 -1 -0.75]; ... % NV
[-1 -0.75 -0.5 ]; ... % NL
[-0.75 -0.5 -0.25]; ... % NM
[-0.5 -0.25 0 ]; ... % NS
[-0.25 0 0.25]; ... % ZR
[ 0 0.25 0.5 ]; ... % PS
[ 0.25 0.5 0.75]; ... % PM
[ 0.5 0.75 1 ]; ... % PL
[ 0.75 1 1.25]; ... % PV
];
% Setup input/output
fis = addInput(fis, [-1 1], Name="e");
fis = addInput(fis, [-1 1], Name="de");
fis = addOutput(fis, [-1 1], Name="du");
for k=1:length(mf.Names)
fis = addMF(fis, "e", "trimf", mf.Edges(k, :), Name=mf.Names(k));
fis = addMF(fis, "de", "trimf", mf.Edges(k, :), Name=mf.Names(k));
fis = addMF(fis, "du", "trimf", mf.Edges(k, :), Name=mf.Names(k));
end
% Rules 9x9
% rows = e (NV..PV), cols = de (NV..PV)
ruleTable = [
% de: NV NL NM NS ZR PS PM PL PV
"NV","NV","NV","NV","NV","NL","NM","NS","ZR"; % e = NV
"NV","NV","NV","NV","NL","NM","NS","ZR","PS"; % e = NL
"NV","NV","NV","NL","NM","NS","ZR","PS","PM"; % e = NM
"NV","NV","NL","NM","NS","ZR","PS","PM","PL"; % e = NS
"NV","NL","NM","NS","ZR","PS","PM","PL","PV"; % e = ZR
"NL","NM","NS","ZR","PS","PM","PL","PV","PV"; % e = PS
"NM","NS","ZR","PS","PM","PL","PV","PV","PV"; % e = PM
"NS","ZR","PS","PM","PL","PV","PV","PV","PV"; % e = PL
"ZR","PS","PM","PL","PV","PV","PV","PV","PV" % e = PV
];
for i=1:length(mf.Names)
for j=1:length(mf.Names)
rule = "IF e IS "+mf.Names(i)+" AND de IS "+mf.Names(j)+" THEN du IS "+ruleTable(i,j);
fis = addRule(fis, rule);
end
end
end

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function u = satFZ_PI(fis, e, Ke, Kde, Kdu, Ts)
%SATFZ_PI Calculate the output of the controller
% Must be called every Ts
%
% Output:
% u: Output
% Inputs:
% fis: FIS to use
% e: error
% Ke: error gain
% Kde: error derivative gain = a*Ke
% Kdu: du gain
% Ts: Sampling period
persistent prev_e;
persistent prev_u;
if isempty(prev_e) % first call
prev_e = 0;
prev_u = 0;
end
% Saturation between min: m and max: M
sat = @(x, m, M) max(m, min(M, x));
% calculate error diff
de = (e - prev_e)/Ts;
prev_e = e;
% Normalize e and de
en = sat(Ke*e, -1, 1);
den = sat(Kde*de, -1, 1);
% evaluate FIS
dun = evalfis(fis, [en den]);
% De-normalize dun
du = Kdu * dun;
% Update outputs
u = du + prev_u;
prev_u = u;
end

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%% Satellite - Classical PI (Part A)
%
% Classical control script for Assignment 1 in Fuzzy systems
%
% author:
% Christos Choutouridis ΑΕΜ 8997
% cchoutou@ece.auth.gr
%
% -------------------------------------------------------
% Givens
% 10
% Plant: Gp(s) = ------------
% (s+1)(s+9)
%
% s + c
% PI: Gc(s) = Kp + Ki/s = Kp --------- , with c = Ki/Kp
% s
clear; clc; close all;
s = tf('s');
% Givens
% -------------------------------------------------------
Gp = 10/((s+1)*(s+9)); % given plant
spec.Mp_max = 0.10; % 10% overshoot
spec.Ts_max = 2.0; % 2sec settling time
spec.SteadyStateValue = 1.0; % step of 1
% Configuration
config.PI_zero = -1;
config.stepresp_time = 5;
% Control
Gc = @(c) (s + c)/s; % No gain controller
L0 = @(c) 0.1 * Gc(c) * Gp; % No gain open loop
Lk = @(K, c) K * L0(c); % open-loop with K [requested by the assignment]
% Utilities to extract Kp, Ki from K [variable requested by the assignment]
Kp = @(K) 0.1*K;
Ki = @(K, c) c*Kp(K);
% ---------- Brute force Root-locus exploration for fixed zero ----------
c = -config.PI_zero; % zero location
best = struct('cost',Inf);
for K = linspace(0, 100, 400)
CL = feedback(Lk(K, c), 1, -1); % closed loop unity feedback
info = stepinfo(CL);
if ~isfinite(info.SettlingTime) || isnan(info.Overshoot)
continue
end
% First check hard specs
if info.Overshoot/100 <= spec.Mp_max && ...
info.SettlingTime <= spec.Ts_max
%
% Select the best CL based on a more appropriate cost function
% (ITAE-like): integral of t*|e(t)| approximated by weights
%
[y, t] = step(CL, 0:0.001:config.stepresp_time);
e = spec.SteadyStateValue - y;
cost = trapz(t, t.*abs(e));
if cost < best.cost
best.cost = cost;
best.K = K;
best.info = info;
best.CL = CL;
best.ess = e(end);
end
end
end
fprintf('Best match: Kp=%.3g, Ki=%.3g\n', Kp(best.K), Ki(c, best.K));
fprintf('Poles:\n');
p = pole(best.CL);
for k = 1:numel(p)
fprintf(' Pole %d: %.5f %+.5fi\n', k, real(p(k)), imag(p(k)));
end
fprintf('Step response:\n');
fprintf(' RiseTime : %.4g s\n', best.info.RiseTime);
fprintf(' SettlingTime : %.4g s\n', best.info.SettlingTime);
fprintf(' Overshoot : %.2f%%\n', best.info.Overshoot);
fprintf(' Peak : %.4g\n', best.info.Peak);
fprintf(' PeakTime : %.4g s\n', best.info.PeakTime);
fprintf(' SS error : %.4g s\n', best.ess);
f1 = figure( ...
'Color','w', ...
'Name',sprintf('Root Locus - c=%.3g', c), ...
'Position',[100 100 1200 800] ...
);
h = rlocusplot(L0(c));
setoptions(h, 'XLim', [-12 2], 'YLim', [-8 8]);
ax = findobj(h, 'Type','Axes');
set(ax,'NextPlot','add');
grid(ax,'on');
% Overlays
p_cl = pole(best.CL);
hCL = plot(ax, real(p_cl), imag(p_cl), 'ro', 'MarkerSize', 8, ...
'MarkerFaceColor','r', 'DisplayName', ...
sprintf('CL poles: K_p=%.3g, K_i=%.3g', Kp(best.K), Ki(best.K, c)));
infoRL = sprintf([ ...
'K_p = %.3g\n' ...
'K_i = %.3g\n' ...
'c = %.3g\n' ...
'Poles:\n' ...
' %.4f%+.4fi\n' ...
' %.4f%+.4fi\n' ...
' %.4f%+.4fi'], ...
Kp(best.K), Ki(c,best.K), c, ...
real(p_cl(1)), imag(p_cl(1)), ...
real(p_cl(2)), imag(p_cl(2)), ...
real(p_cl(3)), imag(p_cl(3)));
p_ol = pole(L0(c));
hOL = plot(ax, real(p_ol), imag(p_ol), 'kx', 'MarkerSize', 9, ...
'LineWidth', 1.4, 'DisplayName','OL poles');
% z_ol = zero(L0(c));
% hZ = plot(ax, real(z_ol), imag(z_ol), 's', 'MarkerSize', 8, ...
% 'MarkerFaceColor',[1 0.9 0.2], 'MarkerEdgeColor','k', ...
% 'DisplayName','OL zero');
% Legend - annotations
lg = legend(ax, [hCL hOL], {'CL poles','OL poles'}, ...
'Location','best','AutoUpdate','off');
annotation(f1, 'textbox', [0.75 0.05 0.4 0.3], ...
'String', infoRL, 'Interpreter','tex', ...
'FontName','monospaced', 'FontSize',12, ...
'FitBoxToText','on', 'BackgroundColor', 'w', 'EdgeColor', [1 1 1]);
% titles
% xlabel(ax,'Real Axis (s^{-1})'); ylabel(ax,'Imaginary Axis (s^{-1})');
% title(ax, sprintf('Root Locus (c=%.3g)', c));
drawnow;
% save figure
exportgraphics(f1, sprintf('Root Locus c%.3g.png', c), 'Resolution', 300);
% exportgraphics(f1, sprintf('Root Locus c%.3g.pdf', c));
f2 = figure( ...
'Color','w', ...
'Name',sprintf('Step responce - c=%.3g, Kp=%.3g, Ki=%.3g', c, Kp(best.K), Ki(best.K, c)), ...
'Position',[200 200 1200 800] ...
);
step(best.CL);
xlabel('Time (s)');
ylabel('Amplitude');
title(sprintf('Step Response - c=%.3g, Kp=%.3g, Ki=%.3g', c, Kp(best.K), Ki(best.K, c)));
grid on;
infoStep = sprintf(['RiseTime : %.4g s\n' ...
'Settling : %.4g s\n' ...
'Overshoot : %.2f %%\n' ...
'Peak : %.4g (at %.4g s)\n' ...
'SS error : %.3f'], ...
best.info.RiseTime, best.info.SettlingTime, best.info.Overshoot, ...
best.info.Peak, best.info.PeakTime, best.ess);
annotation(f2, 'textbox', [0.7 0.05 0.4 0.25], ...
'String', infoStep, 'Interpreter','tex', ...
'FontName','monospaced', 'FontSize',12, ...
'FitBoxToText','on', 'BackgroundColor','w', 'EdgeColor',[1 1 1]);
% save figure
exportgraphics(f2, sprintf('Step Responce c%.3g_Kp%.3g_Ki%.3g.png', c, Kp(best.K), Ki(best.K, c)), 'Resolution', 300);
% exportgraphics(f2, sprintf('Step Responce c%.3g_Kp%.3g_Ki%.3g.pdf', c, Kp(best.K), Ki(best.K, c)));

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%% Satellite - Scenario 1 tune FZ-PI
%
% Assignment 1 in Fuzzy systems
%
% author:
% Christos Choutouridis ΑΕΜ 8997
% cchoutou@ece.auth.gr
%
%
clear; clc; close all;
s = tf('s');
% Givens
% -------------------------------------------------------
Gp = 10/((s+1)*(s+9)); % given plant
spec.Mp_max = 0.07; % 7% overshoot
spec.Tr_max = 0.6; % 0.6sec rise time
spec.SteadyStateValue = 1.0; % step of 1
Ts = 0.01;
% Configuration
tEnd = 5;
Ke = 1;
fis = mkFIS();
best = struct('cost',Inf);
for Kde = 0.2:0.01:0.35
for Kdu = 0.3:0.01:0.5
% Convert Gp -> A,B,C,D (z)
Gz = c2d(Gp, Ts, 'zoh');
Gd = ss(Gz);
Ad=Gd.A; Bd=Gd.B; Cd=Gd.C; Dd=Gd.D;
%figure('Name','FLC surface'); gensurf(fis); grid on;
t = 0:Ts:tEnd;
r = ones(size(t));
x = zeros(size(Ad,1),1);
y = 0;
% logs
Y = zeros(size(t)); U = zeros(size(t)); E = zeros(size(t));
clear satFZ_PI; % Init satFZ_PI
for k = 1:numel(t)
% calculate error
e = r(k) - y;
%evaluate controller
u = satFZ_PI(fis, e, Ke, Kde, Kdu, Ts);
% plant update (ZOH)
x = Ad*x + Bd*u;
y = Cd*x + Dd*u;
% keep logs
Y(k) = y; U(k) = u; E(k) = e;
end
info = stepinfo(Y, t, 1);
% First check hard specs
if info.Overshoot/100 <= spec.Mp_max && ...
