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);

 

mean_values = (y_1 + y_2 + y_3)/3;

 

figure;

plot(mean_values, 'LineWidth', 1.5);

title('Semnalul mediu');

xlabel('Puncte de date');

ylabel('Amplitudine');

grid on;

Informatii despre sistem:

Timp tranzitoriu

y_stationar = mean(mean_values(end-10:end));

 

threshold = 0.02 * y_stationar;

 

tt_idx = find(abs(mean_values - y_stationar) > threshold, 1, 'last');

tt = time1(tt_idx);

Timp de crestere

tc_10 = 0.1 * y_stationar;

 

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:

N1 = 42;

N2 = 50;

 

Ts = 0.1;

 

T0 = (N2 - N1) * 2

fprintf('T0 determinat din grafic = %.2f s ', T0);

 

Mp   = suprareglaj;

lnMp = log(Mp);

zeta = -lnMp / sqrt(pi^2 + (lnMp)^2);

 

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

 

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

 

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

 

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).');

    disp('G NU este stabil (exista poli cu parte reala >= 0).');

Calculul PID:

Kr = 3.62

Ti = 1.99

Tf = 0.28

Td = 0.6

Calculul RST:

 

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]

 

 

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

 

RST: