From ac92f4c154cacd993d00e708741e5988481d44f8 Mon Sep 17 00:00:00 2001 From: Christos Choutouridis Date: Thu, 3 Apr 2025 23:02:19 +0300 Subject: [PATCH] Work 1: Add problem 2 matlab + report --- Work 1/report/Work1_report.pdf | Bin 259979 -> 424112 bytes Work 1/report/Work1_report.tex | 115 +++++++++++++-- Work 1/scripts/Prob1_responce_20s.png | Bin 80028 -> 80319 bytes Work 1/scripts/Prob1_responce_90s.png | Bin 105016 -> 107807 bytes Work 1/scripts/Prob2_20s_Ts0.1.png | Bin 0 -> 73852 bytes Work 1/scripts/Prob2b_20s_Ts0.1.png | Bin 0 -> 75120 bytes Work 1/scripts/Problem1.m | 23 +-- Work 1/scripts/Problem2a.m | 79 ++++++++++ Work 1/scripts/Problem2b.m | 88 +++++++++++ Work 1/scripts/problem1_data.csv | 202 ++++++++++++++++++++++++++ Work 1/scripts/sample_data.m | 39 +++++ 11 files changed, 524 insertions(+), 22 deletions(-) create mode 100644 Work 1/scripts/Prob2_20s_Ts0.1.png create mode 100644 Work 1/scripts/Prob2b_20s_Ts0.1.png create mode 100644 Work 1/scripts/Problem2a.m create 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Time span for 20s simulation tspan = [0 20]; -dt = 1e-3; +dt = 1e-4; t_eval = 0:dt:20; % ODE Function @@ -20,28 +22,29 @@ odefun = @(t, x) [ x0 = [0; 0]; % Initial conditions [t, x] = ode45(odefun, t_eval, x0); % Solve -% Plots +% Plots for 20 sec figure('Name', 'System responce', 'Position', [100, 100, 1280, 860]); subplot(2,1,1); plot(t, x(:,1)); ylabel('q(t) [rad]'); grid on; title('Γωνία'); subplot(2,1,2); plot(t, x(:,2), 'r'); ylabel('dq(t) [rad/s]'); xlabel('t [sec]'); grid on; title('Γωνιακή Ταχύτητα'); - saveas(gcf, 'Prob1_responce_20s.png'); +% === Sampling for Problem 2 === +Ts = 0.1; % Sampling period +sample_data(t, x, Ts, A0, omega, 'problem1_data.csv'); -% Time span +% --- Extended simulation to 90 sec --- tspan = [0 90]; t_eval = 0:dt:90; -x0 = [0; 0]; % Initial conditions -[t, x] = ode45(odefun, t_eval, x0); % Solve +x0 = [0; 0]; +[t, x] = ode45(odefun, t_eval, x0); -% Plots +% Plots for 90 sec figure('Name', 'System responce', 'Position', [100, 100, 1280, 860]); subplot(2,1,1); plot(t, x(:,1)); ylabel('q(t) [rad]'); grid on; title('Γωνία'); subplot(2,1,2); plot(t, x(:,2), 'r'); ylabel('dq(t) [rad/s]'); xlabel('t [sec]'); grid on; title('Γωνιακή Ταχύτητα'); - -saveas(gcf, 'Prob1_responce_90s.png'); \ No newline at end of file +saveas(gcf, 'Prob1_responce_90s.png'); diff --git a/Work 1/scripts/Problem2a.m b/Work 1/scripts/Problem2a.m new file mode 100644 index 0000000..eef38b5 --- /dev/null +++ b/Work 1/scripts/Problem2a.m @@ -0,0 +1,79 @@ +% === Problem 2: Parameter Estimation using Least Squares === + +% True data for comparison +m = 0.75; +L = 1.25; +c_true = 0.15; +g = 9.81; + +mL2_true = m * L^2; +mgL_true = m * g * L; + +theta_true = [mL2_true; c_true; mgL_true]; + +% Load sampled data from Problem 1 +data = readtable('problem1_data.csv'); +t = data.t; +q = data.q; +dq = data.dq; +ddq = data.ddq; +u = data.u; + +% Build regression matrix X and target vector y = u +X = [ddq, dq, q]; % columns correspond to coefficients of [mL^2, c, mgL] +y = u; + +% Least Squares estimation: theta_hat = [mL^2; c; mgL] +theta_hat = (X' * X) \ (X' * y); + +% Extract individual parameters (optional interpretation) +mL2_est = theta_hat(1); +c_est = theta_hat(2); +mgL_est = theta_hat(3); + +% Reconstruct ddq_hat using the estimated parameters +ddq_hat = (1 / mL2_est) * (u - c_est * dq - mgL_est * q); + +% Numerical integration to recover dq̂(t) and q̂(t) +Ts = t(2) - t(1); +N = length(t); +dq_hat = zeros(N,1); +q_hat = zeros(N,1); + +% Initial conditions +dq_hat(1) = dq(1); +q_hat(1) = q(1); + +for k = 2:N + dq_hat(k) = dq_hat(k-1) + Ts * ddq_hat(k-1); + q_hat(k) = q_hat(k-1) + Ts * dq_hat(k-1); +end + +% Estimation error +e_q = q - q_hat; + +% === Plots === +figure('Name', 'Problem 2 - LS Estimation', 'Position', [100, 100, 1280, 800]); + +subplot(3,1,1); +plot(t, q, 'b', t, q_hat, 'r--'); +legend('q(t)', 'q̂(t)'); +title('Actual vs Estimated Angle'); +ylabel('Angle [rad]'); +grid on; + +subplot(3,1,2); +plot(t, e_q, 'k'); +title('Estimation Error e_q(t) = q(t) - q̂(t)'); +ylabel('Error [rad]'); +grid on; + +subplot(3,1,3); +bar(["mL^2", "c", "mgL"], theta_hat); +title('Estimated Parameters'); +ylabel('Value'); +grid on; +saveas(gcf, 'Prob2_20s_Ts0.1.png'); + +fprintf(' Actual Parameters: mL^2=%f, c=%f, mgL=%f\n', theta_true(1), theta_true(2), theta_true(3)); +fprintf('Estimated Parameters: mL^2=%f, c=%f, mgL=%f\n', theta_hat(1), theta_hat(2), theta_hat(3)); diff --git a/Work 1/scripts/Problem2b.m b/Work 1/scripts/Problem2b.m new file mode 100644 index 0000000..dee06ea --- /dev/null +++ b/Work 1/scripts/Problem2b.m @@ -0,0 +1,88 @@ +% === Problem 2b: Estimation using only q(t) and u(t) === + +% True parameter values +m = 0.75; +L = 1.25; +c_true = 0.15; +g = 9.81; + +mL2_true = m * L^2; +mgL_true = m * g * L; + +theta_true = [mL2_true; c_true; mgL_true]; + +% Load sampled data +data = readtable('problem1_data.csv'); +t = data.t; +q = data.q; +u = data.u; + +Ts = t(2) - t(1); +N = length(t); + +% Compute dq and ddq using central differences +dq = zeros(N, 1); +ddq = zeros(N, 1); + +for k = 2:N-1 + dq(k) = (q(k+1) - q(k-1)) / (2 * Ts); + ddq(k) = (q(k+1) - 2*q(k) + q(k-1)) / Ts^2; +end + +% Build regression matrix and output vector +X = [ddq, dq, q]; +y = u; + +% Least Squares estimation +theta_hat = (X' * X) \ (X' * y); + +% Parameter extraction +mL2_est = theta_hat(1); +c_est = theta_hat(2); +mgL_est = theta_hat(3); + +% Reconstruct ddq_hat from estimated parameters +ddq_hat = (1 / mL2_est) * (u - c_est * dq - mgL_est * q); + +% Integrate to get dq_hat and q_hat +dq_hat = zeros(N,1); +q_hat = zeros(N,1); +dq_hat(1) = dq(1); +q_hat(1) = q(1); + +for k = 2:N + dq_hat(k) = dq_hat(k-1) + Ts * ddq_hat(k-1); + q_hat(k) = q_hat(k-1) + Ts * dq_hat(k-1); +end + +% Estimation error +e_q = q - q_hat; + +% === Plots === +figure('Name', 'Problem 2b - LS Estimation from q only', 'Position', [100, 100, 1280, 800]); + +subplot(3,1,1); +plot(t, q, 'b', t, q_hat, 'r--'); +legend('q(t)', 'q̂(t)'); +title('Actual vs Estimated Angle from q(t) only'); +ylabel('Angle [rad]'); +grid on; + +subplot(3,1,2); +plot(t, e_q, 'k'); +title('Estimation Error e_q(t) = q(t) - q̂(t)'); +ylabel('Error [rad]'); +grid on; + +subplot(3,1,3); +bar(["mL^2", "c", "mgL"], theta_hat); +title('Estimated Parameters'); +ylabel('Value'); +grid on; + +% Save figure +saveas(gcf, 'Prob2b_20s_Ts0.1.png'); + +% Print results +fprintf(' Actual Parameters: mL^2=%f, c=%f, mgL=%f\n', theta_true(1), theta_true(2), theta_true(3)); +fprintf('Estimated Parameters: mL^2=%f, c=%f, mgL=%f\n', theta_hat(1), theta_hat(2), theta_hat(3)); diff --git a/Work 1/scripts/problem1_data.csv b/Work 1/scripts/problem1_data.csv new file mode 100644 index 0000000..2a5f2d2 --- /dev/null +++ b/Work 1/scripts/problem1_data.csv @@ -0,0 +1,202 @@ +t,q,dq,ddq,u +0,0,0,0,0 +0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245 +0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346 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Resamples pendulum simulation data and exports to CSV +% +% Usage: +% sample_pendulum_data(t, x, Ts, A0, omega, filename) +% +% Inputs: +% t - time vector from ODE solver (e.g., from ode45) +% x - state matrix [q(t), dq(t)] +% Ts - sampling period (in seconds) +% A0 - input amplitude for u(t) = A0 * sin(omega * t) +% omega - input frequency (in rad/s) +% filename - output CSV filename + + % Time vector for resampling + t_sampled = t(1):Ts:t(end); + + % Resample q and dq using interpolation + q_sampled = interp1(t, x(:,1), t_sampled); + dq_sampled = interp1(t, x(:,2), t_sampled); + + % Estimate second derivative using central finite differences + ddq_sampled = zeros(size(q_sampled)); + N = length(q_sampled); + + for k = 2:N-1 + ddq_sampled(k) = (q_sampled(k+1) - 2*q_sampled(k) + q_sampled(k-1)) / Ts^2; + end + + % Evaluate input u(t) + u_sampled = A0 * sin(omega * t_sampled); + + % Create table and export to CSV + T = table(t_sampled', q_sampled', dq_sampled', ddq_sampled', u_sampled', ... + 'VariableNames', {'t', 'q', 'dq', 'ddq', 'u'}); + + writetable(T, filename); + fprintf('Sampling data saved to file: %s\n', filename); +end