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