Tema SCPI
Incarcarea datelor
clear all
data1 = load('Set1.mat');
data2 = load('Set2.mat');
data3 = load('Set3.mat');

time1 = data1.set_date_n_n_1.Time;
values1 = data1.set_date_n_n_1.Data;
plot(time1, values1);
xlabel('Timp [s]');
ylabel('Valori');
title('Date initiale');

time2 = data2.set_date_n_n_2.Time;
values2 = data2.set_date_n_n_2.Data;
plot(time2, values2);
xlabel('Timp [s]');
ylabel('Valori');
title('Date initiale');

time3 = data3.set_date_n_n_3.Time;
values3 = data3.set_date_n_n_3.Data;
plot(time3, values3);
xlabel('Timp [s]');
ylabel('Valori');
title('Date initiale');
Filtrarea datelor
Set 1
x_1 = data1.set_date_n_n_1.Data;
a = 1;
Ws1 = 5; % il alegem ca sa arate graficul cat mai bine
b = (1/Ws1) * ones(1, Ws1);
y_1 = filter(b, a, x_1)

figure;
plot(time1, values1, 'b', time1, y_1, 'r');
title('Filtrare date - Set 1');
legend('Date brute', 'Date filtrate');
Set 2
x_2 = data2.set_date_n_n_2.Data;
a = 1;
Ws2 = 5; % il alegem ca sa arate graficul cat mai bine
b = (1/Ws2) * ones(1, Ws2);
y_2 = filter(b, a, x_2)

figure;
plot(time2, values2, 'b', time2, y_2, 'r');
title('Filtrare date - Set 2');
legend('Date brute', 'Date filtrate');
Set 3
x_3 = data3.set_date_n_n_3.Data;
a = 1;
Ws3 = 5; % il alegem ca sa arate graficul cat mai bine
b = (1/Ws3) * ones(1, Ws3);
y_3 = filter(b, a, x_3)

figure;
plot(time3, values3, 'b', time3, y_3, 'r');
title('Filtrare date - Set 3');
legend('Date brute', 'Date filtrate');
Afisarea raspunsului mediu
min_length = min([length(y_1), length(y_2), length(y_3)]);
y_1 = y_1(1:min_length);
y_2 = y_2(1:min_length);
y_3 = y_3(1:min_length);

% Calculul mediei aritmetice
mean_values = (y_1 + y_2 + y_3)/3;

% Afisarea noului semnal
figure;
plot(mean_values, 'LineWidth', 1.5);
title('Semnalul mediu');
xlabel('Puncte de date');
ylabel('Amplitudine');
grid on;
Informatii despre sistem:
Timp tranzitoriu
% Valoarea stationara
y_stationar = mean(mean_values(end-10:end));

% Prag de 2%
threshold = 0.02 * y_stationar;

% Identificarea timpului tranzitoriu
tt_idx = find(abs(mean_values - y_stationar) > threshold, 1, 'last');
tt = time1(tt_idx);
Timp de crestere
% 10% din valoarea stationara
tc_10 = 0.1 * y_stationar;

% 90% din valoarea stationara
tc_90 = 0.9 * y_stationar;

tc_idx_10 = find(mean_values >= tc_10, 1);
tc_idx_90 = find(mean_values >= tc_90, 1);

tc = time1(tc_idx_90) - time1(tc_idx_10);
Timp mort
threshold_mort = 0.01 * y_stationar;

timp_mort_idx = find(mean_values > threshold_mort, 1);

timp_mort = time1(timp_mort_idx);
Suprareglaj
max_val = max(mean_values);
suprareglaj = ((max_val - y_stationar) / y_stationar);
Te (Constanta de timp echivalenta)
Te_min = tc / 16;
Te_max = tc / 9;
Valoarea stationara
y_stationar = mean(mean_values(end-10:end));
Tabel cu rezultate
results = table(tt, tc, timp_mort, suprareglaj, Te_min, y_stationar, ...
    'VariableNames', {'Timp_tranzitoriu', 'Timp_crestere', 'Timp_mort', ...
                      'Suprareglaj', 'Te_min', 'y_stationar'});
disp(results);
Identificarea ordinului sistemului:
disp('Intrucat suprareglajul > 0 si observam oscilatii, sistemul este de ordin 2.');
Identificarea sistemului:
%% Determinarea lui T0 din varfurile alese
% Varfuri la indexurile 39 și 47
N1 = 42;
N2 = 50;