info.RiseTime <= spec.Tr_max
%
% Select the best CL based on a more appropriate cost function
% (ITAE-like): integral of t*|e(t)| approximated by weights
%
cost = trapz(t, t.*abs(E));
if cost < best.cost
best.cost = cost;
best.Kdu = Kdu;
best.Kde = Kde;
best.info = info;
best.ess = E(end);
end
end
end
end
fprintf('Best match: Kde=%.3g, Kdu=%.3g\n', best.Kde, best.Kdu);
fprintf('Step response:\n');
fprintf(' RiseTime : %.4g s\n', best.info.RiseTime);
fprintf(' SettlingTime : %.4g s\n', best.info.SettlingTime);
fprintf(' Overshoot : %.2f%%\n', best.info.Overshoot);
fprintf(' Peak : %.4g\n', best.info.Peak);
fprintf(' PeakTime : %.4g s\n', best.info.PeakTime);
fprintf(' SS error : %.4g s\n', best.ess);

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%% Satellite - Scenario 1a
%
% Assignment 1 in Fuzzy systems
%
% author:
% Christos Choutouridis ΑΕΜ 8997
% cchoutou@ece.auth.gr
%
%
clear; clc; close all;
s = tf('s');
% Givens
% -------------------------------------------------------
Gp = 10/((s+1)*(s+9)); % given plant
spec.Mp_max = 0.07; % 7% overshoot
spec.Tr_max = 0.6; % 0.6sec rise time
spec.SteadyStateValue = 1.0; % step of 1
Ts = 0.01;
% Configuration
tEnd = 5;
Ke = 1;
Kde=0.29; % Calculated with scenario1_tune.m
Kdu=0.33;
fis = mkFIS();
Gz = c2d(Gp, Ts, 'zoh');
Gd = ss(Gz);
Ad=Gd.A; Bd=Gd.B; Cd=Gd.C; Dd=Gd.D;
t = 0:Ts:tEnd;
r = ones(size(t));
x = zeros(size(Ad,1),1);
y = 0;
% logs
Y = zeros(size(t)); U = zeros(size(t)); E = zeros(size(t));
clear satFZ_PI; % Init satFZ_PI
for k = 1:numel(t)
% calculate error
e = r(k) - y;
%evaluate controller
u = satFZ_PI(fis, e, Ke, Kde, Kdu, Ts);
% plant update (ZOH)
x = Ad*x + Bd*u;
y = Cd*x + Dd*u;
% keep logs
Y(k) = y; U(k) = u; E(k) = e;
end
info = stepinfo(Y, t, 1);
f1 = figure( ...
'Color','w', ...
'Name',sprintf('Step responce - Kde=%.3g, Kdu=%.3g', Kde, Kdu), ...
'Position',[200 200 1200 800] ...
);
plot(t, Y);
xlabel('Time (s)');
ylabel('Amplitude');
title(sprintf('Step responce - Kde=%.3g, Kdu=%.3g', Kde, Kdu));
grid on;
infoStep = sprintf(['RiseTime : %.4g s\n' ...
'Settling : %.4g s\n' ...
'Overshoot : %.2f %%\n' ...
'Peak : %.4g (at %.4g s)\n' ...
'SS error : %.3f'], ...
info.RiseTime, info.SettlingTime, info.Overshoot, ...
info.Peak, info.PeakTime, E(end));
annotation(f1, 'textbox', [0.7 0.05 0.4 0.25], ...
'String', infoStep, 'Interpreter','tex', ...
'FontName','monospaced', 'FontSize',12, ...
'FitBoxToText','on', 'BackgroundColor','w', 'EdgeColor',[1 1 1]);
% save figure
exportgraphics(f1, sprintf('Step Responce_FZ.png'), 'Resolution', 300);
% exportgraphics(f1, sprintf('Step Responce_FZ.pdf'));

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%% Satellite - Scenario 1b, 1c
%
% Assignment 1 in Fuzzy systems
%
% author:
% Christos Choutouridis ΑΕΜ 8997
% cchoutou@ece.auth.gr
%
%
clear; clc; close all;
% load fuzzy controller
flc = mkFIS();
% test controller
% e=NM for ex: -0.41
% de=ZR for ex: 0.03
evalfis(flc, [0.41 0.03]);
ruleview(flc);
f1 = figure('Name','FLC surface'); gensurf(fis); grid on;
exportgraphics(f1, sprintf('FLC surface.png'), 'Resolution', 300);
% exportgraphics(f1, sprintf('FLC surface.pdf'));

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%% Satellite - Scenario 2
%
% Assignment 1 in Fuzzy systems
%
% author:
% Christos Choutouridis ΑΕΜ 8997
% cchoutou@ece.auth.gr
%
%
clear; clc; close all;
s = tf('s');
% Givens
% -------------------------------------------------------
Gp = 10/((s+1)*(s+9)); % given plant
spec.Mp_max = 0.07; % 7% overshoot
spec.Tr_max = 0.6; % 0.6sec rise time
spec.SteadyStateValue = 1.0; % step of 1
Ts = 0.01;
% Configuration
Ke = 1;
Kde=0.29; % Calculated with scenario1_tune.m
Kdu=0.33;
fis = mkFIS();
Gz = c2d(Gp, Ts, 'zoh');
Gd = ss(Gz);
Ad=Gd.A; Bd=Gd.B; Cd=Gd.C; Dd=Gd.D;
% Control inputs
tEnd = 16;
t = 0:Ts:tEnd;
% 2a
r_step = zeros(size(t));
r_step(t < 4) = 60;
r_step(t >= 4 & t < 8) = 20;
r_step(t >= 8) = 40;
x = zeros(size(Ad,1),1);
y = 0;
% logs
Y = zeros(size(t)); U = zeros(size(t)); E = zeros(size(t));
clear satFZ_PI; % Init satFZ_PI
for k = 1:numel(t)
% calculate error
e = r_step(k)/60 - y;
%evaluate controller
u = satFZ_PI(fis, e, Ke, Kde, Kdu, Ts);
% plant update (ZOH)
x = Ad*x + Bd*u;
y = Cd*x + Dd*u;
% keep logs
Y(k) = y; U(k) = u; E(k) = e;
end
f1 = figure( ...
'Color','w', ...
'Name',sprintf('MultiStep responce'), ...
'Position',[200 200 1200 800] ...
);
plot(t, r_step, 'k--', 'LineWidth',1.2); hold on;
plot(t, Y*60, 'b', 'LineWidth',1.2);
grid on; xlabel('Time (s)'); ylabel('Amplitude');
title('Scenario 2A: multi-step (60->20->40)');
legend('r','y','Location','best');
% save figure
exportgraphics(f1, sprintf('MultiStep Responce_FZ.png'), 'Resolution', 300);
% exportgraphics(f1, sprintf('Step Responce_FZ.pdf'));
% 2b
r_trap = zeros(size(t));
ix = (t <= 5);
r_trap(ix) = 60/5 * t(ix);
ix = (t > 5 & t <= 8);
r_trap(ix) = 60;
ix = (t > 8 & t <= 16);
r_trap(ix) = 60 * (1 - (t(ix) - 8)/(16 - 8));
x = zeros(size(Ad,1),1);
y = 0;
% logs
Y = zeros(size(t)); U = zeros(size(t)); E = zeros(size(t));
clear satFZ_PI; % Init satFZ_PI
for k = 1:numel(t)
% calculate error
e = r_trap(k)/60 - y;
%evaluate controller
u = satFZ_PI(fis, e, Ke, Kde, Kdu, Ts);
% plant update (ZOH)
x = Ad*x + Bd*u;
y = Cd*x + Dd*u;
% keep logs
Y(k) = y; U(k) = u; E(k) = e;
end
info = stepinfo(Y, t, 1);
f2 = figure( ...
'Color','w', ...
'Name',sprintf('Trapezoid responce'), ...
'Position',[200 200 1200 800] ...
);
plot(t, r_trap, 'k--', 'LineWidth',1.2); hold on;
plot(t, Y*60, 'b', 'LineWidth',1.2);
grid on; xlabel('Time (s)'); ylabel('Amplitude');
title('Scenario 2B: trapezoid (0->60, hold, 60->0)');
legend('r','y','Location','best');
% save figure
exportgraphics(f2, sprintf('Trapezoid Responce_FZ.png'), 'Resolution', 300);
% exportgraphics(f2, sprintf('Step Responce_FZ.pdf'));

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