From 6324f1dafc75dd0a7ee23df12538d74d76042064 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 15 Feb 2022 14:16:10 +0100 Subject: [PATCH] Initial commit --- .gitignore | 62 + X_tal_cage_PID.dat | 2 + X_tal_cage_PID_20Hz.dat | 2 + X_tal_cage_PID_40Hz.dat | 2 + dcm_feedback.html | 1693 ++++++++++++++++ dcm_feedback.org | 2293 ++++++++++++++++++++++ figs/bode_plot_cur_controller.pdf | Bin 0 -> 50614 bytes figs/bode_plot_cur_controller.png | Bin 0 -> 89380 bytes figs/bode_plot_dcm_dynamics.pdf | Bin 0 -> 262633 bytes figs/bode_plot_dcm_dynamics.png | Bin 0 -> 181567 bytes figs/bode_plot_ident_noise.pdf | 1895 ++++++++++++++++++ figs/bode_plot_ident_noise.png | Bin 0 -> 202546 bytes figs/coherence_id_dcm_dyn.pdf | Bin 0 -> 75132 bytes figs/coherence_id_dcm_dyn.png | Bin 0 -> 66886 bytes figs/coherence_ident_noise.pdf | Bin 0 -> 42406 bytes figs/coherence_ident_noise.png | Bin 0 -> 71751 bytes figs/loci_loop_gain_comp_controllers.pdf | Bin 0 -> 1399184 bytes figs/loci_loop_gain_comp_controllers.png | Bin 0 -> 60278 bytes figs/loop_gain_compare.pdf | 1385 +++++++++++++ figs/loop_gain_compare.png | Bin 0 -> 173362 bytes figs/loop_gain_compare_added_gain.pdf | Bin 0 -> 59505 bytes figs/loop_gain_compare_added_gain.png | Bin 0 -> 122292 bytes figs/loop_gain_dcm_contr_simple.pdf | Bin 0 -> 73053 bytes figs/loop_gain_dcm_contr_simple.png | Bin 0 -> 146411 bytes figs/loop_gain_diag_old_new_contr.pdf | 1523 ++++++++++++++ figs/loop_gain_diag_old_new_contr.png | Bin 0 -> 161617 bytes figs/noise_budget_no_mov_asd.pdf | Bin 0 -> 84461 bytes figs/noise_budget_no_mov_asd.png | Bin 0 -> 94925 bytes figs/noise_budget_no_mov_cas.pdf | Bin 0 -> 73268 bytes figs/noise_budget_no_mov_cas.png | Bin 0 -> 52995 bytes figs/nyquist_after_gain_frequency.pdf | Bin 0 -> 291252 bytes figs/nyquist_after_gain_frequency.png | Bin 0 -> 60826 bytes figs/nyquist_compare.pdf | Bin 0 -> 600914 bytes figs/nyquist_compare.png | Bin 0 -> 61891 bytes figs/sensitivity_comp.pdf | Bin 0 -> 34231 bytes figs/sensitivity_comp.png | Bin 0 -> 83082 bytes figs/sensitivity_function_compare.pdf | Bin 0 -> 41879 bytes figs/sensitivity_function_compare.png | Bin 0 -> 87225 bytes figs/sensitivity_function_drx_est.pdf | Bin 0 -> 22253 bytes figs/sensitivity_function_drx_est.png | Bin 0 -> 51071 bytes figs/sensitivity_new_gain_compare.pdf | Bin 0 -> 46360 bytes figs/sensitivity_new_gain_compare.png | Bin 0 -> 98866 bytes index.html | 1 + ref.bib | 11 + 44 files changed, 8869 insertions(+) create mode 100644 .gitignore create mode 100644 X_tal_cage_PID.dat create mode 100644 X_tal_cage_PID_20Hz.dat create mode 100644 X_tal_cage_PID_40Hz.dat create mode 100644 dcm_feedback.html create mode 100644 dcm_feedback.org create mode 100644 figs/bode_plot_cur_controller.pdf create mode 100644 figs/bode_plot_cur_controller.png create mode 100644 figs/bode_plot_dcm_dynamics.pdf create mode 100644 figs/bode_plot_dcm_dynamics.png create mode 100644 figs/bode_plot_ident_noise.pdf create mode 100644 figs/bode_plot_ident_noise.png create mode 100644 figs/coherence_id_dcm_dyn.pdf create mode 100644 figs/coherence_id_dcm_dyn.png create mode 100644 figs/coherence_ident_noise.pdf create mode 100644 figs/coherence_ident_noise.png create mode 100644 figs/loci_loop_gain_comp_controllers.pdf create mode 100644 figs/loci_loop_gain_comp_controllers.png create mode 100644 figs/loop_gain_compare.pdf create mode 100644 figs/loop_gain_compare.png create mode 100644 figs/loop_gain_compare_added_gain.pdf create mode 100644 figs/loop_gain_compare_added_gain.png create mode 100644 figs/loop_gain_dcm_contr_simple.pdf create mode 100644 figs/loop_gain_dcm_contr_simple.png create mode 100644 figs/loop_gain_diag_old_new_contr.pdf create mode 100644 figs/loop_gain_diag_old_new_contr.png create mode 100644 figs/noise_budget_no_mov_asd.pdf create mode 100644 figs/noise_budget_no_mov_asd.png create mode 100644 figs/noise_budget_no_mov_cas.pdf create mode 100644 figs/noise_budget_no_mov_cas.png create mode 100644 figs/nyquist_after_gain_frequency.pdf create mode 100644 figs/nyquist_after_gain_frequency.png create mode 100644 figs/nyquist_compare.pdf create mode 100644 figs/nyquist_compare.png create mode 100644 figs/sensitivity_comp.pdf create mode 100644 figs/sensitivity_comp.png create mode 100644 figs/sensitivity_function_compare.pdf create mode 100644 figs/sensitivity_function_compare.png create mode 100644 figs/sensitivity_function_drx_est.pdf create mode 100644 figs/sensitivity_function_drx_est.png create mode 100644 figs/sensitivity_new_gain_compare.pdf create mode 100644 figs/sensitivity_new_gain_compare.png create mode 120000 index.html create mode 100644 ref.bib diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..448bf18 --- /dev/null +++ b/.gitignore @@ -0,0 +1,62 @@ +auto/ +*.tex +*.blg +*-blx.bib +*.bbl +*.aux +*.bcf +*.fdb_latexmk +*.log +*.out +*.pyg +*.toc +*.fls +*.synctex.gz +.auctex-auto/ +_minted* + +# Emacs +auto/ + +# Simulink Real Time +*bio.m +*pt.m +*ref.m +*ri.m +*xcp.m +*.mldatx +*.slxc +*.xml +*_slrt_rtw/ + +# data +data/ + +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +*.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Octave session info +octave-workspace diff --git a/X_tal_cage_PID.dat b/X_tal_cage_PID.dat new file mode 100644 index 0000000..c915b55 --- /dev/null +++ b/X_tal_cage_PID.dat @@ -0,0 +1,2 @@ +5.162191577102395387e-03 -2.053193047675045887e-02 3.437100092354096470e-02 -3.190511345800899762e-02 1.825561277900273824e-02 -6.730753847845586182e-03 1.609313664393750756e-03 -2.418167184233736648e-04 2.080021948522915606e-05 -7.826806603216290806e-07 +1.000000000000000000e+00 -3.972465476658959549e+00 6.626337189494686086e+00 -6.128136890264569203e+00 3.494831182648804546e+00 -1.284884631665979438e+00 3.064788332575871244e-01 -4.595824894480127903e-02 3.946314534021262352e-03 -1.482724007899167095e-04 diff --git a/X_tal_cage_PID_20Hz.dat b/X_tal_cage_PID_20Hz.dat new file mode 100644 index 0000000..2b1c2c2 --- /dev/null +++ b/X_tal_cage_PID_20Hz.dat @@ -0,0 +1,2 @@ +0.000000000000000000e+00 5.123345318801274849e-08 4.465059381121026680e-07 -5.539687913181512777e-07 -2.501743723287252284e-07 4.670510404558542367e-07 -1.815336333351060151e-07 2.192959428607522490e-08 1.252880670660841008e-09 -3.204886304414573431e-10 +1.000000000000000000e+00 -6.060746556447895728e+00 1.578415410735246915e+01 -2.307024251152614625e+01 2.074784976168569983e+01 -1.185054476238084575e+01 4.286436819918846730e+00 -9.472094817634837405e-01 1.163875141380739525e-01 -6.084890976718200159e-03 diff --git a/X_tal_cage_PID_40Hz.dat b/X_tal_cage_PID_40Hz.dat new file mode 100644 index 0000000..0056390 --- /dev/null +++ b/X_tal_cage_PID_40Hz.dat @@ -0,0 +1,2 @@ +0.000000000000000000e+00 3.916109097006016097e-07 2.515883048071752841e-06 -1.090504899940038926e-05 1.026142643551294789e-05 4.402028213713516958e-06 -1.146749093764098578e-05 5.276493222335721915e-06 -3.762905854779865629e-07 -9.858859748285918252e-08 +1.000000000000000000e+00 -8.082077716891920005e+00 2.883885831460112215e+01 -5.954352319604579691e+01 7.824427684619810464e+01 -6.768295458210708659e+01 3.839583227756439499e+01 -1.369753827515415878e+01 2.763766524255220958e+00 -2.366401924198855977e-01 diff --git a/dcm_feedback.html b/dcm_feedback.html new file mode 100644 index 0000000..3fef167 --- /dev/null +++ b/dcm_feedback.html @@ -0,0 +1,1693 @@ + + + + + + +ESRF Double Crystal Monochromator - Feedback Controller + + + + + + +
+ UP + | + HOME +
+

ESRF Double Crystal Monochromator - Feedback Controller

+ +
+

This report is also available as a pdf.

+
+ +
+

1. Estimation of Sensitivity Function

+
+
+
+

1.1. Load Data

+
+

+Two scans are performed: +

+
    +
  • 1.1 in mode B
    • +
  • 3.1 in mode C
    • +
+ +

+The difference between the two is that mode C adds the feedback controller. +

+ +
+
%% Load Data of the new LUT method
+Ts = 0.1;
+
+ol_drx = 1e-9*double(h5read('xanes_0003.h5','/1.1/measurement/xtal_111_drx_filter')); % Rx [rad]
+cl_drx = 1e-9*double(h5read('xanes_0003.h5','/3.1/measurement/xtal_111_drx_filter')); % Rx [rad]
+
+ol_dry = 1e-9*double(h5read('xanes_0003.h5','/1.1/measurement/xtal_111_dry_filter')); % Ry [rad]
+cl_dry = 1e-9*double(h5read('xanes_0003.h5','/3.1/measurement/xtal_111_dry_filter')); % Ry [rad]
+
+t = linspace(Ts, Ts*length(ol_drx), length(ol_drx));
+
+
+ +

+By comparison the frequency content of the crystal orientation errors between mode B and mode C, it is possible to estimate the Sensitivity transfer function (Figure 1). +

+
+
win = hanning(ceil(1/Ts));
+
+[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts);
+[pxx_cl_drx, ~] = pwelch(cl_drx, win, [], [], 1/Ts);
+
+[pxx_ol_dry, ~] = pwelch(ol_dry, win, [], [], 1/Ts);
+[pxx_cl_dry, ~] = pwelch(cl_dry, win, [], [], 1/Ts);
+
+
+ + +
+

sensitivity_function_drx_est.png +

+

Figure 1: Estimation of the sensitivity transfer function magnitude

+
+
+
+ + +
+

1.2. Controller

+
+
+
load('X_tal_cage_PID.mat', 'K');
+
+
+ + +
+

bode_plot_cur_controller.png +

+

Figure 2: Bode Plot of the Controller

+
+
+
+ +
+

1.3. Test

+
+
+
Ts = 5e-3;
+cl_drx = 1e-9*double(h5read('xanes_0003.h5','/16.1/measurement/xtal_111_drx_filter')); % Rx [rad]
+ol_drx = 1e-9*double(h5read('xanes_0003.h5','/18.1/measurement/xtal_111_drx_filter')); % Rx [rad]
+
+t = linspace(Ts, Ts*length(ol_drx), length(ol_drx));
+
+
+ +
+
figure;
+hold on;
+plot(t, ol_drx)
+plot(t, cl_drx)
+
+
+ +
+
win = hanning(ceil(10/Ts));
+
+[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts);
+[pxx_cl_drx, ~] = pwelch(cl_drx, win, [], [], 1/Ts);
+
+
+
+
+
+ +
+

2. System Identification

+
+
+
+

2.1. Identification

+
+
+
ur = load('FJPUR_step.mat');
+uh = load('FJPUH_step.mat');
+d  = load('FJPD_step.mat');
+
+
+ + + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1dz311
2dry311
3drx311
4dz111
5dry111
6drx111
7fjpur
8fjpuh
9fjpd
10bragg
+ +
+
ur.time = ur.time - ur.time(1);
+ur.allValues(:, 1) = ur.allValues(:, 1) - mean(ur.allValues(ur.time<1, 1));
+ur.allValues(:, 2) = ur.allValues(:, 2) - mean(ur.allValues(ur.time<1, 2));
+ur.allValues(:, 3) = ur.allValues(:, 3) - mean(ur.allValues(ur.time<1, 3));
+
+t_filt = ur.time > 48 & ur.time < 60;
+
+ur.u = ur.allValues(t_filt, 7);
+ur.y_111 = [-ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)];
+
+
+ +
+
uh.time = uh.time - uh.time(1);
+uh.allValues(:, 1) = uh.allValues(:, 1) - mean(uh.allValues(uh.time<1, 1));
+uh.allValues(:, 2) = uh.allValues(:, 2) - mean(uh.allValues(uh.time<1, 2));
+uh.allValues(:, 3) = uh.allValues(:, 3) - mean(uh.allValues(uh.time<1, 3));
+
+uh.u = uh.allValues(t_filt, 8);
+uh.y_111 = [-uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)];
+
+
+ +
+
d.time = d.time - d.time(1);
+d.allValues(:, 1) = d.allValues(:, 1) - mean(d.allValues(d.time<1, 1));
+d.allValues(:, 2) = d.allValues(:, 2) - mean(d.allValues(d.time<1, 2));
+d.allValues(:, 3) = d.allValues(:, 3) - mean(d.allValues(d.time<1, 3));
+
+d.u = d.allValues(t_filt, 9);
+d.y_111 = [-d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)];
+
+
+ +
+
J_a_111 = [1,  0.14, -0.0675
+           1,  0.14,  0.1525
+           1, -0.14,  0.0425];
+
+J_a_311 = [1,  0.14, -0.1525
+           1,  0.14,  0.0675
+           1, -0.14, -0.0425];
+
+ur.y = [J_a_311 * ur.y_111']';
+uh.y = [J_a_311 * uh.y_111']';
+d.y  = [J_a_311 * d.y_111']';
+
+
+ +
+
%% Sampling Time and Frequency
+Ts = 1e-4; % [s]
+Fs = 1/Ts; % [Hz]
+
+% Hannning Windows
+win = hanning(ceil(5*Fs));
+
+
+ +
+
%% And we get the frequency vector
+[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1/Ts);
+[G_uh, ~] = tfestimate(uh.u, uh.y, win, [], [], 1/Ts);
+[G_d,  ~] = tfestimate(d.u,  d.y,  win, [], [], 1/Ts);
+
+
+ +
+
[coh_ur, ~] = mscohere(ur.u, ur.y, win, [], [], 1/Ts);
+[coh_uh, ~] = mscohere(uh.u, uh.y, win, [], [], 1/Ts);
+[coh_d,  ~] = mscohere(d.u,  d.y,  win, [], [], 1/Ts);
+
+
+ + +
+

coherence_id_dcm_dyn.png +

+

Figure 3: Coherence

+
+ + + +
+

bode_plot_dcm_dynamics.png +

+

Figure 4: Bode Plot of the DCM dynamics in the frame of the fast jack.

+
+ + +
+
%% Previously used controller
+load('X_tal_cage_PID.mat', 'K');
+
+
+ +
+
%% Controller design
+s = tf('s');
+
+% Lead
+a  = 4;  % Amount of phase lead / width of the phase lead / high frequency gain
+wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s]
+
+% Low Pass Filter
+w0 = 2*pi*100; % Cut-off frequency [rad/s]
+xi = 0.4; % Damping Ratio
+
+Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);;
+
+
+ + +
+

loop_gain_dcm_contr_simple.png +

+

Figure 5: Loop gain

+
+ + + +
+

loop_gain_diag_old_new_contr.png +

+

Figure 6: Loop gain

+
+ +

+Compare Sensitivity functions +

+ +
+

sensitivity_comp.png +

+

Figure 7: Comparison of sensitivity functions

+
+ + +
+
L  = zeros(3, 3, length(f));
+Lb = zeros(3, 3, length(f));
+
+for i_f = 1:length(f)
+    L(:,:,i_f)  = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz');
+    Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz');
+end
+
+
+ + +
+

loci_loop_gain_comp_controllers.png +

+

Figure 8: Root Locus

+
+
+
+ + +
+

2.2. Identification - New

+
+
+
ur = load('FJPUR_step_new.mat');
+uh = load('FJPUH_step_new.mat');
+d  = load('FJPD_step_new.mat');
+
+
+ + + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1dz311
2dry311
3drx311
4dz111
5dry111
6drx111
7fjpur
8fjpuh
9fjpd
10bragg
+ +
+
ur.time = ur.time - ur.time(1);
+ur.allValues(:, 1) = ur.allValues(:, 1) - mean(ur.allValues(ur.time<0.1, 1));
+ur.allValues(:, 2) = ur.allValues(:, 2) - mean(ur.allValues(ur.time<0.1, 2));
+ur.allValues(:, 3) = ur.allValues(:, 3) - mean(ur.allValues(ur.time<0.1, 3));
+
+t_filt = ur.time < 5;
+
+ur.u = ur.allValues(t_filt, 7);
+ur.y_111 = [-ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)];
+
+
+ +
+
uh.time = uh.time - uh.time(1);
+uh.allValues(:, 1) = uh.allValues(:, 1) - mean(uh.allValues(uh.time<0.1, 1));
+uh.allValues(:, 2) = uh.allValues(:, 2) - mean(uh.allValues(uh.time<0.1, 2));
+uh.allValues(:, 3) = uh.allValues(:, 3) - mean(uh.allValues(uh.time<0.1, 3));
+
+uh.u = uh.allValues(t_filt, 8);
+uh.y_111 = [-uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)];
+
+
+ +
+
d.time = d.time - d.time(1);
+d.allValues(:, 1) = d.allValues(:, 1) - mean(d.allValues(d.time<0.1, 1));
+d.allValues(:, 2) = d.allValues(:, 2) - mean(d.allValues(d.time<0.1, 2));
+d.allValues(:, 3) = d.allValues(:, 3) - mean(d.allValues(d.time<0.1, 3));
+
+d.u = d.allValues(t_filt, 9);
+d.y_111 = [-d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)];
+
+
+ +
+
J_a_111 = [1,  0.14, -0.0675
+           1,  0.14,  0.1525
+           1, -0.14,  0.0425];
+
+J_a_311 = [1,  0.14, -0.1525
+           1,  0.14,  0.0675
+           1, -0.14, -0.0425];
+
+ur.y = [J_a_311 * ur.y_111']';
+uh.y = [J_a_311 * uh.y_111']';
+d.y  = [J_a_311 * d.y_111']';
+
+
+ +
+
%% Sampling Time and Frequency
+Ts = 1e-4; % [s]
+Fs = 1/Ts; % [Hz]
+
+% Hannning Windows
+win = hanning(ceil(5*Fs));
+
+
+ +
+
%% And we get the frequency vector
+[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1/Ts);
+[G_uh, ~] = tfestimate(uh.u, uh.y, win, [], [], 1/Ts);
+[G_d,  ~] = tfestimate(d.u,  d.y,  win, [], [], 1/Ts);
+
+
+ +
+
[coh_ur, ~] = mscohere(ur.u, ur.y, win, [], [], 1/Ts);
+[coh_uh, ~] = mscohere(uh.u, uh.y, win, [], [], 1/Ts);
+[coh_d,  ~] = mscohere(d.u,  d.y,  win, [], [], 1/Ts);
+
+
+ +
+
%% Previously used controller
+load('X_tal_cage_PID.mat', 'K');
+
+
+ +
+
%% Controller design
+s = tf('s');
+
+% Lead
+a  = 4;  % Amount of phase lead / width of the phase lead / high frequency gain
+wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s]
+
+% Low Pass Filter
+w0 = 2*pi*100; % Cut-off frequency [rad/s]
+xi = 0.4; % Damping Ratio
+
+Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);;
+
+
+ +

+Compare Sensitivity functions +

+ +
+

sensitivity_comp.png +

+

Figure 9: Comparison of sensitivity functions

+
+ + +
+
L  = zeros(3, 3, length(f));
+Lb = zeros(3, 3, length(f));
+
+for i_f = 1:length(f)
+    L(:,:,i_f)  = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz');
+    Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz');
+end
+
+
+ + +
+

loci_loop_gain_comp_controllers.png +

+

Figure 10: Root Locus

+
+
+
+ + +
+

2.3. Identification - White noise

+
+
+
ur = load('fjpur_white_noise.mat');
+uh = load('fjpuh_white_noise.mat');
+d  = load('fjpd_white_noise.mat');
+
+
+ + + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1dz111
2dry111
3drx111
4fjpur
5fjpuh
6fjpd
7bragg
+ +
+
ur.time = ur.time - ur.time(1);
+
+ur.drx = ur.drx - mean(ur.drx);
+ur.dry = ur.dry - mean(ur.dry);
+ur.dz  = ur.dz  - mean(ur.dz);
+
+
+ +
+
uh.time = uh.time - uh.time(1);
+
+uh.drx = uh.drx - mean(uh.drx);
+uh.dry = uh.dry - mean(uh.dry);
+uh.dz  = uh.dz  - mean(uh.dz);
+
+
+ +
+
d.time = d.time - d.time(1);
+
+d.drx = d.drx - mean(d.drx);
+d.dry = d.dry - mean(d.dry);
+d.dz  = d.dz  - mean(d.dz);
+
+
+ +
+
J_a_111 = [1,  0.14, -0.0675
+           1,  0.14,  0.1525
+           1, -0.14,  0.0425];
+
+ur.y = [J_a_111 * [-ur.dz, ur.dry, ur.drx]']';
+uh.y = [J_a_111 * [-uh.dz, uh.dry, uh.drx]']';
+d.y  = [J_a_111 * [-d.dz, d.dry, d.drx]']';
+
+
+ +
+
%% Sampling Time and Frequency
+Ts = 1e-4; % [s]
+Fs = 1/Ts; % [Hz]
+
+% Hannning Windows
+win = hanning(ceil(0.5*Fs));
+
+
+ +
+
%% And we get the frequency vector
+[G_ur, f] = tfestimate(ur.fjpur, ur.y, win, [], [], 1/Ts);
+[G_uh, ~] = tfestimate(uh.fjpuh, uh.y, win, [], [], 1/Ts);
+[G_d,  ~] = tfestimate(d.fjpd,   d.y,  win, [], [], 1/Ts);
+
+
+ +
+
[coh_ur, ~] = mscohere(ur.fjpur, ur.y, win, [], [], 1/Ts);
+[coh_uh, ~] = mscohere(uh.fjpuh, uh.y, win, [], [], 1/Ts);
+[coh_d,  ~] = mscohere(d.fjpd,   d.y,  win, [], [], 1/Ts);
+
+
+ + +
+

coherence_ident_noise.png +

+

Figure 11: description

+
+ + +
+

bode_plot_ident_noise.png +

+

Figure 12: Bode Plot of the DCM dynamics in the frame of the fast jack.

+
+ + +
+
%% Previously used controller
+load('X_tal_cage_PID.mat', 'K');
+
+
+ +
+
%% Controller design
+s = tf('s');
+
+% Lead
+a  = 8;  % Amount of phase lead / width of the phase lead / high frequency gain
+wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s]
+
+% Low Pass Filter
+w0 = 2*pi*80; % Cut-off frequency [rad/s]
+xi = 0.4; % Damping Ratio
+
+Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);;
+
+
+ + +
+

loop_gain_dcm_contr_simple.png +

+

Figure 13: Loop gain

+
+ + +
+

loop_gain_diag_old_new_contr.png +

+

Figure 14: Loop gain

+
+ +

+Compare Sensitivity functions +

+ +
+

sensitivity_comp.png +

+

Figure 15: Comparison of sensitivity functions

+
+ + +
+
L  = zeros(3, 3, length(f));
+Lb = zeros(3, 3, length(f));
+
+for i_f = 1:length(f)
+    L(:,:,i_f)  = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz');
+    Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz');
+end
+
+
+ + +
+

loci_loop_gain_comp_controllers.png +

+

Figure 16: Root Locus

+
+
+
+ + +
+

2.4. Test

+
+
+
%% Notch
+gm = 0.015;
+xi = 0.1;
+wn = 2*pi*208;
+
+K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
+
+
+ +
+
%% Double integrator
+w0 = 2*pi*40;
+K_int = (w0^2)/(s^2);
+
+
+ +
+
%% Lead
+a = 3;  % Amount of phase lead / width of the phase lead / high frequency gain
+K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a)));
+K_lead = K_lead*K_lead;
+
+
+ +
+
%% Low Pass Filter
+w0 = 2*pi*120; % Cut-off frequency [rad/s]
+xi = 0.3; % Damping Ratio
+
+K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
+
+
+ +
+
%% Diagonal controller
+Kb =  0.8*eye(3)*K_notch*K_int*K_lead*K_lpf;
+
+
+
+
+
+

2.5. New controller - Higher bandwidth

+
+
+
%% Previously used controller
+load('X_tal_cage_PID.mat', 'K');
+
+
+ +
+
%% Current Controller design
+% Lead
+a  = 8;  % Amount of phase lead / width of the phase lead / high frequency gain
+wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s]
+
+% Low Pass Filter
+w0 = 2*pi*80; % Cut-off frequency [rad/s]
+xi = 0.4; % Damping Ratio
+
+Kb_old = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);;
+
+
+ +
+
%% Notch
+gm = 0.015;
+xi = 0.2;
+wn = 2*pi*208;
+
+K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
+
+
+ +
+
%% Double integrator
+w0 = 2*pi*40;
+K_int = (w0^2)/(s^2);
+
+
+ +
+
%% Lead
+a = 3;  % Amount of phase lead / width of the phase lead / high frequency gain
+w0 = 2*pi*40;
+K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a)));
+K_lead = K_lead*K_lead;
+
+
+ +
+
%% Low Pass Filter
+w0 = 2*pi*120; % Cut-off frequency [rad/s]
+xi = 0.3; % Damping Ratio
+
+K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
+
+
+ +
+
%% Diagonal controller
+Kb =  0.9*eye(3)*K_notch*K_int*K_lead*K_lpf;
+
+
+ + +
+

loop_gain_compare.png +

+

Figure 17: description

+
+ + +
+
L  = zeros(3, 3, length(f));
+Lb = zeros(3, 3, length(f));
+Lb_new = zeros(3, 3, length(f));
+
+for i_f = 1:length(f)
+    L(:,:,i_f)  = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz');
+    Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb_old, f(i_f), 'Hz');
+    Lb_new(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz');
+end
+
+
+ + +
+

nyquist_compare.png +

+

Figure 18: n

+
+ + +
+

sensitivity_function_compare.png +

+

Figure 19: description

+
+
+
+ + + +
+

2.6. Added gain

+
+
+
%% Notch
+gm = 0.015;
+xi = 0.2;
+wn = 2*pi*208;
+
+K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
+
+
+ +
+
%% Double integrator
+w0 = 2*pi*40;
+K_int = (w0^2)/(s^2);
+
+
+ +
+
%% Lead
+a = 3;  % Amount of phase lead / width of the phase lead / high frequency gain
+w0 = 2*pi*40;
+K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a)));
+K_lead = K_lead*K_lead;
+
+
+ +
+
%% Low Pass Filter
+w0 = 2*pi*120; % Cut-off frequency [rad/s]
+xi = 0.3; % Damping Ratio
+
+K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
+
+
+ +
+
gm = 10;
+xi = 0.02;
+wn = 2*pi*15;
+
+H = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
+
+
+ +
+
%% Diagonal controller
+Kb_gain =  0.9*eye(3)*H*K_notch*K_int*K_lead*K_lpf;
+
+
+ +
+
Lb_gain = zeros(3, 3, length(f));
+
+for i_f = 1:length(f)
+    Lb_gain(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb_gain, f(i_f), 'Hz');
+end
+
+
+ + +
+

loop_gain_compare_added_gain.png +

+

Figure 20: description

+
+ + +
+

sensitivity_new_gain_compare.png +

+

Figure 21: description

+
+ + +
+

nyquist_after_gain_frequency.png +

+

Figure 22: nyquist plot

+
+
+
+
+ + +
+

3. Noise Budgeting

+
+
+
+

3.1. No Displacement

+
+ + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1dz311
2dry311
3drx311
4dz111
5dry111
6drx111
7fjpur
8fjpuh
9fjpd
10bragg
+ +
+
data_10_deg = load('no_mov_10.mat');
+data_70_deg = load('no_mov_70.mat');
+
+
+ +
+
data_10_deg = extractDatData('no_mov_10.mat', ...
+                             {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjpur", "fjpuh", "fjpd", "bragg"}, ...
+                             [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]);
+data_10_deg = processMeasData(data_10_deg);
+
+
+ +
+
Ts = 1e-4;
+t = Ts*[1:length(data_10_deg.bragg)];
+
+
+ +
+
data_10_deg.dz  = data_10_deg.allValues(:,4) - mean(data_10_deg.allValues(:,4));
+data_10_deg.dry = data_10_deg.allValues(:,5) - mean(data_10_deg.allValues(:,5));
+data_10_deg.drx = data_10_deg.allValues(:,6) - mean(data_10_deg.allValues(:,6));
+
+
+ +
+
%% Compute motion error in the frame of the fast jack
+J_a_111 = [1,  0.14, -0.1525
+           1,  0.14,  0.0675
+           1, -0.14,  0.0425];
+
+de_111 = [data_10_deg.dz'; data_10_deg.dry'; data_10_deg.drx'];
+de_fj = J_a_111*de_111;
+data_10_deg.fj_ur = de_fj(1,:)';
+data_10_deg.fj_uh = de_fj(2,:)';
+data_10_deg.fj_d  = de_fj(3,:)';
+
+de_111 = [data_70_deg.dz'; data_70_deg.dry'; data_70_deg.drx'];
+de_fj = J_a_111*de_111;
+data_70_deg.fj_ur = de_fj(1,:)';
+data_70_deg.fj_uh = de_fj(2,:)';
+data_70_deg.fj_d  = de_fj(3,:)';
+
+
+ +
+
win = hanning(ceil(1/Ts));
+
+[pxx_10_ur, f] = pwelch(data_10_deg.fj_ur, win, [], [], 1/Ts);
+[pxx_70_ur, ~] = pwelch(data_70_deg.fj_ur, win, [], [], 1/Ts);
+
+[pxx_10_uh, ~] = pwelch(data_10_deg.fj_uh, win, [], [], 1/Ts);
+[pxx_70_uh, ~] = pwelch(data_70_deg.fj_uh, win, [], [], 1/Ts);
+
+[pxx_10_d,  ~] = pwelch(data_10_deg.fj_d,  win, [], [], 1/Ts);
+[pxx_70_d,  ~] = pwelch(data_70_deg.fj_d,  win, [], [], 1/Ts);
+
+
+ +
+
CPS_10_ur = flip(-cumtrapz(flip(f), flip(pxx_10_ur)));
+CPS_10_uh = flip(-cumtrapz(flip(f), flip(pxx_10_uh)));
+CPS_10_d  = flip(-cumtrapz(flip(f), flip(pxx_10_d)));
+
+CPS_70_ur = flip(-cumtrapz(flip(f), flip(pxx_70_ur)));
+CPS_70_uh = flip(-cumtrapz(flip(f), flip(pxx_70_uh)));
+CPS_70_d  = flip(-cumtrapz(flip(f), flip(pxx_70_d)));
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(CPS_10_ur), '-' , 'color', colors(1, :), 'DisplayName', '10 deg - $u_r$')
+plot(f, sqrt(CPS_70_ur), '--', 'color', colors(1, :), 'DisplayName', '70 deg - $u_r$')
+plot(f, sqrt(CPS_10_uh), '-' , 'color', colors(2, :), 'DisplayName', '10 deg - $u_h$')
+plot(f, sqrt(CPS_70_uh), '--', 'color', colors(2, :), 'DisplayName', '70 deg - $u_h$')
+plot(f, sqrt(CPS_10_d),  '-' , 'color', colors(3, :), 'DisplayName', '10 deg - $d$')
+plot(f, sqrt(CPS_70_d),  '--', 'color', colors(3, :), 'DisplayName', '70 deg - $d$')
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(pxx_10_ur))
+plot(f, sqrt(pxx_70_ur))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+ +
+
data_70_deg.dz  = data_70_deg.allValues(:,4) - mean(data_70_deg.allValues(:,4));
+data_70_deg.dry = data_70_deg.allValues(:,5) - mean(data_70_deg.allValues(:,5));
+data_70_deg.drx = data_70_deg.allValues(:,6) - mean(data_70_deg.allValues(:,6));
+
+
+ +
+
win = hanning(ceil(1/Ts));
+
+[pxx_10_drx, f] = pwelch(data_10_deg.drx, win, [], [], 1/Ts);
+[pxx_70_drx, ~] = pwelch(data_70_deg.drx, win, [], [], 1/Ts);
+
+[pxx_10_dry, ~] = pwelch(data_10_deg.dry, win, [], [], 1/Ts);
+[pxx_70_dry, ~] = pwelch(data_70_deg.dry, win, [], [], 1/Ts);
+
+[pxx_10_dz,  ~] = pwelch(data_10_deg.dz,  win, [], [], 1/Ts);
+[pxx_70_dz,  ~] = pwelch(data_70_deg.dz,  win, [], [], 1/Ts);
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(pxx_10_drx))
+plot(f, sqrt(pxx_70_drx))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(pxx_10_dry))
+plot(f, sqrt(pxx_70_dry))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(pxx_10_dz))
+plot(f, sqrt(pxx_70_dz))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nm}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+
+
+ + + +
+

3.2. Scans

+
+ + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1dz311
2dry311
3drx311
4dz111
5dry111
6drx111
7fjpur
8fjpuh
9fjpd
10bragg
+ +
+
%% Load Data
+data_10_70_deg = extractDatData('thtraj_10_70.mat', ...
+                             {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjur", "fjuh", "fjd", "bragg"}, ...
+                             [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]);
+
+Ts = 1e-4;
+t = Ts*[1:length(data_10_70_deg.bragg)];
+
+%% Actuator Jacobian
+J_a_111 = [1,  0.14, -0.0675
+           1,  0.14,  0.1525
+           1, -0.14,  0.0425];
+
+data_10_70_deg.ddz  = 10.5e-3./(2*cos(data_10_70_deg.bragg)) - data_10_70_deg.dz;
+
+%% Computation of the position of the FJ as measured by the interferometers
+error = J_a_111 * [data_10_70_deg.ddz, data_10_70_deg.dry, data_10_70_deg.drx]';
+
+data_10_70_deg.fjur_e = error(1,:)'; % [m]
+data_10_70_deg.fjuh_e = error(2,:)'; % [m]
+data_10_70_deg.fjd_e  = error(3,:)'; % [m]
+
+
+ +
+
%% Load Data
+data_70_10_deg = extractDatData('thtraj_70_10.mat', ...
+                             {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjur", "fjuh", "fjd", "bragg"}, ...
+                             [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]);
+%% Actuator Jacobian
+J_a_111 = [1,  0.14, -0.0675
+           1,  0.14,  0.1525
+           1, -0.14,  0.0425];
+
+data_70_10_deg.ddz  = 10.5e-3./(2*cos(data_70_10_deg.bragg)) - data_70_10_deg.dz;
+
+%% Computation of the position of the FJ as measured by the interferometers
+error = J_a_111 * [data_70_10_deg.ddz, data_70_10_deg.dry, data_70_10_deg.drx]';
+
+data_70_10_deg.fjur_e = error(1,:)'; % [m]
+data_70_10_deg.fjuh_e = error(2,:)'; % [m]
+data_70_10_deg.fjd_e  = error(3,:)'; % [m]
+
+
+ +
+
win = hanning(ceil(1/Ts));
+
+[pxx_10_70_ur, f] = pwelch(data_10_70_deg.fjur_e(t<100), win, [], [], 1/Ts);
+[pxx_70_10_ur, ~] = pwelch(data_70_10_deg.fjur_e(t<100), win, [], [], 1/Ts);
+
+[pxx_10_70_uh, ~] = pwelch(data_10_70_deg.fjuh_e(t<100), win, [], [], 1/Ts);
+[pxx_70_10_uh, ~] = pwelch(data_70_10_deg.fjuh_e(t<100), win, [], [], 1/Ts);
+
+[pxx_10_70_d,  ~] = pwelch(data_10_70_deg.fjd_e(t<100),  win, [], [], 1/Ts);
+[pxx_70_10_d,  ~] = pwelch(data_70_10_deg.fjd_e(t<100),  win, [], [], 1/Ts);
+
+
+ +
+
CPS_10_70_ur = flip(-cumtrapz(flip(f), flip(pxx_10_70_ur)));
+CPS_10_70_uh = flip(-cumtrapz(flip(f), flip(pxx_10_70_uh)));
+CPS_10_70_d  = flip(-cumtrapz(flip(f), flip(pxx_10_70_d)));
+
+CPS_70_10_ur = flip(-cumtrapz(flip(f), flip(pxx_70_10_ur)));
+CPS_70_10_uh = flip(-cumtrapz(flip(f), flip(pxx_70_10_uh)));
+CPS_70_10_d  = flip(-cumtrapz(flip(f), flip(pxx_70_10_d)));
+
+
+ +
+
figure;
+hold on;
+plot(f, 1e9*sqrt(CPS_10_70_ur))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+ +
+
figure;
+hold on;
+plot(f, sqrt(pxx_10_70_ur))
+plot(f, sqrt(pxx_70_10_ur))
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]');
+legend('location', 'northwest');
+xlim([1, 1e3]);
+
+
+
+
+ +
+

3.3. Noise budgeting - No rotation

+
+

+First, we look at the position errors when the bragg axis is not moving +

+ +
+
%% Load Measurement Data
+ol_data = load('FJPUR_step.mat');
+
+
+ +
+
%% Pre-processing
+ol_time = ol_data.time - ol_data.time(1);
+
+ol_drx = ol_data.allValues(ol_time < 45, 6);
+ol_dry = ol_data.allValues(ol_time < 45, 5);
+ol_dz  = ol_data.allValues(ol_time < 45, 4);
+
+ol_drx = ol_drx - mean(ol_drx);
+ol_dry = ol_dry - mean(ol_dry);
+ol_dz = ol_dz - mean(ol_dz);
+
+ol_time = ol_time(ol_time < 45);
+
+
+ +
+
figure;
+plot(ol_time, ol_drx)
+
+
+ +
+
%% Parameters for Spectral Analysis
+Ts = 1e-4;
+win = hanning(ceil(1/Ts));
+
+
+ +
+
%% Computation of the PSD
+[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts);
+[pxx_ol_dry, ~] = pwelch(ol_dry, win, [], [], 1/Ts);
+[pxx_ol_dz,  ~] = pwelch(ol_dz,  win, [], [], 1/Ts);
+
+
+ + +
+

noise_budget_no_mov_asd.png +

+

Figure 23: Amplitude Spectral Density

+
+ +
+
%% Cumulative Spectral Density
+CPS_drx = flip(-cumtrapz(flip(f), flip(pxx_ol_drx)));
+CPS_dry = flip(-cumtrapz(flip(f), flip(pxx_ol_dry)));
+CPS_dz  = flip(-cumtrapz(flip(f), flip(pxx_ol_dz)));
+
+
+ +
+
%% Cumulative Spectral Density
+CPS_drx = cumtrapz(f, pxx_ol_drx);
+CPS_dry = cumtrapz(f, pxx_ol_dry);
+CPS_dz  = cumtrapz(f, pxx_ol_dz);
+
+
+ + +
+

noise_budget_no_mov_cas.png +

+

Figure 24: Cumulative Amplitude Spectrum

+
+
+
+ + +
+

3.4. Noise budgeting - Bragg rotation

+
+
+ +
+

4. Test Mode C

+
+
+
+

4.1. Mode B and Mode C

+
+
+
data_B = extractDatData(sprintf("/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s","lut_const_fj_vel_19012022_1450.dat"), ...
+                             {"bragg", "dz", "dry", "drx", "fjur", "fjuh", "fjd"}, ...
+                             [pi/180, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8]);
+data_B = processMeasData(data_B);
+
+
+ +
+
data_C = extractDatData(sprintf("/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s","lut_const_fj_vel_19012022_1454.dat"), ...
+                             {"bragg", "dz", "dry", "drx", "fjur", "fjuh", "fjd"}, ...
+                             [pi/180, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8]);
+data_C = processMeasData(data_C);
+
+
+ +
+
figure;
+hold on;
+plot(180/pi*data_B.bragg, 1e9*data_B.drx)
+hold off;
+xlabel('Bragg Angle [deg]'); ylabel('DRX [nrad]');
+
+
+ +
+
figure;
+hold on;
+plot(180/pi*data_B.bragg, 1e9*data_B.fjur_e_filt)
+plot(180/pi*data_C.bragg, 1e9*data_C.fjur_e_filt)
+hold off;
+xlabel('Bragg Angle [deg]'); ylabel('FJUR Error [nm]');
+
+
+ +
+
figure;
+hold on;
+plot(180/pi*data_B.bragg, 1e9*data_B.fjur_e)
+plot(180/pi*data_C.bragg, 1e9*data_C.fjur_e)
+hold off;
+xlabel('Bragg Angle [deg]'); ylabel('FJUR Error [nm]');
+
+
+ +
+
%% FIR Filter
+Fs = 1e4; % Sampling Frequency [Hz]
+fir_order = 5000; % Filter's order
+delay = fir_order/2; % Delay induced by the filter
+B_fir = firls(5000, ... % Filter's order
+              [0 5/(Fs/2)  10/(Fs/2) 1], ... % Frequencies [Hz]
+              [1 1          0        0]); % Wanted Magnitudes
+
+
+ +
+
%% Filtering all measured Fast Jack Position using the FIR filter
+data_B.drx_filter = filter(B_fir, 1, data_B.drx);
+data_B.drx_filter(1:end-delay) = data_B.drx_filter(delay+1:end);
+
+data_C.drx_filter = filter(B_fir, 1, data_C.drx);
+data_C.drx_filter(1:end-delay) = data_C.drx_filter(delay+1:end);
+
+
+ +
+
figure;
+hold on;
+plot(180/pi*data_B.bragg, 1e9*data_B.drx_filter)
+plot(180/pi*data_C.bragg, 1e9*data_C.drx_filter)
+hold off;
+xlabel('Bragg Angle [deg]'); ylabel('DRX [nrad]');
+
+
+ +
+
Ts = 1e-4;
+win = hanning(ceil(1/Ts));
+
+[pxx_B_drx, f] = pwelch(data_B.drx, win, [], [], 1/Ts);
+[pxx_C_drx, ~] = pwelch(data_C.drx, win, [], [], 1/Ts);
+
+
+
+
+
+ +
+

5. Export numerator and denominator

+
+
+
+

5.1. Export

+
+
+
K_order = 10;
+
+
+ +
+
load('X_tal_cage_PID.mat', 'K');
+K_order = order(K(1,1));
+Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4);
+[num, den] = tfdata(Kz, 'v');
+
+formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n';
+fileID = fopen('X_tal_cage_PID.dat', 'w');
+fprintf(fileID, formatSpec, [num; den]');
+fclose(fileID);
+
+
+ +
+
load('X_tal_cage_PID_20Hz.mat', 'K');
+K_order = order(K(1,1));
+Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4);
+[num, den] = tfdata(Kz, 'v');
+
+formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n';
+fileID = fopen('X_tal_cage_PID_20Hz.dat', 'w');
+fprintf(fileID, formatSpec, [num; den]');
+fclose(fileID);
+
+
+ +
+
load('X_tal_cage_PID_40Hz.mat', 'K');
+K_order = order(K(1,1));
+Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4);
+[num, den] = tfdata(Kz, 'v');
+
+formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n';
+fileID = fopen('X_tal_cage_PID_40Hz.dat', 'w');
+fprintf(fileID, formatSpec, [num; den]');
+fclose(fileID);
+
+
+
+
+ +
+

5.2. Verify

+
+
+
K_data = importdata('X_tal_cage_PID_20Hz.dat');
+K = tf(K_data(1,:), K_data(2,:), 1e-4)
+
+
+
+
+
+
+
+

Author: Dehaeze Thomas

+

Created: 2022-02-15 mar. 14:15

+
+ + diff --git a/dcm_feedback.org b/dcm_feedback.org new file mode 100644 index 0000000..bfb5ea7 --- /dev/null +++ b/dcm_feedback.org @@ -0,0 +1,2293 @@ +#+TITLE: ESRF Double Crystal Monochromator - Feedback Controller +:DRAWER: +#+LANGUAGE: en +#+EMAIL: dehaeze.thomas@gmail.com +#+AUTHOR: Dehaeze Thomas + +#+HTML_LINK_HOME: ../index.html +#+HTML_LINK_UP: ../index.html + +#+HTML_HEAD: +#+HTML_HEAD: + +#+BIND: org-latex-image-default-option "scale=1" +#+BIND: org-latex-image-default-width "" + +#+LaTeX_CLASS: scrreprt +#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full] +#+LaTeX_HEADER_EXTRA: \input{preamble.tex} +#+LATEX_HEADER_EXTRA: \bibliography{ref} + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :tangle no +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :noweb yes +#+PROPERTY: header-args:matlab+ :mkdirp yes +#+PROPERTY: header-args:matlab+ :output-dir figs + +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}") +#+PROPERTY: header-args:latex+ :imagemagick t :fit yes +#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 +#+PROPERTY: header-args:latex+ :imoutoptions -quality 100 +#+PROPERTY: header-args:latex+ :results file raw replace +#+PROPERTY: header-args:latex+ :buffer no +#+PROPERTY: header-args:latex+ :tangle no +#+PROPERTY: header-args:latex+ :eval no-export +#+PROPERTY: header-args:latex+ :exports results +#+PROPERTY: header-args:latex+ :mkdirp yes +#+PROPERTY: header-args:latex+ :output-dir figs +#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") +:END: + +#+begin_export html +
+

This report is also available as a pdf.

+
+#+end_export + +#+latex: \clearpage + +* Introduction :ignore: + +* Estimation of Sensitivity Function +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no :noweb yes +<> +#+end_src + +#+begin_src matlab :eval no :noweb yes +<> +#+end_src + +#+begin_src matlab :noweb yes +<> +#+end_src + +** Load Data +Two scans are performed: +- =1.1= in mode B +- =3.1= in mode C + +The difference between the two is that mode C adds the feedback controller. + +#+begin_src matlab +%% Load Data of the new LUT method +Ts = 0.1; + +ol_drx = 1e-9*double(h5read('xanes_0003.h5','/1.1/measurement/xtal_111_drx_filter')); % Rx [rad] +cl_drx = 1e-9*double(h5read('xanes_0003.h5','/3.1/measurement/xtal_111_drx_filter')); % Rx [rad] + +ol_dry = 1e-9*double(h5read('xanes_0003.h5','/1.1/measurement/xtal_111_dry_filter')); % Ry [rad] +cl_dry = 1e-9*double(h5read('xanes_0003.h5','/3.1/measurement/xtal_111_dry_filter')); % Ry [rad] + +t = linspace(Ts, Ts*length(ol_drx), length(ol_drx)); +#+end_src + +By comparison the frequency content of the crystal orientation errors between mode B and mode C, it is possible to estimate the Sensitivity transfer function (Figure [[fig:sensitivity_function_drx_est]]). +#+begin_src matlab +win = hanning(ceil(1/Ts)); + +[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts); +[pxx_cl_drx, ~] = pwelch(cl_drx, win, [], [], 1/Ts); + +[pxx_ol_dry, ~] = pwelch(ol_dry, win, [], [], 1/Ts); +[pxx_cl_dry, ~] = pwelch(cl_dry, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Estimation of Sensitivity function +figure; +hold on; +plot(f, sqrt(pxx_cl_drx)./sqrt(pxx_ol_drx), 'DisplayName', '$R_x$'); +plot(f, sqrt(pxx_cl_dry)./sqrt(pxx_ol_dry), 'DisplayName', '$R_y$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Sensitivity Function'); +legend('location', 'northwest'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_function_drx_est.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:sensitivity_function_drx_est +#+caption: Estimation of the sensitivity transfer function magnitude +#+RESULTS: +[[file:figs/sensitivity_function_drx_est.png]] + + +** Controller +#+begin_src matlab +load('X_tal_cage_PID.mat', 'K'); +#+end_src + +#+begin_src matlab :exports none +%% Bode plot for the controller +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(freqs, abs(squeeze(freqresp(K(1,1), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [-]'); set(gca, 'XTickLabel',[]); + +ax2 = nexttile; +hold on; +plot(freqs, 180/pi*angle(squeeze(freqresp(K(1,1), freqs, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); +ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/bode_plot_cur_controller.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:bode_plot_cur_controller +#+caption: Bode Plot of the Controller +#+RESULTS: +[[file:figs/bode_plot_cur_controller.png]] + +** Test +#+begin_src matlab +Ts = 5e-3; +cl_drx = 1e-9*double(h5read('xanes_0003.h5','/16.1/measurement/xtal_111_drx_filter')); % Rx [rad] +ol_drx = 1e-9*double(h5read('xanes_0003.h5','/18.1/measurement/xtal_111_drx_filter')); % Rx [rad] + +t = linspace(Ts, Ts*length(ol_drx), length(ol_drx)); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(t, ol_drx) +plot(t, cl_drx) +#+end_src + +#+begin_src matlab +win = hanning(ceil(10/Ts)); + +[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts); +[pxx_cl_drx, ~] = pwelch(cl_drx, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Estimation of Sensitivity function +figure; +hold on; +plot(f, sqrt(pxx_cl_drx)./sqrt(pxx_ol_drx), 'DisplayName', '$R_x$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Sensitivity Function'); +legend('location', 'northwest'); +#+end_src + +#+begin_src matlab :exports none +%% Estimation of Sensitivity function +figure; +hold on; +plot(f, sqrt(pxx_ol_drx), 'DisplayName', '$R_x$ - OL'); +plot(f, sqrt(pxx_cl_drx), 'DisplayName', '$R_x$ - CL'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density [$m/\sqrt{Hz}$]'); +legend('location', 'northwest'); +#+end_src + +* System Identification +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no :noweb yes +<> +#+end_src + +#+begin_src matlab :eval no :noweb yes +<> +#+end_src + +#+begin_src matlab :noweb yes +<> +#+end_src + +** Identification +#+begin_src matlab +ur = load('FJPUR_step.mat'); +uh = load('FJPUH_step.mat'); +d = load('FJPD_step.mat'); +#+end_src + +| 1 | dz311 | +| 2 | dry311 | +| 3 | drx311 | +| 4 | dz111 | +| 5 | dry111 | +| 6 | drx111 | +| 7 | fjpur | +| 8 | fjpuh | +| 9 | fjpd | +| 10 | bragg | + +#+begin_src matlab +ur.time = ur.time - ur.time(1); +ur.allValues(:, 1) = ur.allValues(:, 1) - mean(ur.allValues(ur.time<1, 1)); +ur.allValues(:, 2) = ur.allValues(:, 2) - mean(ur.allValues(ur.time<1, 2)); +ur.allValues(:, 3) = ur.allValues(:, 3) - mean(ur.allValues(ur.time<1, 3)); + +t_filt = ur.time > 48 & ur.time < 60; + +ur.u = ur.allValues(t_filt, 7); +ur.y_111 = [-ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +uh.time = uh.time - uh.time(1); +uh.allValues(:, 1) = uh.allValues(:, 1) - mean(uh.allValues(uh.time<1, 1)); +uh.allValues(:, 2) = uh.allValues(:, 2) - mean(uh.allValues(uh.time<1, 2)); +uh.allValues(:, 3) = uh.allValues(:, 3) - mean(uh.allValues(uh.time<1, 3)); + +uh.u = uh.allValues(t_filt, 8); +uh.y_111 = [-uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +d.time = d.time - d.time(1); +d.allValues(:, 1) = d.allValues(:, 1) - mean(d.allValues(d.time<1, 1)); +d.allValues(:, 2) = d.allValues(:, 2) - mean(d.allValues(d.time<1, 2)); +d.allValues(:, 3) = d.allValues(:, 3) - mean(d.allValues(d.time<1, 3)); + +d.u = d.allValues(t_filt, 9); +d.y_111 = [-d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; + +J_a_311 = [1, 0.14, -0.1525 + 1, 0.14, 0.0675 + 1, -0.14, -0.0425]; + +ur.y = [J_a_311 * ur.y_111']'; +uh.y = [J_a_311 * uh.y_111']'; +d.y = [J_a_311 * d.y_111']'; +#+end_src + +#+begin_src matlab +%% Sampling Time and Frequency +Ts = 1e-4; % [s] +Fs = 1/Ts; % [Hz] + +% Hannning Windows +win = hanning(ceil(5*Fs)); +#+end_src + +#+begin_src matlab +%% And we get the frequency vector +[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1/Ts); +[G_uh, ~] = tfestimate(uh.u, uh.y, win, [], [], 1/Ts); +[G_d, ~] = tfestimate(d.u, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +[coh_ur, ~] = mscohere(ur.u, ur.y, win, [], [], 1/Ts); +[coh_uh, ~] = mscohere(uh.u, uh.y, win, [], [], 1/Ts); +[coh_d, ~] = mscohere(d.u, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Coherence +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); +hold on; +plot(f, coh_ur(:,1), 'DisplayName', '$u_r$'); +plot(f, coh_uh(:,2), 'DisplayName', '$u_h$'); +plot(f, coh_d( :,3), 'DisplayName', '$u_d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Coherence'); +legend('location', 'southeast'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/coherence_id_dcm_dyn.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:coherence_id_dcm_dyn +#+caption: Coherence +#+RESULTS: +[[file:figs/coherence_id_dcm_dyn.png]] + + +#+begin_src matlab :exports none +%% Bode plot of the DCM dynamics in the frame of the Fast Jacks +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1)), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2)), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3)), 'DisplayName', '$u_d$'); +plot(f, abs(G_ur(:,2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', 'Off Diagonal'); +plot(f, abs(G_ur(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,2)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-2, 1e2]); +legend('location', 'southeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1))); +plot(f, 180/pi*angle(G_uh(:,2))); +plot(f, 180/pi*angle(G_d(:,3))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); +% ylim([-45, 45]); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/bode_plot_dcm_dynamics.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:bode_plot_dcm_dynamics +#+caption: Bode Plot of the DCM dynamics in the frame of the fast jack. +#+RESULTS: +[[file:figs/bode_plot_dcm_dynamics.png]] + + +#+begin_src matlab +%% Previously used controller +load('X_tal_cage_PID.mat', 'K'); +#+end_src + +#+begin_src matlab +%% Controller design +s = tf('s'); + +% Lead +a = 4; % Amount of phase lead / width of the phase lead / high frequency gain +wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s] + +% Low Pass Filter +w0 = 2*pi*100; % Cut-off frequency [rad/s] +xi = 0.4; % Damping Ratio + +Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);; +#+end_src + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz'))), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3).*squeeze(freqresp(Kb(3,3), f, 'Hz'))), 'DisplayName', '$d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); +legend('location', 'northeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_uh(:,2).*squeeze(freqresp(K(2,2), f, 'Hz')))); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(K(3,3), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_dcm_contr_simple.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_dcm_contr_simple +#+caption: Loop gain +#+RESULTS: +[[file:figs/loop_gain_dcm_contr_simple.png]] + + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, abs(G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_diag_old_new_contr.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_diag_old_new_contr +#+caption: Loop gain +#+RESULTS: +[[file:figs/loop_gain_diag_old_new_contr.png]] + +Compare Sensitivity functions +#+begin_src matlab :exports none +%% Sensitivity function +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +hold on; +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude'); +ylim([1e-2, 1e1]); xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_comp.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:sensitivity_comp +#+caption: Comparison of sensitivity functions +#+RESULTS: +[[file:figs/sensitivity_comp.png]] + + +#+begin_src matlab +L = zeros(3, 3, length(f)); +Lb = zeros(3, 3, length(f)); + +for i_f = 1:length(f) + L(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz'); + Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz'); +end +#+end_src + +#+begin_src matlab :exports none +%% Compute the Eigenvalues of the loop gain +Ldet = zeros(3, length(f)); +Ldetb = zeros(3, length(f)); + +% Loop gain +for i_f = 1:length(f) + Ldet( :, i_f) = eig(squeeze(L( :,:,i_f))); + Ldetb(:, i_f) = eig(squeeze(Lb(:,:,i_f))); +end +#+end_src + +#+begin_src matlab :exports none +%% Plot of the eigenvalues of L in the complex plane +figure; +hold on; +for i = 1:size(Ldet,1) + plot(real(Ldet(i,:)), imag(Ldet(i,:)), '.', 'color', colors(1, :)); + plot(real(Ldet(i,:)), -imag(Ldet(i,:)), '.', 'color', colors(1, :)); + + plot(real(Ldetb(i,:)), imag(Ldetb(i,:)), '.', 'color', colors(2, :)); + plot(real(Ldetb(i,:)), -imag(Ldetb(i,:)), '.', 'color', colors(2, :)); +end +plot(-1, 0, 'kx', 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin'); +xlabel('Real'); ylabel('Imag'); +xlim([-3, 1]); ylim([-2, 2]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loci_loop_gain_comp_controllers.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+caption: Root Locus +#+RESULTS: +[[file:figs/loci_loop_gain_comp_controllers.png]] + + +** Identification - New +#+begin_src matlab +ur = load('FJPUR_step_new.mat'); +uh = load('FJPUH_step_new.mat'); +d = load('FJPD_step_new.mat'); +#+end_src + +| 1 | dz311 | +| 2 | dry311 | +| 3 | drx311 | +| 4 | dz111 | +| 5 | dry111 | +| 6 | drx111 | +| 7 | fjpur | +| 8 | fjpuh | +| 9 | fjpd | +| 10 | bragg | + +#+begin_src matlab +ur.time = ur.time - ur.time(1); +ur.allValues(:, 1) = ur.allValues(:, 1) - mean(ur.allValues(ur.time<0.1, 1)); +ur.allValues(:, 2) = ur.allValues(:, 2) - mean(ur.allValues(ur.time<0.1, 2)); +ur.allValues(:, 3) = ur.allValues(:, 3) - mean(ur.allValues(ur.time<0.1, 3)); + +t_filt = ur.time < 5; + +ur.u = ur.allValues(t_filt, 7); +ur.y_111 = [-ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +uh.time = uh.time - uh.time(1); +uh.allValues(:, 1) = uh.allValues(:, 1) - mean(uh.allValues(uh.time<0.1, 1)); +uh.allValues(:, 2) = uh.allValues(:, 2) - mean(uh.allValues(uh.time<0.1, 2)); +uh.allValues(:, 3) = uh.allValues(:, 3) - mean(uh.allValues(uh.time<0.1, 3)); + +uh.u = uh.allValues(t_filt, 8); +uh.y_111 = [-uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +d.time = d.time - d.time(1); +d.allValues(:, 1) = d.allValues(:, 1) - mean(d.allValues(d.time<0.1, 1)); +d.allValues(:, 2) = d.allValues(:, 2) - mean(d.allValues(d.time<0.1, 2)); +d.allValues(:, 3) = d.allValues(:, 3) - mean(d.allValues(d.time<0.1, 3)); + +d.u = d.allValues(t_filt, 9); +d.y_111 = [-d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)]; +#+end_src + +#+begin_src matlab +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; + +J_a_311 = [1, 0.14, -0.1525 + 1, 0.14, 0.0675 + 1, -0.14, -0.0425]; + +ur.y = [J_a_311 * ur.y_111']'; +uh.y = [J_a_311 * uh.y_111']'; +d.y = [J_a_311 * d.y_111']'; +#+end_src + +#+begin_src matlab +%% Sampling Time and Frequency +Ts = 1e-4; % [s] +Fs = 1/Ts; % [Hz] + +% Hannning Windows +win = hanning(ceil(5*Fs)); +#+end_src + +#+begin_src matlab +%% And we get the frequency vector +[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1/Ts); +[G_uh, ~] = tfestimate(uh.u, uh.y, win, [], [], 1/Ts); +[G_d, ~] = tfestimate(d.u, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +[coh_ur, ~] = mscohere(ur.u, ur.y, win, [], [], 1/Ts); +[coh_uh, ~] = mscohere(uh.u, uh.y, win, [], [], 1/Ts); +[coh_d, ~] = mscohere(d.u, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Coherence +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); +hold on; +plot(f, coh_ur(:,1), 'DisplayName', '$u_r$'); +plot(f, coh_uh(:,2), 'DisplayName', '$u_h$'); +plot(f, coh_d( :,3), 'DisplayName', '$u_d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Coherence'); +legend('location', 'southeast'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :exports none +%% Bode plot of the DCM dynamics in the frame of the Fast Jacks +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1)), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2)), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3)), 'DisplayName', '$u_d$'); +plot(f, abs(G_ur(:,2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', 'Off Diagonal'); +plot(f, abs(G_ur(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,2)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-2, 1e2]); +legend('location', 'southeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1))); +plot(f, 180/pi*angle(G_uh(:,2))); +plot(f, 180/pi*angle(G_d(:,3))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); +% ylim([-45, 45]); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +%% Previously used controller +load('X_tal_cage_PID.mat', 'K'); +#+end_src + +#+begin_src matlab +%% Controller design +s = tf('s'); + +% Lead +a = 4; % Amount of phase lead / width of the phase lead / high frequency gain +wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s] + +% Low Pass Filter +w0 = 2*pi*100; % Cut-off frequency [rad/s] +xi = 0.4; % Damping Ratio + +Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);; +#+end_src + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz'))), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3).*squeeze(freqresp(Kb(3,3), f, 'Hz'))), 'DisplayName', '$d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); +legend('location', 'northeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_uh(:,2).*squeeze(freqresp(K(2,2), f, 'Hz')))); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(K(3,3), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +Compare Sensitivity functions +#+begin_src matlab :exports none +%% Sensitivity function +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + + +hold on; +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude'); +ylim([1e-2, 1e1]); xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_comp.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:sensitivity_comp +#+caption: Comparison of sensitivity functions +#+RESULTS: +[[file:figs/sensitivity_comp.png]] + + +#+begin_src matlab +L = zeros(3, 3, length(f)); +Lb = zeros(3, 3, length(f)); + +for i_f = 1:length(f) + L(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz'); + Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz'); +end +#+end_src + +#+begin_src matlab :exports none +%% Compute the Eigenvalues of the loop gain +Ldet = zeros(3, length(f)); +Ldetb = zeros(3, length(f)); + +% Loop gain +for i_f = 1:length(f) + Ldet( :, i_f) = eig(squeeze(L( :,:,i_f))); + Ldetb(:, i_f) = eig(squeeze(Lb(:,:,i_f))); +end +#+end_src + +#+begin_src matlab :exports none +%% Plot of the eigenvalues of L in the complex plane +figure; +hold on; +for i = 1:size(Ldet,1) + plot(real(Ldet(i,:)), imag(Ldet(i,:)), '.', 'color', colors(1, :)); + plot(real(Ldet(i,:)), -imag(Ldet(i,:)), '.', 'color', colors(1, :)); + + plot(real(Ldetb(i,:)), imag(Ldetb(i,:)), '.', 'color', colors(2, :)); + plot(real(Ldetb(i,:)), -imag(Ldetb(i,:)), '.', 'color', colors(2, :)); +end +plot(-1, 0, 'kx', 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin'); +xlabel('Real'); ylabel('Imag'); +xlim([-3, 1]); ylim([-2, 2]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loci_loop_gain_comp_controllers.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+caption: Root Locus +#+RESULTS: +[[file:figs/loci_loop_gain_comp_controllers.png]] + + +** Identification - White noise +#+begin_src matlab +ur = load('fjpur_white_noise.mat'); +uh = load('fjpuh_white_noise.mat'); +d = load('fjpd_white_noise.mat'); +#+end_src + +| 1 | dz111 | +| 2 | dry111 | +| 3 | drx111 | +| 4 | fjpur | +| 5 | fjpuh | +| 6 | fjpd | +| 7 | bragg | + +#+begin_src matlab +ur.time = ur.time - ur.time(1); + +ur.drx = ur.drx - mean(ur.drx); +ur.dry = ur.dry - mean(ur.dry); +ur.dz = ur.dz - mean(ur.dz); +#+end_src + +#+begin_src matlab +uh.time = uh.time - uh.time(1); + +uh.drx = uh.drx - mean(uh.drx); +uh.dry = uh.dry - mean(uh.dry); +uh.dz = uh.dz - mean(uh.dz); +#+end_src + +#+begin_src matlab +d.time = d.time - d.time(1); + +d.drx = d.drx - mean(d.drx); +d.dry = d.dry - mean(d.dry); +d.dz = d.dz - mean(d.dz); +#+end_src + +#+begin_src matlab +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; + +ur.y = [J_a_111 * [-ur.dz, ur.dry, ur.drx]']'; +uh.y = [J_a_111 * [-uh.dz, uh.dry, uh.drx]']'; +d.y = [J_a_111 * [-d.dz, d.dry, d.drx]']'; +#+end_src + +#+begin_src matlab +%% Sampling Time and Frequency +Ts = 1e-4; % [s] +Fs = 1/Ts; % [Hz] + +% Hannning Windows +win = hanning(ceil(0.5*Fs)); +#+end_src + +#+begin_src matlab +%% And we get the frequency vector +[G_ur, f] = tfestimate(ur.fjpur, ur.y, win, [], [], 1/Ts); +[G_uh, ~] = tfestimate(uh.fjpuh, uh.y, win, [], [], 1/Ts); +[G_d, ~] = tfestimate(d.fjpd, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +[coh_ur, ~] = mscohere(ur.fjpur, ur.y, win, [], [], 1/Ts); +[coh_uh, ~] = mscohere(uh.fjpuh, uh.y, win, [], [], 1/Ts); +[coh_d, ~] = mscohere(d.fjpd, d.y, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Coherence +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); +hold on; +plot(f, coh_ur(:,1), 'DisplayName', '$u_r$'); +plot(f, coh_uh(:,2), 'DisplayName', '$u_h$'); +plot(f, coh_d(:,3), 'DisplayName', '$d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Coherence'); +legend('location', 'southeast'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/coherence_ident_noise.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:coherence_ident_noise +#+caption: description +#+RESULTS: +[[file:figs/coherence_ident_noise.png]] + +#+begin_src matlab :exports none +%% Bode plot of the DCM dynamics in the frame of the Fast Jacks +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1)), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2)), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3)), 'DisplayName', '$u_d$'); +plot(f, abs(G_ur(:,2)), 'color', [0, 0, 0, 0.2], ... + 'DisplayName', 'Off Diagonal'); +plot(f, abs(G_ur(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_uh(:,3)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,1)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,2)), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-2, 1e2]); +legend('location', 'northwest'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1))); +plot(f, 180/pi*angle(G_uh(:,2))); +plot(f, 180/pi*angle(G_d(:,3))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); +% ylim([-45, 45]); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/bode_plot_ident_noise.pdf', 'width', 'full', 'height', 'tall'); +#+end_src + +#+name: fig:bode_plot_ident_noise +#+caption: Bode Plot of the DCM dynamics in the frame of the fast jack. +#+RESULTS: +[[file:figs/bode_plot_ident_noise.png]] + + +#+begin_src matlab +%% Previously used controller +load('X_tal_cage_PID.mat', 'K'); +#+end_src + +#+begin_src matlab +%% Controller design +s = tf('s'); + +% Lead +a = 8; % Amount of phase lead / width of the phase lead / high frequency gain +wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s] + +% Low Pass Filter +w0 = 2*pi*80; % Cut-off frequency [rad/s] +xi = 0.4; % Damping Ratio + +Kb = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);; +#+end_src + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', '$u_r$'); +plot(f, abs(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz'))), 'DisplayName', '$u_h$'); +plot(f, abs(G_d( :,3).*squeeze(freqresp(Kb(3,3), f, 'Hz'))), 'DisplayName', '$d$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); +legend('location', 'northeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz')))); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(Kb(3,3), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_dcm_contr_simple.pdf', 'width', 'full', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_dcm_contr_simple +#+caption: Loop gain +#+RESULTS: +[[file:figs/loop_gain_dcm_contr_simple.png]] + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'Old K'); +plot(f, abs(G_uh(:,2).*squeeze(freqresp(K(2,2), f, 'Hz'))), 'color', colors(1,:), 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,3).*squeeze(freqresp(K(3,3), f, 'Hz'))), 'color', colors(1,:), 'HandleVisibility', 'off'); +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'New K'); +plot(f, abs(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz'))), 'color', colors(2,:), 'HandleVisibility', 'off'); +plot(f, abs(G_d(:,3).*squeeze(freqresp(Kb(3,3), f, 'Hz'))), 'color', colors(2,:), 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); +legend('location', 'northeast'); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'color', colors(1,:)); +plot(f, 180/pi*angle(G_uh(:,2).*squeeze(freqresp(K(2,2), f, 'Hz'))), 'color', colors(1,:)); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(K(3,3), f, 'Hz'))), 'color', colors(1,:)); +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'color', colors(2,:)); +plot(f, 180/pi*angle(G_uh(:,2).*squeeze(freqresp(Kb(2,2), f, 'Hz'))), 'color', colors(2,:)); +plot(f, 180/pi*angle(G_d(:,3).*squeeze(freqresp(Kb(3,3), f, 'Hz'))), 'color', colors(2,:)); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_diag_old_new_contr.pdf', 'width', 'full', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_diag_old_new_contr +#+caption: Loop gain +#+RESULTS: +[[file:figs/loop_gain_diag_old_new_contr.png]] + +Compare Sensitivity functions +#+begin_src matlab :exports none +%% Sensitivity function +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +hold on; +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'DisplayName', 'Old K'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', 'New K'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude'); +ylim([1e-2, 1e1]); xlim([1, 1e3]); +legend('location', 'southeast'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_comp.pdf', 'width', 'full', 'height', 'tall'); +#+end_src + +#+name: fig:sensitivity_comp +#+caption: Comparison of sensitivity functions +#+RESULTS: +[[file:figs/sensitivity_comp.png]] + + +#+begin_src matlab +L = zeros(3, 3, length(f)); +Lb = zeros(3, 3, length(f)); + +for i_f = 1:length(f) + L(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz'); + Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz'); +end +#+end_src + +#+begin_src matlab :exports none +%% Compute the Eigenvalues of the loop gain +Ldet = zeros(3, length(f)); +Ldetb = zeros(3, length(f)); + +% Loop gain +for i_f = 1:length(f) + Ldet( :, i_f) = eig(squeeze(L( :,:,i_f))); + Ldetb(:, i_f) = eig(squeeze(Lb(:,:,i_f))); +end +#+end_src + +#+begin_src matlab :exports none +%% Plot of the eigenvalues of L in the complex plane +figure; +hold on; +for i = 1:size(Ldet,1) + plot(real(Ldet(i,:)), imag(Ldet(i,:)), '.', 'color', colors(1, :)); + plot(real(Ldet(i,:)), -imag(Ldet(i,:)), '.', 'color', colors(1, :)); + + plot(real(Ldetb(i,:)), imag(Ldetb(i,:)), '.', 'color', colors(2, :)); + plot(real(Ldetb(i,:)), -imag(Ldetb(i,:)), '.', 'color', colors(2, :)); +end +plot(-1, 0, 'kx', 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin'); +xlabel('Real'); ylabel('Imag'); +xlim([-3, 1]); ylim([-2, 2]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loci_loop_gain_comp_controllers.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+caption: Root Locus +#+RESULTS: +[[file:figs/loci_loop_gain_comp_controllers.png]] + + +** Test +#+begin_src matlab +%% Notch +gm = 0.015; +xi = 0.1; +wn = 2*pi*208; + +K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); +#+end_src + +#+begin_src matlab +%% Double integrator +w0 = 2*pi*40; +K_int = (w0^2)/(s^2); +#+end_src + +#+begin_src matlab +%% Lead +a = 3; % Amount of phase lead / width of the phase lead / high frequency gain +K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a))); +K_lead = K_lead*K_lead; +#+end_src + +#+begin_src matlab +%% Low Pass Filter +w0 = 2*pi*120; % Cut-off frequency [rad/s] +xi = 0.3; % Damping Ratio + +K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2); +#+end_src + +#+begin_src matlab +%% Diagonal controller +Kb = 0.8*eye(3)*K_notch*K_int*K_lead*K_lpf; +#+end_src +** New controller - Higher bandwidth + +#+begin_src matlab +%% Previously used controller +load('X_tal_cage_PID.mat', 'K'); +#+end_src + +#+begin_src matlab +%% Current Controller design +% Lead +a = 8; % Amount of phase lead / width of the phase lead / high frequency gain +wc = 2*pi*20; % Frequency with the maximum phase lead [rad/s] + +% Low Pass Filter +w0 = 2*pi*80; % Cut-off frequency [rad/s] +xi = 0.4; % Damping Ratio + +Kb_old = eye(3)*(2*pi*20)^2/(s^2) *1/(sqrt(a))* (1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a))) * 1/(1 + 2*xi/w0*s + s^2/w0^2);; +#+end_src + +#+begin_src matlab +%% Notch +gm = 0.015; +xi = 0.2; +wn = 2*pi*208; + +K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); +#+end_src + +#+begin_src matlab +%% Double integrator +w0 = 2*pi*40; +K_int = (w0^2)/(s^2); +#+end_src + +#+begin_src matlab +%% Lead +a = 3; % Amount of phase lead / width of the phase lead / high frequency gain +w0 = 2*pi*40; +K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a))); +K_lead = K_lead*K_lead; +#+end_src + +#+begin_src matlab +%% Low Pass Filter +w0 = 2*pi*120; % Cut-off frequency [rad/s] +xi = 0.3; % Damping Ratio + +K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2); +#+end_src + +#+begin_src matlab +%% Diagonal controller +Kb = 0.9*eye(3)*K_notch*K_int*K_lead*K_lpf; +#+end_src + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'DisplayName', 'PID'); +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb_old(1,1), f, 'Hz'))), 'DisplayName', 'Double Integrator + Lead'); +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', 'Double Integrator + Lead + Notch'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-3, 1e3]); +legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(K(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb_old(1,1), f, 'Hz')))); +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz')))); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_compare.pdf', 'width', 'full', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_compare +#+caption: description +#+RESULTS: +[[file:figs/loop_gain_compare.png]] + + +#+begin_src matlab +L = zeros(3, 3, length(f)); +Lb = zeros(3, 3, length(f)); +Lb_new = zeros(3, 3, length(f)); + +for i_f = 1:length(f) + L(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(K , f(i_f), 'Hz'); + Lb(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb_old, f(i_f), 'Hz'); + Lb_new(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb, f(i_f), 'Hz'); +end +#+end_src + +#+begin_src matlab :exports none +%% Compute the Eigenvalues of the loop gain +Ldet = zeros(3, length(f)); +Ldetb = zeros(3, length(f)); +Ldetb_new = zeros(3, length(f)); + +% Loop gain +for i_f = 1:length(f) + Ldet( :, i_f) = eig(squeeze(L( :,:,i_f))); + Ldetb(:, i_f) = eig(squeeze(Lb(:,:,i_f))); + Ldetb_new(:, i_f) = eig(squeeze(Lb_new(:,:,i_f))); +end +#+end_src + +#+begin_src matlab :exports none +%% Plot of the eigenvalues of L in the complex plane +figure; +hold on; +plot(real(Ldet(1,:)), imag(Ldet(1,:)), '.', 'color', colors(1, :), 'DisplayName', 'PID'); +plot(real(Ldet(1,:)), -imag(Ldet(1,:)), '.', 'color', colors(1, :), 'HandleVisibility', 'off'); + +plot(real(Ldetb(1,:)), imag(Ldetb(1,:)), '.', 'color', colors(2, :), 'DisplayName', 'Double Integrator + Lead'); +plot(real(Ldetb(1,:)), -imag(Ldetb(1,:)), '.', 'color', colors(2, :), 'HandleVisibility', 'off'); + +plot(real(Ldetb_new(1,:)), imag(Ldetb_new(1,:)), '.', 'color', colors(3, :), 'DisplayName', 'Double Integrator + Lead + Notch'); +plot(real(Ldetb_new(1,:)), -imag(Ldetb_new(1,:)), '.', 'color', colors(3, :), 'HandleVisibility', 'off'); +for i = 2:size(Ldet,1) + plot(real(Ldet(i,:)), imag(Ldet(i,:)), '.', 'color', colors(1, :), 'HandleVisibility', 'off'); + plot(real(Ldet(i,:)), -imag(Ldet(i,:)), '.', 'color', colors(1, :), 'HandleVisibility', 'off'); + + plot(real(Ldetb(i,:)), imag(Ldetb(i,:)), '.', 'color', colors(2, :), 'HandleVisibility', 'off'); + plot(real(Ldetb(i,:)), -imag(Ldetb(i,:)), '.', 'color', colors(2, :), 'HandleVisibility', 'off'); + + plot(real(Ldetb_new(i,:)), imag(Ldetb_new(i,:)), '.', 'color', colors(3, :), 'HandleVisibility', 'off'); + plot(real(Ldetb_new(i,:)), -imag(Ldetb_new(i,:)), '.', 'color', colors(3, :), 'HandleVisibility', 'off'); +end +plot(-1, 0, 'kx', 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin'); +xlabel('Real'); ylabel('Imag'); +xlim([-3, 1]); ylim([-2, 2]); +axis square; +legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/nyquist_compare.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:nyquist_compare +#+caption: n +#+RESULTS: +[[file:figs/nyquist_compare.png]] + +#+begin_src matlab :exports none +%% Sensitivity function +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +hold on; +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'DisplayName', 'PID'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb_old(1,1), f, 'Hz'))), 'DisplayName', 'Double Integrator + Lead'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', 'Double Integrator + Lead + Notch'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude'); +ylim([1e-2, 1e1]); xlim([1, 1e3]); +legend('location', 'southeast'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_function_compare.pdf', 'width', 'normal', 'height', 'tall'); +#+end_src + +#+name: fig:sensitivity_function_compare +#+caption: description +#+RESULTS: +[[file:figs/sensitivity_function_compare.png]] + + + +** Added gain +#+begin_src matlab +%% Notch +gm = 0.015; +xi = 0.2; +wn = 2*pi*208; + +K_notch = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); +#+end_src + +#+begin_src matlab +%% Double integrator +w0 = 2*pi*40; +K_int = (w0^2)/(s^2); +#+end_src + +#+begin_src matlab +%% Lead +a = 3; % Amount of phase lead / width of the phase lead / high frequency gain +w0 = 2*pi*40; +K_lead = 1/(sqrt(a))*(1 + s/(w0/sqrt(a)))/(1 + s/(w0*sqrt(a))); +K_lead = K_lead*K_lead; +#+end_src + +#+begin_src matlab +%% Low Pass Filter +w0 = 2*pi*120; % Cut-off frequency [rad/s] +xi = 0.3; % Damping Ratio + +K_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2); +#+end_src + +#+begin_src matlab +gm = 10; +xi = 0.02; +wn = 2*pi*15; + +H = (s^2 + 2*gm*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); +#+end_src + +#+begin_src matlab +%% Diagonal controller +Kb_gain = 0.9*eye(3)*H*K_notch*K_int*K_lead*K_lpf; +#+end_src + +#+begin_src matlab +Lb_gain = zeros(3, 3, length(f)); + +for i_f = 1:length(f) + Lb_gain(:,:,i_f) = [G_ur(i_f,:); G_uh(i_f,:); G_d(i_f,:)]*freqresp(Kb_gain, f(i_f), 'Hz'); +end +#+end_src + +#+begin_src matlab :exports none +%% Compute the Eigenvalues of the loop gain +Ldetb_gain = zeros(3, length(f)); + +% Loop gain +for i_f = 1:length(f) + Ldetb_gain(:, i_f) = eig(squeeze(Lb_gain(:,:,i_f))); +end +#+end_src + +#+begin_src matlab :exports none +%% Loop Gain +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'color', colors(3, :)); +plot(f, abs(G_ur(:,1).*squeeze(freqresp(Kb_gain(1,1), f, 'Hz'))), 'color', colors(4, :)); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude'); set(gca, 'XTickLabel',[]); +ylim([1e-4, 1e2]); + +ax2 = nexttile; +hold on; +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'color', colors(3, :)); +plot(f, 180/pi*angle(G_ur(:,1).*squeeze(freqresp(Kb_gain(1,1), f, 'Hz'))), 'color', colors(4, :)); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +yticks(-360:90:360); + +linkaxes([ax1,ax2],'x'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/loop_gain_compare_added_gain.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:loop_gain_compare_added_gain +#+caption: description +#+RESULTS: +[[file:figs/loop_gain_compare_added_gain.png]] + +#+begin_src matlab :exports none +%% Sensitivity function +figure; +tiledlayout(1, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +hold on; +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(K(1,1), f, 'Hz'))), 'DisplayName', 'Old K'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb_old(1,1), f, 'Hz'))), 'DisplayName', 'Act K'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb(1,1), f, 'Hz'))), 'DisplayName', 'New K'); +plot(f, 1./abs(1 + G_d(:,3).*squeeze(freqresp(Kb_gain(1,1), f, 'Hz'))), 'DisplayName', 'New K'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Amplitude'); +ylim([1e-2, 1e1]); xlim([1, 1e3]); +legend('location', 'southeast'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/sensitivity_new_gain_compare.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:sensitivity_new_gain_compare +#+caption: description +#+RESULTS: +[[file:figs/sensitivity_new_gain_compare.png]] + +#+begin_src matlab :exports none +%% Plot of the eigenvalues of L in the complex plane +figure; +hold on; +for i = 1:size(Ldet,1) + plot(real(Ldetb_new(i,:)), imag(Ldetb_new(i,:)), '.', 'color', colors(3, :)); + plot(real(Ldetb_new(i,:)), -imag(Ldetb_new(i,:)), '.', 'color', colors(3, :)); + plot(real(Ldetb_gain(i,:)), imag(Ldetb_gain(i,:)), '.', 'color', colors(4, :)); + plot(real(Ldetb_gain(i,:)), -imag(Ldetb_gain(i,:)), '.', 'color', colors(4, :)); +end +plot(-1, 0, 'kx', 'HandleVisibility', 'off'); +hold off; +set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin'); +xlabel('Real'); ylabel('Imag'); +xlim([-3, 1]); ylim([-2, 2]); +axis square; +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/nyquist_after_gain_frequency.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:nyquist_after_gain_frequency +#+caption: nyquist plot +#+RESULTS: +[[file:figs/nyquist_after_gain_frequency.png]] + + +* Noise Budgeting +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no :noweb yes +<> +#+end_src + +#+begin_src matlab :eval no :noweb yes +<> +#+end_src + +#+begin_src matlab :noweb yes +<> +#+end_src + +** No Displacement + +| 1 | dz311 | +| 2 | dry311 | +| 3 | drx311 | +| 4 | dz111 | +| 5 | dry111 | +| 6 | drx111 | +| 7 | fjpur | +| 8 | fjpuh | +| 9 | fjpd | +| 10 | bragg | + +#+begin_src matlab +data_10_deg = load('no_mov_10.mat'); +data_70_deg = load('no_mov_70.mat'); +#+end_src + +#+begin_src matlab +data_10_deg = extractDatData('no_mov_10.mat', ... + {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjpur", "fjpuh", "fjpd", "bragg"}, ... + [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]); +data_10_deg = processMeasData(data_10_deg); +#+end_src + +#+begin_src matlab +Ts = 1e-4; +t = Ts*[1:length(data_10_deg.bragg)]; +#+end_src + +#+begin_src matlab +data_10_deg.dz = data_10_deg.allValues(:,4) - mean(data_10_deg.allValues(:,4)); +data_10_deg.dry = data_10_deg.allValues(:,5) - mean(data_10_deg.allValues(:,5)); +data_10_deg.drx = data_10_deg.allValues(:,6) - mean(data_10_deg.allValues(:,6)); +#+end_src + +#+begin_src matlab +%% Compute motion error in the frame of the fast jack +J_a_111 = [1, 0.14, -0.1525 + 1, 0.14, 0.0675 + 1, -0.14, 0.0425]; + +de_111 = [data_10_deg.dz'; data_10_deg.dry'; data_10_deg.drx']; +de_fj = J_a_111*de_111; +data_10_deg.fj_ur = de_fj(1,:)'; +data_10_deg.fj_uh = de_fj(2,:)'; +data_10_deg.fj_d = de_fj(3,:)'; + +de_111 = [data_70_deg.dz'; data_70_deg.dry'; data_70_deg.drx']; +de_fj = J_a_111*de_111; +data_70_deg.fj_ur = de_fj(1,:)'; +data_70_deg.fj_uh = de_fj(2,:)'; +data_70_deg.fj_d = de_fj(3,:)'; +#+end_src + +#+begin_src matlab +win = hanning(ceil(1/Ts)); + +[pxx_10_ur, f] = pwelch(data_10_deg.fj_ur, win, [], [], 1/Ts); +[pxx_70_ur, ~] = pwelch(data_70_deg.fj_ur, win, [], [], 1/Ts); + +[pxx_10_uh, ~] = pwelch(data_10_deg.fj_uh, win, [], [], 1/Ts); +[pxx_70_uh, ~] = pwelch(data_70_deg.fj_uh, win, [], [], 1/Ts); + +[pxx_10_d, ~] = pwelch(data_10_deg.fj_d, win, [], [], 1/Ts); +[pxx_70_d, ~] = pwelch(data_70_deg.fj_d, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +CPS_10_ur = flip(-cumtrapz(flip(f), flip(pxx_10_ur))); +CPS_10_uh = flip(-cumtrapz(flip(f), flip(pxx_10_uh))); +CPS_10_d = flip(-cumtrapz(flip(f), flip(pxx_10_d))); + +CPS_70_ur = flip(-cumtrapz(flip(f), flip(pxx_70_ur))); +CPS_70_uh = flip(-cumtrapz(flip(f), flip(pxx_70_uh))); +CPS_70_d = flip(-cumtrapz(flip(f), flip(pxx_70_d))); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(CPS_10_ur), '-' , 'color', colors(1, :), 'DisplayName', '10 deg - $u_r$') +plot(f, sqrt(CPS_70_ur), '--', 'color', colors(1, :), 'DisplayName', '70 deg - $u_r$') +plot(f, sqrt(CPS_10_uh), '-' , 'color', colors(2, :), 'DisplayName', '10 deg - $u_h$') +plot(f, sqrt(CPS_70_uh), '--', 'color', colors(2, :), 'DisplayName', '70 deg - $u_h$') +plot(f, sqrt(CPS_10_d), '-' , 'color', colors(3, :), 'DisplayName', '10 deg - $d$') +plot(f, sqrt(CPS_70_d), '--', 'color', colors(3, :), 'DisplayName', '70 deg - $d$') +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(pxx_10_ur)) +plot(f, sqrt(pxx_70_ur)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +data_70_deg.dz = data_70_deg.allValues(:,4) - mean(data_70_deg.allValues(:,4)); +data_70_deg.dry = data_70_deg.allValues(:,5) - mean(data_70_deg.allValues(:,5)); +data_70_deg.drx = data_70_deg.allValues(:,6) - mean(data_70_deg.allValues(:,6)); +#+end_src + +#+begin_src matlab +win = hanning(ceil(1/Ts)); + +[pxx_10_drx, f] = pwelch(data_10_deg.drx, win, [], [], 1/Ts); +[pxx_70_drx, ~] = pwelch(data_70_deg.drx, win, [], [], 1/Ts); + +[pxx_10_dry, ~] = pwelch(data_10_deg.dry, win, [], [], 1/Ts); +[pxx_70_dry, ~] = pwelch(data_70_deg.dry, win, [], [], 1/Ts); + +[pxx_10_dz, ~] = pwelch(data_10_deg.dz, win, [], [], 1/Ts); +[pxx_70_dz, ~] = pwelch(data_70_deg.dz, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(pxx_10_drx)) +plot(f, sqrt(pxx_70_drx)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(pxx_10_dry)) +plot(f, sqrt(pxx_70_dry)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(pxx_10_dz)) +plot(f, sqrt(pxx_70_dz)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nm}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + + + +** Scans + +| 1 | dz311 | +| 2 | dry311 | +| 3 | drx311 | +| 4 | dz111 | +| 5 | dry111 | +| 6 | drx111 | +| 7 | fjpur | +| 8 | fjpuh | +| 9 | fjpd | +| 10 | bragg | + +#+begin_src matlab +%% Load Data +data_10_70_deg = extractDatData('thtraj_10_70.mat', ... + {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjur", "fjuh", "fjd", "bragg"}, ... + [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]); + +Ts = 1e-4; +t = Ts*[1:length(data_10_70_deg.bragg)]; + +%% Actuator Jacobian +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; + +data_10_70_deg.ddz = 10.5e-3./(2*cos(data_10_70_deg.bragg)) - data_10_70_deg.dz; + +%% Computation of the position of the FJ as measured by the interferometers +error = J_a_111 * [data_10_70_deg.ddz, data_10_70_deg.dry, data_10_70_deg.drx]'; + +data_10_70_deg.fjur_e = error(1,:)'; % [m] +data_10_70_deg.fjuh_e = error(2,:)'; % [m] +data_10_70_deg.fjd_e = error(3,:)'; % [m] +#+end_src + +#+begin_src matlab +%% Load Data +data_70_10_deg = extractDatData('thtraj_70_10.mat', ... + {"dz311", "dry311", "drx311", "dz", "dry", "drx", "fjur", "fjuh", "fjd", "bragg"}, ... + [1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8, pi/180]); +%% Actuator Jacobian +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; + +data_70_10_deg.ddz = 10.5e-3./(2*cos(data_70_10_deg.bragg)) - data_70_10_deg.dz; + +%% Computation of the position of the FJ as measured by the interferometers +error = J_a_111 * [data_70_10_deg.ddz, data_70_10_deg.dry, data_70_10_deg.drx]'; + +data_70_10_deg.fjur_e = error(1,:)'; % [m] +data_70_10_deg.fjuh_e = error(2,:)'; % [m] +data_70_10_deg.fjd_e = error(3,:)'; % [m] +#+end_src + +#+begin_src matlab +win = hanning(ceil(1/Ts)); + +[pxx_10_70_ur, f] = pwelch(data_10_70_deg.fjur_e(t<100), win, [], [], 1/Ts); +[pxx_70_10_ur, ~] = pwelch(data_70_10_deg.fjur_e(t<100), win, [], [], 1/Ts); + +[pxx_10_70_uh, ~] = pwelch(data_10_70_deg.fjuh_e(t<100), win, [], [], 1/Ts); +[pxx_70_10_uh, ~] = pwelch(data_70_10_deg.fjuh_e(t<100), win, [], [], 1/Ts); + +[pxx_10_70_d, ~] = pwelch(data_10_70_deg.fjd_e(t<100), win, [], [], 1/Ts); +[pxx_70_10_d, ~] = pwelch(data_70_10_deg.fjd_e(t<100), win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +CPS_10_70_ur = flip(-cumtrapz(flip(f), flip(pxx_10_70_ur))); +CPS_10_70_uh = flip(-cumtrapz(flip(f), flip(pxx_10_70_uh))); +CPS_10_70_d = flip(-cumtrapz(flip(f), flip(pxx_10_70_d))); + +CPS_70_10_ur = flip(-cumtrapz(flip(f), flip(pxx_70_10_ur))); +CPS_70_10_uh = flip(-cumtrapz(flip(f), flip(pxx_70_10_uh))); +CPS_70_10_d = flip(-cumtrapz(flip(f), flip(pxx_70_10_d))); +#+end_src + +#+begin_src matlab :exports none +%% Spectrogram +figure; +hold on; +pspectrum(data_10_70_deg.fjuh_e(t<100), 1e4, 'spectrogram', ... + 'FrequencyResolution', 1e0, ... + 'OverlapPercent', 99, ... + 'FrequencyLimits', [1, 400]); +hold off; +% xlim([0.03, 1.14]); ylim([1, 400]); +% caxis([-160, -130]) +title(''); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, 1e9*sqrt(CPS_10_70_ur)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(f, sqrt(pxx_10_70_ur)) +plot(f, sqrt(pxx_70_10_ur)) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +** Noise budgeting - No rotation +First, we look at the position errors when the bragg axis is not moving + +#+begin_src matlab +%% Load Measurement Data +ol_data = load('FJPUR_step.mat'); +#+end_src + +#+begin_src matlab +%% Pre-processing +ol_time = ol_data.time - ol_data.time(1); + +ol_drx = ol_data.allValues(ol_time < 45, 6); +ol_dry = ol_data.allValues(ol_time < 45, 5); +ol_dz = ol_data.allValues(ol_time < 45, 4); + +ol_drx = ol_drx - mean(ol_drx); +ol_dry = ol_dry - mean(ol_dry); +ol_dz = ol_dz - mean(ol_dz); + +ol_time = ol_time(ol_time < 45); +#+end_src + +#+begin_src matlab +figure; +plot(ol_time, ol_drx) +#+end_src + +#+begin_src matlab +%% Parameters for Spectral Analysis +Ts = 1e-4; +win = hanning(ceil(1/Ts)); +#+end_src + +#+begin_src matlab +%% Computation of the PSD +[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1/Ts); +[pxx_ol_dry, ~] = pwelch(ol_dry, win, [], [], 1/Ts); +[pxx_ol_dz, ~] = pwelch(ol_dz, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Amplitude Spectral Density +figure; +hold on; +plot(f, sqrt(pxx_ol_drx), 'DisplayName', '$R_x$'); +plot(f, sqrt(pxx_ol_dry), 'DisplayName', '$R_y$'); +plot(f, sqrt(pxx_ol_dz), 'DisplayName', '$D_z$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$\frac{nm,nrad}{\sqrt{Hz}}$]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/noise_budget_no_mov_asd.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:noise_budget_no_mov_asd +#+caption: Amplitude Spectral Density +#+RESULTS: +[[file:figs/noise_budget_no_mov_asd.png]] + +#+begin_src matlab +%% Cumulative Spectral Density +CPS_drx = flip(-cumtrapz(flip(f), flip(pxx_ol_drx))); +CPS_dry = flip(-cumtrapz(flip(f), flip(pxx_ol_dry))); +CPS_dz = flip(-cumtrapz(flip(f), flip(pxx_ol_dz))); +#+end_src + +#+begin_src matlab +%% Cumulative Spectral Density +CPS_drx = cumtrapz(f, pxx_ol_drx); +CPS_dry = cumtrapz(f, pxx_ol_dry); +CPS_dz = cumtrapz(f, pxx_ol_dz); +#+end_src + +#+begin_src matlab :exports none +%% Cumulative Spectral Density +figure; +hold on; +plot(f, sqrt(CPS_drx), 'DisplayName', '$R_x$'); +plot(f, sqrt(CPS_dry), 'DisplayName', '$R_y$'); +plot(f, sqrt(CPS_dz), 'DisplayName', '$D_z$'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('CAS [nm, nrad rms]'); +legend('location', 'northwest'); +xlim([1, 1e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/noise_budget_no_mov_cas.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:noise_budget_no_mov_cas +#+caption: Cumulative Amplitude Spectrum +#+RESULTS: +[[file:figs/noise_budget_no_mov_cas.png]] + + +** TODO Noise budgeting - Bragg rotation + +* Test Mode C +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no :noweb yes +<> +#+end_src + +#+begin_src matlab :eval no :noweb yes +<> +#+end_src + +#+begin_src matlab :noweb yes +<> +#+end_src + +** Mode B and Mode C +#+begin_src matlab +data_B = extractDatData(sprintf("/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s","lut_const_fj_vel_19012022_1450.dat"), ... + {"bragg", "dz", "dry", "drx", "fjur", "fjuh", "fjd"}, ... + [pi/180, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8]); +data_B = processMeasData(data_B); +#+end_src + +#+begin_src matlab +data_C = extractDatData(sprintf("/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s","lut_const_fj_vel_19012022_1454.dat"), ... + {"bragg", "dz", "dry", "drx", "fjur", "fjuh", "fjd"}, ... + [pi/180, 1e-9, 1e-9, 1e-9, 1e-8, 1e-8, 1e-8]); +data_C = processMeasData(data_C); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*data_B.bragg, 1e9*data_B.drx) +hold off; +xlabel('Bragg Angle [deg]'); ylabel('DRX [nrad]'); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*data_B.bragg, 1e9*data_B.fjur_e_filt) +plot(180/pi*data_C.bragg, 1e9*data_C.fjur_e_filt) +hold off; +xlabel('Bragg Angle [deg]'); ylabel('FJUR Error [nm]'); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*data_B.bragg, 1e9*data_B.fjur_e) +plot(180/pi*data_C.bragg, 1e9*data_C.fjur_e) +hold off; +xlabel('Bragg Angle [deg]'); ylabel('FJUR Error [nm]'); +#+end_src + +#+begin_src matlab +%% FIR Filter +Fs = 1e4; % Sampling Frequency [Hz] +fir_order = 5000; % Filter's order +delay = fir_order/2; % Delay induced by the filter +B_fir = firls(5000, ... % Filter's order + [0 5/(Fs/2) 10/(Fs/2) 1], ... % Frequencies [Hz] + [1 1 0 0]); % Wanted Magnitudes +#+end_src + +#+begin_src matlab +%% Filtering all measured Fast Jack Position using the FIR filter +data_B.drx_filter = filter(B_fir, 1, data_B.drx); +data_B.drx_filter(1:end-delay) = data_B.drx_filter(delay+1:end); + +data_C.drx_filter = filter(B_fir, 1, data_C.drx); +data_C.drx_filter(1:end-delay) = data_C.drx_filter(delay+1:end); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*data_B.bragg, 1e9*data_B.drx_filter) +plot(180/pi*data_C.bragg, 1e9*data_C.drx_filter) +hold off; +xlabel('Bragg Angle [deg]'); ylabel('DRX [nrad]'); +#+end_src + +#+begin_src matlab +Ts = 1e-4; +win = hanning(ceil(1/Ts)); + +[pxx_B_drx, f] = pwelch(data_B.drx, win, [], [], 1/Ts); +[pxx_C_drx, ~] = pwelch(data_C.drx, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab :exports none +%% Estimation of Sensitivity function +figure; +hold on; +plot(f, sqrt(pxx_B_drx), 'DisplayName', 'B'); +plot(f, sqrt(pxx_C_drx), 'DisplayName', 'C'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD'); +legend('location', 'northwest'); +#+end_src + +#+begin_src matlab :exports none +%% Estimation of Sensitivity function +figure; +plot(f, sqrt(pxx_C_drx)./sqrt(pxx_B_drx), 'k-'); +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('Sensitivity Function'); +legend('location', 'northwest'); +#+end_src + +* Export numerator and denominator +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no :noweb yes +<> +#+end_src + +#+begin_src matlab :eval no :noweb yes +<> +#+end_src + +#+begin_src matlab :noweb yes +<> +#+end_src + +** Export +#+begin_src matlab +K_order = 10; +#+end_src + +#+begin_src matlab +load('X_tal_cage_PID.mat', 'K'); +K_order = order(K(1,1)); +Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4); +[num, den] = tfdata(Kz, 'v'); + +formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'; +fileID = fopen('X_tal_cage_PID.dat', 'w'); +fprintf(fileID, formatSpec, [num; den]'); +fclose(fileID); +#+end_src + +#+begin_src matlab +load('X_tal_cage_PID_20Hz.mat', 'K'); +K_order = order(K(1,1)); +Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4); +[num, den] = tfdata(Kz, 'v'); + +formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'; +fileID = fopen('X_tal_cage_PID_20Hz.dat', 'w'); +fprintf(fileID, formatSpec, [num; den]'); +fclose(fileID); +#+end_src + +#+begin_src matlab +load('X_tal_cage_PID_40Hz.mat', 'K'); +K_order = order(K(1,1)); +Kz = c2d(K(1,1)*(1 + s/2/pi/2e3)^(9-K_order)/(1 + s/2/pi/2e3)^(9-K_order), 1e-4); +[num, den] = tfdata(Kz, 'v'); + +formatSpec = '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'; +fileID = fopen('X_tal_cage_PID_40Hz.dat', 'w'); +fprintf(fileID, formatSpec, [num; den]'); +fclose(fileID); +#+end_src + +** Verify +#+begin_src matlab +K_data = importdata('X_tal_cage_PID_20Hz.dat'); +K = tf(K_data(1,:), K_data(2,:), 1e-4) +#+end_src + +* Helping Functions :noexport: +** Initialize Path +#+NAME: m-init-path +#+BEGIN_SRC matlab +%% Path for functions, data and scripts +addpath('./matlab/mat/'); % Path for data +addpath('./matlab/src/'); % Path for functions +addpath('./matlab/'); % Path for scripts +#+END_SRC + +#+NAME: m-init-path-tangle +#+BEGIN_SRC matlab +%% Path for functions, data and scripts +addpath('./mat/'); % Path for data +addpath('./src/'); % Path for functions +#+END_SRC + +** Initialize Simscape Model +#+NAME: m-init-simscape +#+begin_src matlab +#+end_src + +** Initialize other elements +#+NAME: m-init-other +#+BEGIN_SRC matlab +%% Colors for the figures +colors = colororder; + +%% Frequency Vector +freqs = logspace(0, 3, 1000); +#+END_SRC + +** =extractDatData= +:PROPERTIES: +:header-args:matlab+: :tangle matlab/src/extractDatData.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +*** Function Description +#+begin_src matlab +function [data_struct] = extractDatData(dat_file, names, scale) +% extractDatData - +% +% Syntax: extractDatData(data_file, lut_file, args) +% +% Inputs: +% - data_file - Where to load the .mat file +% - lut_file - Where to save the .dat file +#+end_src + +*** Load Data +#+begin_src matlab +%% Load Data +data_array = importdata(dat_file); +#+end_src + +#+begin_src matlab +%% Initialize Struct +data_struct = struct(); +#+end_src + +#+begin_src matlab +%% Populate Struct +for i = 1:length(names) + data_struct.(names{i}) = scale(i)*data_array(:,i); +end +#+end_src + +#+begin_src matlab +%% Add Time +data_struct.time = 1e-4*[1:1:length(data_struct.(names{1}))]; +#+end_src + +** =processMeasData= +:PROPERTIES: +:header-args:matlab+: :tangle matlab/src/processMeasData.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +*** Function Description +#+begin_src matlab +function [data] = processMeasData(data, args) +% processMeasData - +% +% Syntax: processMeasData(data_file, lut_file, args) +% +% Inputs: +% - data +#+end_src + +*** Optional Parameters +#+begin_src matlab +arguments + data + args.fir_order (1,1) double {mustBeNumericOrLogical} = 5000 +end +#+end_src + +*** Process Data +#+begin_src matlab +%% Actuator Jacobian +J_a_111 = [1, 0.14, -0.0675 + 1, 0.14, 0.1525 + 1, -0.14, 0.0425]; +#+end_src + +#+begin_src matlab +%% FIR Filter +Fs = 1e4; % Sampling Frequency [Hz] +fir_order = args.fir_order; % Filter's order +delay = fir_order/2; % Delay induced by the filter +B_fir = firls(args.fir_order, ... % Filter's order + [0 500/(Fs/2) 1e3/(Fs/2) 1], ... % Frequencies [Hz] + [1 1 0 0]); % Wanted Magnitudes +#+end_src + +#+begin_src matlab +data.ddz = 10.5e-3./(2*cos(data.bragg)) - data.dz; + +%% Computation of the position of the FJ as measured by the interferometers +error = J_a_111 * [data.ddz, data.dry, data.drx]'; + +data.fjur_e = error(1,:)'; % [m] +data.fjuh_e = error(2,:)'; % [m] +data.fjd_e = error(3,:)'; % [m] + +%% Filtering all measured Fast Jack Position using the FIR filter +data.fjur_e_filt = filter(B_fir, 1, data.fjur_e); +data.fjuh_e_filt = filter(B_fir, 1, data.fjuh_e); +data.fjd_e_filt = filter(B_fir, 1, data.fjd_e); + +%% Compensation of the delay introduced by the FIR filter +data.fjur_e_filt(1:end-delay) = data.fjur_e_filt(delay+1:end); +data.fjuh_e_filt(1:end-delay) = data.fjuh_e_filt(delay+1:end); +data.fjd_e_filt( 1:end-delay) = data.fjd_e_filt( delay+1:end); +#+end_src + +#+begin_src matlab +%% Re-sample data to have same data points in FJUR +[data.fjur_e_resampl, data.fjur_resampl] = resample(data.fjur_e_filt, data.fjur, 1/100e-9); +[data.fjuh_e_resampl, data.fjuh_resampl] = resample(data.fjuh_e_filt, data.fjuh, 1/100e-9); +[data.fjd_e_resampl, data.fjd_resampl] = resample(data.fjd_e_filt, data.fjd, 1/100e-9); +#+end_src + +* Bibliography :ignore: +#+latex: \printbibliography diff --git a/figs/bode_plot_cur_controller.pdf b/figs/bode_plot_cur_controller.pdf new file mode 100644 index 0000000000000000000000000000000000000000..112f93c9bee9216df78c0f20b96cadd9927185a8 GIT binary patch literal 50614 zcmbT+bx>R3zb0^sI|Qe=Ln#s*io1Jp_u%dn_uyKzIJCHz;u2hoYjM{C#R^M*yLa!M z+0Jx_|MKRX=Q-a)K9huZLZd7$$pmEPK&JWprMvcE 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