% Pas de esantionare: 100 ms = 0.1 s
Ts = 0.1;

% Calcul T0 = (N2 - N1) * Ts
T0 = (N2 - N1) * 2
fprintf('T0 determinat din grafic = %.2f s ', T0);

% Calcul zeta
Mp   = suprareglaj;
lnMp = log(Mp);
zeta = -lnMp / sqrt(pi^2 + (lnMp)^2);

fprintf('Zeta = %.4f\n', zeta);

% Calcul omega_n
omega_n = 2*pi / ( T0 * sqrt(1 - zeta^2) );

fprintf('omega_n = %.4f rad/s\n', omega_n);

% Construirea functiei de transfer
num = omega_n^2;
den = [1, 2*zeta*omega_n, omega_n^2];

G = tf(num, den);  % Obiect Transfer Function

disp('Functia de transfer estimata este:');
tf = sprintf('G(s) = %.3g / ( s^2 + %.3g s + %.3g )', ...
                    omega_n^2, 2*zeta*omega_n, omega_n^2);
disp(tf);
disp(G);
[Stabilitatea lui G]
den = [1 2.26 63];

p = roots(den);

disp('Polii sistemului sunt:');
disp(p);

if all(real(p) < 0)
    disp('G este stabil (toti polii au parte reala negativa).');
else
    disp('G NU este stabil (exista poli cu parte reala >= 0).');
end
Calculul PID:
Kr = 3.62
Ti = 1.99
Tf = 0.28
Td = 0.6
Calculul RST:
% G - functia de transfer

T = 0.1;

G_discretized = c2d(G, T, 'zoh')

integrator = tf([1], [1 -1], T); % 1/(1-z^-1)
%%%%%%%%%%%%%%%%%%%%%%%%%
G_integrator = G_discretized * integrator;

[num_discretized, den_discretized] = tfdata(G_discretized, 'v');
num_discretized
den_discretized

clear tf

G_z_minus1 = tf(num_discretized, den_discretized, T, 'Variable', 'z^-1');

G_z_minus1

A = [-1.875 0.8802]
B = [0.002689 0.002577]

omega =  0.5026;
zeta = 0.75;

num = omega^2;
den = [1, 2 * zeta * omega, omega^2];

Hi = tf(num, den)

Hi_discretized = c2d(Hi, T, 'zoh');
Hi_discretized

P = [-1.925 0.9274]

% ns = 1
% nr = 1
% np <= 3

Matrice = [1 0 0 0 ; -1.875 1 0.002689 0 ; 0.8802 -1.875 0.002577 0.002689 ; 0 0.8802 0 0.002577]
P = [1 ; -1.925 ; 0.9274 ; 0]
syms s1 r0 r1
Coloana = [1; s1; r0; r1]

solutii = linsolve(Matrice, P)
R = [-9.1661 8.6594]
S = [1 -0.0254]
Pentru testare:
PID discretizat:
num_PID = [6.34, 8.21, 3.62];
den_PID = [0.56, 1.99, 0];

PID_tf = tf(num_PID, den_PID);

T = 0.1;

PID_tf_discretized = c2d(PID_tf, T, 'zoh')

[num_PID_discretized, den_PID_discretized] = tfdata(PID_tf_discretized, 'v');

num_PID_discretized
den_PID_discretized

% A mers pentru referinta 90 si comanda 169 la pornire si dupa 255
RST: