Tangle files

index.org

@@ -104,18 +104,28 @@
 ** Time Domain Data
 #+begin_src matlab
   figure;
-
+  plot(t, y)
-  subplot(1,2,1);
-  plot(data(:, 3), data(:, 1))
-  ylabel('Input Voltage [V]'); xlabel('Time [s]');
-
-
-  subplot(1,2,2);
-  plot(data(:, 3), data(:, 2))
   ylabel('Output Displacement [m]'); xlabel('Time [s]');
 #+end_src
 
 ** PSD of Measurement Noise
+#+begin_src matlab
+  Ts = t(end)/(length(t)-1);
+  Fs = 1/Ts;
+ 
+  win = hanning(ceil(1*Fs));
+#+end_src
+
+#+begin_src matlab
+  [pxx, f] = pwelch(y, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab
+  figure;
+  plot(f, sqrt(pxx));
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+#+end_src
 
 * Transfer Function Estimation with m=5kg
 :PROPERTIES:
@@ -125,7 +135,8 @@
 
 ** Load Data
 #+begin_src matlab
-  load('./mat/huddle_test.mat', 't', 'u', 'y');
+  ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
+  load('./mat/apa95ml_5kg.mat', 't', 'u', 'y');
 #+end_src
 
 ** Time Domain Data
@@ -133,15 +144,39 @@
   figure;
 
   subplot(1,2,1);
-  plot(data(:, 3), data(:, 1))
+  plot(t, u)
   ylabel('Input Voltage [V]'); xlabel('Time [s]');
 
 
   subplot(1,2,2);
-  plot(data(:, 3), data(:, 2))
+  plot(t, y)
   ylabel('Output Displacement [m]'); xlabel('Time [s]');
 #+end_src
 
+** Comparison of the PSD with Huddle Test
+#+begin_src matlab
+  Ts = t(end)/(length(t)-1);
+  Fs = 1/Ts;
+
+  win = hanning(ceil(1*Fs));
+#+end_src
+
+#+begin_src matlab
+  [pxx, f] = pwelch(y, win, [], [], Fs);
+  [pht, ~] = pwelch(ht.y, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab
+  figure;
+  hold on;
+  plot(f, sqrt(pxx), 'DisplayName', '5kg');
+  plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+  legend('locaation', 'norteast');
+#+end_src
+
 ** Compute TF estimate and Coherence
 #+begin_src matlab
   win = hann(ceil(1/Ts));

matlab/huddle_test.m

@@ -0,0 +1,23 @@
+% Load Data
+
+load('./mat/huddle_test.mat', 't', 'u', 'y');
+
+% Time Domain Data
+
+figure;
+plot(t, y)
+ylabel('Output Displacement [m]'); xlabel('Time [s]');
+
+% PSD of Measurement Noise
+
+Ts = t(end)/(length(t)-1);
+Fs = 1/Ts;
+
+win = hanning(ceil(1*Fs));
+
+[pxx, f] = pwelch(y, win, [], [], Fs);
+
+figure;
+plot(f, sqrt(pxx));
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');

matlab/run_experiment.m

@@ -0,0 +1,11 @@
+% Load Data
+
+data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
+
+% Save Data
+
+u = data(:, 1); % Input Voltage [V]
+y = data(:, 2); % Output Displacement [m]
+t = data(:, 3); % Time [s]
+
+save('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');

matlab/setup_experiment.m

@@ -0,0 +1,9 @@
+% Parameters
+
+Ts = 1e-4;
+
+% Filter White Noise
+
+Glpf = 1/(1 + s/2/pi/500);
+
+Gz = c2d(Glpf, Ts, 'tustin');

matlab/tf_estimation.m

@@ -0,0 +1,74 @@
+% Load Data
+
+ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
+load('./mat/apa95ml_5kg.mat', 't', 'u', 'y');
+
+% Time Domain Data
+
+figure;
+
+subplot(1,2,1);
+plot(t, u)
+ylabel('Input Voltage [V]'); xlabel('Time [s]');
+
+
+subplot(1,2,2);
+plot(t, y)
+ylabel('Output Displacement [m]'); xlabel('Time [s]');
+
+% Comparison of the PSD with Huddle Test
+
+Ts = t(end)/(length(t)-1);
+Fs = 1/Ts;
+
+win = hanning(ceil(1*Fs));
+
+[pxx, f] = pwelch(y, win, [], [], Fs);
+[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+
+figure;
+hold on;
+plot(f, sqrt(pxx), 'DisplayName', '5kg');
+plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+legend('locaation', 'norteast');
+
+% Compute TF estimate and Coherence
+
+win = hann(ceil(1/Ts));
+
+[tf_est, f] = tfestimate(data(:, 1), -data(:, 2), win, [], [], 1/Ts);
+[co_est, ~] = mscohere(  data(:, 1), -data(:, 2), win, [], [], 1/Ts);
+
+% Coherence
+
+figure;
+
+hold on;
+plot(f, co_est, 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Coherence'); xlabel('Frequency [Hz]');
+hold off;
+
+% Transfer Function
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(f, abs(tf_est), 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('Amplitude'); xlabel('Frequency [Hz]');
+hold off;
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(f, 180/pi*angle(tf_est), 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Phase'); xlabel('Frequency [Hz]');
+legend();
+hold off;
+
+linkaxes([ax1,ax2], 'x');
+xlim([10, 5000]);