115 rindas
3.6 KiB
Matlab
115 rindas
3.6 KiB
Matlab
% === Problem 3a: Effect of Noise on Parameter Estimation ===
|
||
|
||
clear; close all;
|
||
|
||
% True system parameters
|
||
m = 0.75;
|
||
L = 1.25;
|
||
c = 0.15;
|
||
g = 9.81;
|
||
|
||
mL2_true = m * L^2;
|
||
mgL_true = m * g * L;
|
||
theta_true = [mL2_true; c; mgL_true];
|
||
|
||
% Load clean data
|
||
data = readtable('output/problem1_data.csv');
|
||
t = data.t;
|
||
q_clean = data.q;
|
||
u = data.u;
|
||
Ts = t(2) - t(1);
|
||
N = length(t);
|
||
|
||
% Derivatives from clean q
|
||
dq_clean = zeros(N,1);
|
||
ddq_clean = zeros(N,1);
|
||
for k = 2:N-1
|
||
dq_clean(k) = (q_clean(k+1) - q_clean(k-1)) / (2*Ts);
|
||
ddq_clean(k) = (q_clean(k+1) - 2*q_clean(k) + q_clean(k-1)) / Ts^2;
|
||
end
|
||
|
||
% LS estimation on clean data
|
||
X_clean = [ddq_clean, dq_clean, q_clean];
|
||
theta_hat_clean = (X_clean' * X_clean) \ (X_clean' * u);
|
||
rel_error_clean = abs((theta_hat_clean - theta_true) ./ theta_true) * 100;
|
||
|
||
% Reconstruct q̂_clean
|
||
q_hat_clean = zeros(N, 1);
|
||
dq_hat_clean = zeros(N, 1);
|
||
q_hat_clean(1) = q_clean(1);
|
||
dq_hat_clean(1) = dq_clean(1);
|
||
for k = 2:N
|
||
ddq_hat_clean_k = (1/theta_hat_clean(1)) * ...
|
||
(u(k-1) - theta_hat_clean(2)*dq_clean(k-1) - theta_hat_clean(3)*q_clean(k-1));
|
||
dq_hat_clean(k) = dq_hat_clean(k-1) + Ts * ddq_hat_clean_k;
|
||
q_hat_clean(k) = q_hat_clean(k-1) + Ts * dq_hat_clean(k-1);
|
||
end
|
||
|
||
% === Loop over noise levels ===
|
||
noise_levels = [0.001, 0.0025];
|
||
|
||
for i = 1:length(noise_levels)
|
||
noise_std = noise_levels(i);
|
||
q_noisy = q_clean + noise_std * randn(size(q_clean));
|
||
|
||
% Derivatives from noisy q
|
||
dq_noisy = zeros(N,1);
|
||
ddq_noisy = zeros(N,1);
|
||
for k = 2:N-1
|
||
dq_noisy(k) = (q_noisy(k+1) - q_noisy(k-1)) / (2*Ts);
|
||
ddq_noisy(k) = (q_noisy(k+1) - 2*q_noisy(k) + q_noisy(k-1)) / Ts^2;
|
||
end
|
||
|
||
% LS estimation on noisy data
|
||
X_noisy = [ddq_noisy, dq_noisy, q_noisy];
|
||
theta_hat_noisy = (X_noisy' * X_noisy) \ (X_noisy' * u);
|
||
rel_error_noisy = abs((theta_hat_noisy - theta_true) ./ theta_true) * 100;
|
||
|
||
% Reconstruct q̂_noisy
|
||
q_hat_noisy = zeros(N,1);
|
||
dq_hat_noisy = zeros(N,1);
|
||
q_hat_noisy(1) = q_noisy(1);
|
||
dq_hat_noisy(1) = dq_noisy(1);
|
||
for k = 2:N
|
||
ddq_hat_noisy_k = (1/theta_hat_noisy(1)) * ...
|
||
(u(k-1) - theta_hat_noisy(2)*dq_noisy(k-1) - theta_hat_noisy(3)*q_noisy(k-1));
|
||
dq_hat_noisy(k) = dq_hat_noisy(k-1) + Ts * ddq_hat_noisy_k;
|
||
q_hat_noisy(k) = q_hat_noisy(k-1) + Ts * dq_hat_noisy(k-1);
|
||
end
|
||
|
||
% Print results
|
||
fprintf('\n--- Noise std = %.4f ---\n', noise_std);
|
||
fprintf('Clean: mL2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
|
||
theta_hat_clean(1), rel_error_clean(1), ...
|
||
theta_hat_clean(2), rel_error_clean(2), ...
|
||
theta_hat_clean(3), rel_error_clean(3));
|
||
fprintf('Noisy: mL2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
|
||
theta_hat_noisy(1), rel_error_noisy(1), ...
|
||
theta_hat_noisy(2), rel_error_noisy(2), ...
|
||
theta_hat_noisy(3), rel_error_noisy(3));
|
||
|
||
% === Combined plot ===
|
||
figure('Name', sprintf('Noise std = %.4f', noise_std), 'Position', [100, 100, 1000, 800]);
|
||
|
||
subplot(2,1,1);
|
||
plot(t, q_clean, 'b', ...
|
||
t, q_hat_clean, 'g--', ...
|
||
t, q_hat_noisy, 'r:');
|
||
legend('Actual q(t)', 'Estimated (clean)', 'Estimated (noisy)');
|
||
title(sprintf('Estimated Output (σ = %.4f)', noise_std));
|
||
ylabel('q(t) [rad]');
|
||
grid on;
|
||
|
||
subplot(2,1,2);
|
||
bar([rel_error_clean, rel_error_noisy]);
|
||
set(gca, 'XTickLabel', {'mL^2', 'c', 'mgL'});
|
||
legend({'No Noise', sprintf('With Noise (σ=%.4f)', noise_std)}, 'Location', 'northwest');
|
||
ylabel('Relative Error [%]');
|
||
title('Estimation Error');
|
||
grid on;
|
||
|
||
% Save figure
|
||
filename = sprintf('output/Prob3a_NoiseStd%.4f.png', noise_std);
|
||
saveas(gcf, filename);
|
||
end
|