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< title > ESRF Double Crystal Monochromator - Feedback Controller< / title >
< meta name = "author" content = "Dehaeze Thomas" / >
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< h1 class = "title" > ESRF Double Crystal Monochromator - Feedback Controller< / h1 >
< div id = "table-of-contents" role = "doc-toc" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" role = "doc-toc" >
< ul >
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< li > < a href = "#org8576b4a" > 1. Estimation of Sensitivity Function< / a >
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< ul >
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< li > < a href = "#orgdf402a0" > 1.1. Load Data< / a > < / li >
< li > < a href = "#org8107511" > 1.2. Controller< / a > < / li >
< li > < a href = "#org0a01799" > 1.3. Test< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org9a5bd10" > 2. System Identification< / a >
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< ul >
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< li > < a href = "#orgaafe900" > 2.1. Identification< / a > < / li >
< li > < a href = "#orga4b6967" > 2.2. Identification - New< / a > < / li >
< li > < a href = "#org3ea3501" > 2.3. Identification - White noise< / a > < / li >
< li > < a href = "#org2f67dfc" > 2.4. Test< / a > < / li >
< li > < a href = "#org675289a" > 2.5. New controller - Higher bandwidth< / a > < / li >
< li > < a href = "#org2f12e07" > 2.6. Added gain< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orge30c950" > 3. Noise Budgeting< / a >
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< ul >
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< li > < a href = "#org8aeec43" > 3.1. No Displacement< / a > < / li >
< li > < a href = "#org2e15aa7" > 3.2. Scans< / a > < / li >
< li > < a href = "#org26d025b" > 3.3. Noise budgeting - No rotation< / a > < / li >
< li > < a href = "#org8945ee2" > 3.4. Noise budgeting - Bragg rotation< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgc0ab5d1" > 4. Test Mode C< / a >
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< ul >
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< li > < a href = "#org9996dc6" > 4.1. Mode B and Mode C< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org1c0791b" > 5. Export numerator and denominator< / a >
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< ul >
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< li > < a href = "#org22487de" > 5.1. Export< / a > < / li >
< li > < a href = "#org2b8461a" > 5.2. Verify< / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
< hr >
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< p > This report is also available as a < a href = "./dcm-feedback-control.pdf" > pdf< / a > .< / p >
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< hr >
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< div id = "outline-container-org8576b4a" class = "outline-2" >
< h2 id = "org8576b4a" > < span class = "section-number-2" > 1.< / span > Estimation of Sensitivity Function< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< / div >
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< div id = "outline-container-orgdf402a0" class = "outline-3" >
< h3 id = "orgdf402a0" > < span class = "section-number-3" > 1.1.< / span > Load Data< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
Two scans are performed:
< / p >
< ul class = "org-ul" >
< li > < code > 1.1< / code > in mode B< / li >
< li > < code > 3.1< / code > in mode C< / li >
< / ul >
< p >
The difference between the two is that mode C adds the feedback controller.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Load Data of the new LUT method< / span >
Ts = 0.1;
ol_drx = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/1.1/measurement/xtal_111_drx_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Rx [rad]< / span >
cl_drx = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/3.1/measurement/xtal_111_drx_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Rx [rad]< / span >
ol_dry = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/1.1/measurement/xtal_111_dry_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Ry [rad]< / span >
cl_dry = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/3.1/measurement/xtal_111_dry_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Ry [rad]< / span >
t = linspace(Ts, Ts< span class = "org-builtin" > *< / span > length(ol_drx), length(ol_drx));
< / pre >
< / div >
< p >
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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 < a href = "#orgb0c8317" > 1< / a > ).
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_cl_drx, < span class = "org-builtin" > ~< / span > ] = pwelch(cl_drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_ol_dry, < span class = "org-builtin" > ~< / span > ] = pwelch(ol_dry, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_cl_dry, < span class = "org-builtin" > ~< / span > ] = pwelch(cl_dry, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
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< div id = "orgb0c8317" class = "figure" >
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< p > < img src = "figs/sensitivity_function_drx_est.png" alt = "sensitivity_function_drx_est.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Estimation of the sensitivity transfer function magnitude< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org8107511" class = "outline-3" >
< h3 id = "org8107511" > < span class = "section-number-3" > 1.2.< / span > Controller< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
< / pre >
< / div >
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< div id = "orgabcb99b" class = "figure" >
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< p > < img src = "figs/bode_plot_cur_controller.png" alt = "bode_plot_cur_controller.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Bode Plot of the Controller< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0a01799" class = "outline-3" >
< h3 id = "org0a01799" > < span class = "section-number-3" > 1.3.< / span > Test< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Ts = 5e< span class = "org-builtin" > -< / span > 3;
cl_drx = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/16.1/measurement/xtal_111_drx_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Rx [rad]< / span >
ol_drx = 1e< span class = "org-builtin" > -< / span > 9< span class = "org-builtin" > *< / span > double(h5read(< span class = "org-string" > 'xanes_0003.h5'< / span > ,< span class = "org-string" > '/18.1/measurement/xtal_111_drx_filter'< / span > )); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Rx [rad]< / span >
t = linspace(Ts, Ts< span class = "org-builtin" > *< / span > length(ol_drx), length(ol_drx));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (t, ol_drx)
< span class = "org-builtin" > plot< / span > (t, cl_drx)
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(10< span class = "org-builtin" > /< / span > Ts));
[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_cl_drx, < span class = "org-builtin" > ~< / span > ] = pwelch(cl_drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org9a5bd10" class = "outline-2" >
< h2 id = "org9a5bd10" > < span class = "section-number-2" > 2.< / span > System Identification< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< / div >
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< div id = "outline-container-orgaafe900" class = "outline-3" >
< h3 id = "orgaafe900" > < span class = "section-number-3" > 2.1.< / span > Identification< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur = load(< span class = "org-string" > 'FJPUR_step.mat'< / span > );
uh = load(< span class = "org-string" > 'FJPUH_step.mat'< / span > );
d = load(< span class = "org-string" > 'FJPD_step.mat'< / span > );
< / pre >
< / div >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > dz311< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > dry311< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > drx311< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > dz111< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > dry111< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > drx111< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > fjpur< / td >
< / tr >
< tr >
< td class = "org-right" > 8< / td >
< td class = "org-left" > fjpuh< / td >
< / tr >
< tr >
< td class = "org-right" > 9< / td >
< td class = "org-left" > fjpd< / td >
< / tr >
< tr >
< td class = "org-right" > 10< / td >
< td class = "org-left" > bragg< / td >
< / tr >
< / tbody >
< / table >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur.time = ur.time < span class = "org-builtin" > -< / span > ur.time(1);
ur.allValues(< span class = "org-builtin" > :< / span > , 1) = ur.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 1, 1));
ur.allValues(< span class = "org-builtin" > :< / span > , 2) = ur.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 1, 2));
ur.allValues(< span class = "org-builtin" > :< / span > , 3) = ur.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 1, 3));
t_filt = ur.time < span class = "org-builtin" > > < / span > 48 < span class = "org-builtin" > & < / span > ur.time < span class = "org-builtin" > < < / span > 60;
ur.u = ur.allValues(t_filt, 7);
ur.y_111 = [< span class = "org-builtin" > -< / span > ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > uh.time = uh.time < span class = "org-builtin" > -< / span > uh.time(1);
uh.allValues(< span class = "org-builtin" > :< / span > , 1) = uh.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 1, 1));
uh.allValues(< span class = "org-builtin" > :< / span > , 2) = uh.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 1, 2));
uh.allValues(< span class = "org-builtin" > :< / span > , 3) = uh.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 1, 3));
uh.u = uh.allValues(t_filt, 8);
uh.y_111 = [< span class = "org-builtin" > -< / span > uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > d.time = d.time < span class = "org-builtin" > -< / span > d.time(1);
d.allValues(< span class = "org-builtin" > :< / span > , 1) = d.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 1, 1));
d.allValues(< span class = "org-builtin" > :< / span > , 2) = d.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 1, 2));
d.allValues(< span class = "org-builtin" > :< / span > , 3) = d.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 1, 3));
d.u = d.allValues(t_filt, 9);
d.y_111 = [< span class = "org-builtin" > -< / span > d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.0675
1, 0.14, 0.1525
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
J_a_311 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.1525
1, 0.14, 0.0675
1, < span class = "org-builtin" > -< / span > 0.14, < span class = "org-builtin" > -< / span > 0.0425];
ur.y = [J_a_311 < span class = "org-builtin" > *< / span > ur.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
uh.y = [J_a_311 < span class = "org-builtin" > *< / span > uh.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
d.y = [J_a_311 < span class = "org-builtin" > *< / span > d.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Sampling Time and Frequency< / span >
Ts = 1e< span class = "org-builtin" > -< / span > 4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [s]< / span >
Fs = 1< span class = "org-builtin" > /< / span > Ts; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [Hz]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Hannning Windows< / span >
win = hanning(ceil(5< span class = "org-builtin" > *< / span > Fs));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% And we get the frequency vector< / span >
[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_uh, < span class = "org-builtin" > ~< / span > ] = tfestimate(uh.u, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_d, < span class = "org-builtin" > ~< / span > ] = tfestimate(d.u, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > [coh_ur, < span class = "org-builtin" > ~< / span > ] = mscohere(ur.u, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_uh, < span class = "org-builtin" > ~< / span > ] = mscohere(uh.u, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_d, < span class = "org-builtin" > ~< / span > ] = mscohere(d.u, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
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< div id = "org9466993" class = "figure" >
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< p > < img src = "figs/coherence_id_dcm_dyn.png" alt = "coherence_id_dcm_dyn.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Coherence< / p >
< / div >
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< div id = "org6e09695" class = "figure" >
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< p > < img src = "figs/bode_plot_dcm_dynamics.png" alt = "bode_plot_dcm_dynamics.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Bode Plot of the DCM dynamics in the frame of the fast jack.< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Previously used controller< / span >
load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Controller design< / span >
s = tf(< span class = "org-string" > 's'< / span > );
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Lead< / span >
a = 4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
wc = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Frequency with the maximum phase lead [rad/s]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 100; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
Kb = eye(3)< span class = "org-builtin" > *< / span > (2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20)< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > *< / span > sqrt(a))) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);;
< / pre >
< / div >
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< div id = "org4f0fbea" class = "figure" >
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< p > < img src = "figs/loop_gain_dcm_contr_simple.png" alt = "loop_gain_dcm_contr_simple.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Loop gain< / p >
< / div >
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< div id = "orgf361fc7" class = "figure" >
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< p > < img src = "figs/loop_gain_diag_old_new_contr.png" alt = "loop_gain_diag_old_new_contr.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Loop gain< / p >
< / div >
< p >
Compare Sensitivity functions
< / p >
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< div id = "orgb76f72d" class = "figure" >
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< p > < img src = "figs/sensitivity_comp.png" alt = "sensitivity_comp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Comparison of sensitivity functions< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > L = zeros(3, 3, length(f));
Lb = zeros(3, 3, length(f));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i_f< / span > = < span class = "org-constant" > 1:length(f)< / span >
L(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(K , f(i_f), < span class = "org-string" > 'Hz'< / span > );
Lb(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb, f(i_f), < span class = "org-string" > 'Hz'< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "orgb0888a7" class = "figure" >
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< p > < img src = "figs/loci_loop_gain_comp_controllers.png" alt = "loci_loop_gain_comp_controllers.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Root Locus< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orga4b6967" class = "outline-3" >
< h3 id = "orga4b6967" > < span class = "section-number-3" > 2.2.< / span > Identification - New< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur = load(< span class = "org-string" > 'FJPUR_step_new.mat'< / span > );
uh = load(< span class = "org-string" > 'FJPUH_step_new.mat'< / span > );
d = load(< span class = "org-string" > 'FJPD_step_new.mat'< / span > );
< / pre >
< / div >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > dz311< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > dry311< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > drx311< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > dz111< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > dry111< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > drx111< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > fjpur< / td >
< / tr >
< tr >
< td class = "org-right" > 8< / td >
< td class = "org-left" > fjpuh< / td >
< / tr >
< tr >
< td class = "org-right" > 9< / td >
< td class = "org-left" > fjpd< / td >
< / tr >
< tr >
< td class = "org-right" > 10< / td >
< td class = "org-left" > bragg< / td >
< / tr >
< / tbody >
< / table >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur.time = ur.time < span class = "org-builtin" > -< / span > ur.time(1);
ur.allValues(< span class = "org-builtin" > :< / span > , 1) = ur.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 0.1, 1));
ur.allValues(< span class = "org-builtin" > :< / span > , 2) = ur.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 0.1, 2));
ur.allValues(< span class = "org-builtin" > :< / span > , 3) = ur.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(ur.allValues(ur.time< span class = "org-builtin" > < < / span > 0.1, 3));
t_filt = ur.time < span class = "org-builtin" > < < / span > 5;
ur.u = ur.allValues(t_filt, 7);
ur.y_111 = [< span class = "org-builtin" > -< / span > ur.allValues(t_filt, 1), ur.allValues(t_filt, 2), ur.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > uh.time = uh.time < span class = "org-builtin" > -< / span > uh.time(1);
uh.allValues(< span class = "org-builtin" > :< / span > , 1) = uh.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 0.1, 1));
uh.allValues(< span class = "org-builtin" > :< / span > , 2) = uh.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 0.1, 2));
uh.allValues(< span class = "org-builtin" > :< / span > , 3) = uh.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(uh.allValues(uh.time< span class = "org-builtin" > < < / span > 0.1, 3));
uh.u = uh.allValues(t_filt, 8);
uh.y_111 = [< span class = "org-builtin" > -< / span > uh.allValues(t_filt, 1), uh.allValues(t_filt, 2), uh.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > d.time = d.time < span class = "org-builtin" > -< / span > d.time(1);
d.allValues(< span class = "org-builtin" > :< / span > , 1) = d.allValues(< span class = "org-builtin" > :< / span > , 1) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 0.1, 1));
d.allValues(< span class = "org-builtin" > :< / span > , 2) = d.allValues(< span class = "org-builtin" > :< / span > , 2) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 0.1, 2));
d.allValues(< span class = "org-builtin" > :< / span > , 3) = d.allValues(< span class = "org-builtin" > :< / span > , 3) < span class = "org-builtin" > -< / span > mean(d.allValues(d.time< span class = "org-builtin" > < < / span > 0.1, 3));
d.u = d.allValues(t_filt, 9);
d.y_111 = [< span class = "org-builtin" > -< / span > d.allValues(t_filt, 1), d.allValues(t_filt, 2), d.allValues(t_filt, 3)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.0675
1, 0.14, 0.1525
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
J_a_311 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.1525
1, 0.14, 0.0675
1, < span class = "org-builtin" > -< / span > 0.14, < span class = "org-builtin" > -< / span > 0.0425];
ur.y = [J_a_311 < span class = "org-builtin" > *< / span > ur.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
uh.y = [J_a_311 < span class = "org-builtin" > *< / span > uh.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
d.y = [J_a_311 < span class = "org-builtin" > *< / span > d.y_111< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Sampling Time and Frequency< / span >
Ts = 1e< span class = "org-builtin" > -< / span > 4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [s]< / span >
Fs = 1< span class = "org-builtin" > /< / span > Ts; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [Hz]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Hannning Windows< / span >
win = hanning(ceil(5< span class = "org-builtin" > *< / span > Fs));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% And we get the frequency vector< / span >
[G_ur, f] = tfestimate(ur.u, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_uh, < span class = "org-builtin" > ~< / span > ] = tfestimate(uh.u, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_d, < span class = "org-builtin" > ~< / span > ] = tfestimate(d.u, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > [coh_ur, < span class = "org-builtin" > ~< / span > ] = mscohere(ur.u, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_uh, < span class = "org-builtin" > ~< / span > ] = mscohere(uh.u, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_d, < span class = "org-builtin" > ~< / span > ] = mscohere(d.u, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Previously used controller< / span >
load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Controller design< / span >
s = tf(< span class = "org-string" > 's'< / span > );
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Lead< / span >
a = 4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
wc = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Frequency with the maximum phase lead [rad/s]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 100; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
Kb = eye(3)< span class = "org-builtin" > *< / span > (2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20)< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > *< / span > sqrt(a))) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);;
< / pre >
< / div >
< p >
Compare Sensitivity functions
< / p >
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< div id = "org61be61a" class = "figure" >
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< p > < img src = "figs/sensitivity_comp.png" alt = "sensitivity_comp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > Comparison of sensitivity functions< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > L = zeros(3, 3, length(f));
Lb = zeros(3, 3, length(f));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i_f< / span > = < span class = "org-constant" > 1:length(f)< / span >
L(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(K , f(i_f), < span class = "org-string" > 'Hz'< / span > );
Lb(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb, f(i_f), < span class = "org-string" > 'Hz'< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "org400e20f" class = "figure" >
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< p > < img src = "figs/loci_loop_gain_comp_controllers.png" alt = "loci_loop_gain_comp_controllers.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Root Locus< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org3ea3501" class = "outline-3" >
< h3 id = "org3ea3501" > < span class = "section-number-3" > 2.3.< / span > Identification - White noise< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur = load(< span class = "org-string" > 'fjpur_white_noise.mat'< / span > );
uh = load(< span class = "org-string" > 'fjpuh_white_noise.mat'< / span > );
d = load(< span class = "org-string" > 'fjpd_white_noise.mat'< / span > );
< / pre >
< / div >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > dz111< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > dry111< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > drx111< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > fjpur< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > fjpuh< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > fjpd< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > bragg< / td >
< / tr >
< / tbody >
< / table >
< div class = "org-src-container" >
< pre class = "src src-matlab" > ur.time = ur.time < span class = "org-builtin" > -< / span > ur.time(1);
ur.drx = ur.drx < span class = "org-builtin" > -< / span > mean(ur.drx);
ur.dry = ur.dry < span class = "org-builtin" > -< / span > mean(ur.dry);
ur.dz = ur.dz < span class = "org-builtin" > -< / span > mean(ur.dz);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > uh.time = uh.time < span class = "org-builtin" > -< / span > uh.time(1);
uh.drx = uh.drx < span class = "org-builtin" > -< / span > mean(uh.drx);
uh.dry = uh.dry < span class = "org-builtin" > -< / span > mean(uh.dry);
uh.dz = uh.dz < span class = "org-builtin" > -< / span > mean(uh.dz);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > d.time = d.time < span class = "org-builtin" > -< / span > d.time(1);
d.drx = d.drx < span class = "org-builtin" > -< / span > mean(d.drx);
d.dry = d.dry < span class = "org-builtin" > -< / span > mean(d.dry);
d.dz = d.dz < span class = "org-builtin" > -< / span > mean(d.dz);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.0675
1, 0.14, 0.1525
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
ur.y = [J_a_111 < span class = "org-builtin" > *< / span > [< span class = "org-builtin" > -< / span > ur.dz, ur.dry, ur.drx]< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
uh.y = [J_a_111 < span class = "org-builtin" > *< / span > [< span class = "org-builtin" > -< / span > uh.dz, uh.dry, uh.drx]< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
d.y = [J_a_111 < span class = "org-builtin" > *< / span > [< span class = "org-builtin" > -< / span > d.dz, d.dry, d.drx]< span class = "org-builtin" > '< / span > ]< span class = "org-builtin" > '< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Sampling Time and Frequency< / span >
Ts = 1e< span class = "org-builtin" > -< / span > 4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [s]< / span >
Fs = 1< span class = "org-builtin" > /< / span > Ts; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [Hz]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Hannning Windows< / span >
win = hanning(ceil(0.5< span class = "org-builtin" > *< / span > Fs));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% And we get the frequency vector< / span >
[G_ur, f] = tfestimate(ur.fjpur, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_uh, < span class = "org-builtin" > ~< / span > ] = tfestimate(uh.fjpuh, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[G_d, < span class = "org-builtin" > ~< / span > ] = tfestimate(d.fjpd, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > [coh_ur, < span class = "org-builtin" > ~< / span > ] = mscohere(ur.fjpur, ur.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_uh, < span class = "org-builtin" > ~< / span > ] = mscohere(uh.fjpuh, uh.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[coh_d, < span class = "org-builtin" > ~< / span > ] = mscohere(d.fjpd, d.y, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
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< div id = "org2130cf9" class = "figure" >
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< p > < img src = "figs/coherence_ident_noise.png" alt = "coherence_ident_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > description< / p >
< / div >
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< div id = "org6275987" class = "figure" >
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< p > < img src = "figs/bode_plot_ident_noise.png" alt = "bode_plot_ident_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 12: < / span > Bode Plot of the DCM dynamics in the frame of the fast jack.< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Previously used controller< / span >
load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Controller design< / span >
s = tf(< span class = "org-string" > 's'< / span > );
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Lead< / span >
a = 8; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
wc = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Frequency with the maximum phase lead [rad/s]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 80; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
Kb = eye(3)< span class = "org-builtin" > *< / span > (2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20)< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > *< / span > sqrt(a))) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);;
< / pre >
< / div >
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< div id = "orgde5672c" class = "figure" >
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< p > < img src = "figs/loop_gain_dcm_contr_simple.png" alt = "loop_gain_dcm_contr_simple.png" / >
< / p >
< p > < span class = "figure-number" > Figure 13: < / span > Loop gain< / p >
< / div >
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< div id = "org816756f" class = "figure" >
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< p > < img src = "figs/loop_gain_diag_old_new_contr.png" alt = "loop_gain_diag_old_new_contr.png" / >
< / p >
< p > < span class = "figure-number" > Figure 14: < / span > Loop gain< / p >
< / div >
< p >
Compare Sensitivity functions
< / p >
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< div id = "org9c6d15d" class = "figure" >
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< p > < img src = "figs/sensitivity_comp.png" alt = "sensitivity_comp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 15: < / span > Comparison of sensitivity functions< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > L = zeros(3, 3, length(f));
Lb = zeros(3, 3, length(f));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i_f< / span > = < span class = "org-constant" > 1:length(f)< / span >
L(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(K , f(i_f), < span class = "org-string" > 'Hz'< / span > );
Lb(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb, f(i_f), < span class = "org-string" > 'Hz'< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "orgcf68c9d" class = "figure" >
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< p > < img src = "figs/loci_loop_gain_comp_controllers.png" alt = "loci_loop_gain_comp_controllers.png" / >
< / p >
< p > < span class = "figure-number" > Figure 16: < / span > Root Locus< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org2f67dfc" class = "outline-3" >
< h3 id = "org2f67dfc" > < span class = "section-number-3" > 2.4.< / span > Test< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Notch< / span >
gm = 0.015;
xi = 0.1;
wn = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 208;
K_notch = (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > gm< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Double integrator< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 40;
K_int = (w0< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Lead< / span >
a = 3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
K_lead = 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > *< / span > sqrt(a)));
K_lead = K_lead< span class = "org-builtin" > *< / span > K_lead;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 120; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
K_lpf = 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Diagonal controller< / span >
Kb = 0.8< span class = "org-builtin" > *< / span > eye(3)< span class = "org-builtin" > *< / span > K_notch< span class = "org-builtin" > *< / span > K_int< span class = "org-builtin" > *< / span > K_lead< span class = "org-builtin" > *< / span > K_lpf;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org675289a" class = "outline-3" >
< h3 id = "org675289a" > < span class = "section-number-3" > 2.5.< / span > New controller - Higher bandwidth< / h3 >
2022-02-15 14:16:10 +01:00
< div class = "outline-text-3" id = "text-2-5" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Previously used controller< / span >
load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Current Controller design< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Lead< / span >
a = 8; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
wc = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Frequency with the maximum phase lead [rad/s]< / span >
< span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 80; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
Kb_old = eye(3)< span class = "org-builtin" > *< / span > (2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 20)< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (wc< span class = "org-builtin" > *< / span > sqrt(a))) < span class = "org-builtin" > *< / span > 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Notch< / span >
gm = 0.015;
xi = 0.2;
wn = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 208;
K_notch = (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > gm< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Double integrator< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 40;
K_int = (w0< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Lead< / span >
a = 3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 40;
K_lead = 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > *< / span > sqrt(a)));
K_lead = K_lead< span class = "org-builtin" > *< / span > K_lead;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 120; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
K_lpf = 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Diagonal controller< / span >
Kb = 0.9< span class = "org-builtin" > *< / span > eye(3)< span class = "org-builtin" > *< / span > K_notch< span class = "org-builtin" > *< / span > K_int< span class = "org-builtin" > *< / span > K_lead< span class = "org-builtin" > *< / span > K_lpf;
< / pre >
< / div >
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< div id = "org729d6bc" class = "figure" >
2022-02-15 14:16:10 +01:00
< p > < img src = "figs/loop_gain_compare.png" alt = "loop_gain_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 17: < / span > description< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > L = zeros(3, 3, length(f));
Lb = zeros(3, 3, length(f));
Lb_new = zeros(3, 3, length(f));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i_f< / span > = < span class = "org-constant" > 1:length(f)< / span >
L(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(K , f(i_f), < span class = "org-string" > 'Hz'< / span > );
Lb(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb_old, f(i_f), < span class = "org-string" > 'Hz'< / span > );
Lb_new(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb, f(i_f), < span class = "org-string" > 'Hz'< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "org9b73c58" class = "figure" >
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< p > < img src = "figs/nyquist_compare.png" alt = "nyquist_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 18: < / span > n< / p >
< / div >
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< div id = "orgd808ef9" class = "figure" >
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< p > < img src = "figs/sensitivity_function_compare.png" alt = "sensitivity_function_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 19: < / span > description< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org2f12e07" class = "outline-3" >
< h3 id = "org2f12e07" > < span class = "section-number-3" > 2.6.< / span > Added gain< / h3 >
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< div class = "outline-text-3" id = "text-2-6" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Notch< / span >
gm = 0.015;
xi = 0.2;
wn = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 208;
K_notch = (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > gm< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Double integrator< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 40;
K_int = (w0< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Lead< / span >
a = 3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Amount of phase lead / width of the phase lead / high frequency gain< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 40;
K_lead = 1< span class = "org-builtin" > /< / span > (sqrt(a))< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > /< / span > sqrt(a)))< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > (w0< span class = "org-builtin" > *< / span > sqrt(a)));
K_lead = K_lead< span class = "org-builtin" > *< / span > K_lead;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Low Pass Filter< / span >
w0 = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 120; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Cut-off frequency [rad/s]< / span >
xi = 0.3; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Damping Ratio< / span >
K_lpf = 1< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > ^< / span > 2< span class = "org-builtin" > /< / span > w0< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > gm = 10;
xi = 0.02;
wn = 2< span class = "org-builtin" > *< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > 15;
H = (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > gm< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2)< span class = "org-builtin" > /< / span > (s< span class = "org-builtin" > ^< / span > 2 < span class = "org-builtin" > +< / span > 2< span class = "org-builtin" > *< / span > xi< span class = "org-builtin" > *< / span > wn< span class = "org-builtin" > *< / span > s < span class = "org-builtin" > +< / span > wn< span class = "org-builtin" > ^< / span > 2);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Diagonal controller< / span >
Kb_gain = 0.9< span class = "org-builtin" > *< / span > eye(3)< span class = "org-builtin" > *< / span > H< span class = "org-builtin" > *< / span > K_notch< span class = "org-builtin" > *< / span > K_int< span class = "org-builtin" > *< / span > K_lead< span class = "org-builtin" > *< / span > K_lpf;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Lb_gain = zeros(3, 3, length(f));
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i_f< / span > = < span class = "org-constant" > 1:length(f)< / span >
Lb_gain(< span class = "org-builtin" > :< / span > ,< span class = "org-builtin" > :< / span > ,i_f) = [G_ur(i_f,< span class = "org-builtin" > :< / span > ); G_uh(i_f,< span class = "org-builtin" > :< / span > ); G_d(i_f,< span class = "org-builtin" > :< / span > )]< span class = "org-builtin" > *< / span > freqresp(Kb_gain, f(i_f), < span class = "org-string" > 'Hz'< / span > );
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< div id = "org97a53c6" class = "figure" >
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< p > < img src = "figs/loop_gain_compare_added_gain.png" alt = "loop_gain_compare_added_gain.png" / >
< / p >
< p > < span class = "figure-number" > Figure 20: < / span > description< / p >
< / div >
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< div id = "org63d3ae0" class = "figure" >
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< p > < img src = "figs/sensitivity_new_gain_compare.png" alt = "sensitivity_new_gain_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 21: < / span > description< / p >
< / div >
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< div id = "orgded1447" class = "figure" >
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< p > < img src = "figs/nyquist_after_gain_frequency.png" alt = "nyquist_after_gain_frequency.png" / >
< / p >
< p > < span class = "figure-number" > Figure 22: < / span > nyquist plot< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orge30c950" class = "outline-2" >
< h2 id = "orge30c950" > < span class = "section-number-2" > 3.< / span > Noise Budgeting< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< / div >
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< div id = "outline-container-org8aeec43" class = "outline-3" >
< h3 id = "org8aeec43" > < span class = "section-number-3" > 3.1.< / span > No Displacement< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > dz311< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > dry311< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > drx311< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > dz111< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > dry111< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > drx111< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > fjpur< / td >
< / tr >
< tr >
< td class = "org-right" > 8< / td >
< td class = "org-left" > fjpuh< / td >
< / tr >
< tr >
< td class = "org-right" > 9< / td >
< td class = "org-left" > fjpd< / td >
< / tr >
< tr >
< td class = "org-right" > 10< / td >
< td class = "org-left" > bragg< / td >
< / tr >
< / tbody >
< / table >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_10_deg = load(< span class = "org-string" > 'no_mov_10.mat'< / span > );
data_70_deg = load(< span class = "org-string" > 'no_mov_70.mat'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_10_deg = extractDatData(< span class = "org-string" > 'no_mov_10.mat'< / span > , < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
{< span class = "org-string" > "dz311"< / span > , < span class = "org-string" > "dry311"< / span > , < span class = "org-string" > "drx311"< / span > , < span class = "org-string" > "dz"< / span > , < span class = "org-string" > "dry"< / span > , < span class = "org-string" > "drx"< / span > , < span class = "org-string" > "fjpur"< / span > , < span class = "org-string" > "fjpuh"< / span > , < span class = "org-string" > "fjpd"< / span > , < span class = "org-string" > "bragg"< / span > }, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
[1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 180]);
data_10_deg = processMeasData(data_10_deg);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Ts = 1e< span class = "org-builtin" > -< / span > 4;
t = Ts< span class = "org-builtin" > *< / span > [1< span class = "org-builtin" > :< / span > length(data_10_deg.bragg)];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_10_deg.dz = data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,4) < span class = "org-builtin" > -< / span > mean(data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,4));
data_10_deg.dry = data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,5) < span class = "org-builtin" > -< / span > mean(data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,5));
data_10_deg.drx = data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,6) < span class = "org-builtin" > -< / span > mean(data_10_deg.allValues(< span class = "org-builtin" > :< / span > ,6));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Compute motion error in the frame of the fast jack< / span >
J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.1525
1, 0.14, 0.0675
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
de_111 = [data_10_deg.dz< span class = "org-builtin" > '< / span > ; data_10_deg.dry< span class = "org-builtin" > '< / span > ; data_10_deg.drx< span class = "org-builtin" > '< / span > ];
de_fj = J_a_111< span class = "org-builtin" > *< / span > de_111;
data_10_deg.fj_ur = de_fj(1,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
data_10_deg.fj_uh = de_fj(2,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
data_10_deg.fj_d = de_fj(3,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
de_111 = [data_70_deg.dz< span class = "org-builtin" > '< / span > ; data_70_deg.dry< span class = "org-builtin" > '< / span > ; data_70_deg.drx< span class = "org-builtin" > '< / span > ];
de_fj = J_a_111< span class = "org-builtin" > *< / span > de_111;
data_70_deg.fj_ur = de_fj(1,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
data_70_deg.fj_uh = de_fj(2,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
data_70_deg.fj_d = de_fj(3,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
[pxx_10_ur, f] = pwelch(data_10_deg.fj_ur, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_ur, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.fj_ur, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_uh, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_deg.fj_uh, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_uh, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.fj_uh, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_d, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_deg.fj_d, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_d, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.fj_d, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > CPS_10_ur = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_ur)));
CPS_10_uh = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_uh)));
CPS_10_d = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_d)));
CPS_70_ur = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_ur)));
CPS_70_uh = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_uh)));
CPS_70_d = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_d)));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_10_ur), < span class = "org-string" > '-'< / span > , < span class = "org-string" > 'color'< / span > , colors(1, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '10 deg - $u_r$'< / span > )
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_70_ur), < span class = "org-string" > '--'< / span > , < span class = "org-string" > 'color'< / span > , colors(1, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '70 deg - $u_r$'< / span > )
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_10_uh), < span class = "org-string" > '-'< / span > , < span class = "org-string" > 'color'< / span > , colors(2, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '10 deg - $u_h$'< / span > )
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_70_uh), < span class = "org-string" > '--'< / span > , < span class = "org-string" > 'color'< / span > , colors(2, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '70 deg - $u_h$'< / span > )
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_10_d), < span class = "org-string" > '-'< / span > , < span class = "org-string" > 'color'< / span > , colors(3, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '10 deg - $d$'< / span > )
< span class = "org-builtin" > plot< / span > (f, sqrt(CPS_70_d), < span class = "org-string" > '--'< / span > , < span class = "org-string" > 'color'< / span > , colors(3, < span class = "org-builtin" > :< / span > ), < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '70 deg - $d$'< / span > )
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_10_ur))
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_70_ur))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_70_deg.dz = data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,4) < span class = "org-builtin" > -< / span > mean(data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,4));
data_70_deg.dry = data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,5) < span class = "org-builtin" > -< / span > mean(data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,5));
data_70_deg.drx = data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,6) < span class = "org-builtin" > -< / span > mean(data_70_deg.allValues(< span class = "org-builtin" > :< / span > ,6));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
[pxx_10_drx, f] = pwelch(data_10_deg.drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_drx, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_dry, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_deg.dry, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_dry, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.dry, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_dz, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_deg.dz, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_dz, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_deg.dz, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_10_drx))
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_70_drx))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_10_dry))
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_70_dry))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_10_dz))
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_70_dz))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nm}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< / div >
< / div >
2022-06-02 18:23:48 +02:00
< div id = "outline-container-org2e15aa7" class = "outline-3" >
< h3 id = "org2e15aa7" > < span class = "section-number-3" > 3.2.< / span > Scans< / h3 >
2022-02-15 14:16:10 +01:00
< div class = "outline-text-3" id = "text-3-2" >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > dz311< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > dry311< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > drx311< / td >
< / tr >
< tr >
< td class = "org-right" > 4< / td >
< td class = "org-left" > dz111< / td >
< / tr >
< tr >
< td class = "org-right" > 5< / td >
< td class = "org-left" > dry111< / td >
< / tr >
< tr >
< td class = "org-right" > 6< / td >
< td class = "org-left" > drx111< / td >
< / tr >
< tr >
< td class = "org-right" > 7< / td >
< td class = "org-left" > fjpur< / td >
< / tr >
< tr >
< td class = "org-right" > 8< / td >
< td class = "org-left" > fjpuh< / td >
< / tr >
< tr >
< td class = "org-right" > 9< / td >
< td class = "org-left" > fjpd< / td >
< / tr >
< tr >
< td class = "org-right" > 10< / td >
< td class = "org-left" > bragg< / td >
< / tr >
< / tbody >
< / table >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Load Data< / span >
data_10_70_deg = extractDatData(< span class = "org-string" > 'thtraj_10_70.mat'< / span > , < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
{< span class = "org-string" > "dz311"< / span > , < span class = "org-string" > "dry311"< / span > , < span class = "org-string" > "drx311"< / span > , < span class = "org-string" > "dz"< / span > , < span class = "org-string" > "dry"< / span > , < span class = "org-string" > "drx"< / span > , < span class = "org-string" > "fjur"< / span > , < span class = "org-string" > "fjuh"< / span > , < span class = "org-string" > "fjd"< / span > , < span class = "org-string" > "bragg"< / span > }, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
[1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 180]);
Ts = 1e< span class = "org-builtin" > -< / span > 4;
t = Ts< span class = "org-builtin" > *< / span > [1< span class = "org-builtin" > :< / span > length(data_10_70_deg.bragg)];
< span class = "org-matlab-cellbreak" > %% Actuator Jacobian< / span >
J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.0675
1, 0.14, 0.1525
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
data_10_70_deg.ddz = 10.5e< span class = "org-builtin" > -< / span > 3< span class = "org-builtin" > ./< / span > (2< span class = "org-builtin" > *< / span > cos(data_10_70_deg.bragg)) < span class = "org-builtin" > -< / span > data_10_70_deg.dz;
< span class = "org-matlab-cellbreak" > %% Computation of the position of the FJ as measured by the interferometers< / span >
error = J_a_111 < span class = "org-builtin" > *< / span > [data_10_70_deg.ddz, data_10_70_deg.dry, data_10_70_deg.drx]< span class = "org-builtin" > '< / span > ;
data_10_70_deg.fjur_e = error(1,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
data_10_70_deg.fjuh_e = error(2,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
data_10_70_deg.fjd_e = error(3,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Load Data< / span >
data_70_10_deg = extractDatData(< span class = "org-string" > 'thtraj_70_10.mat'< / span > , < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
{< span class = "org-string" > "dz311"< / span > , < span class = "org-string" > "dry311"< / span > , < span class = "org-string" > "drx311"< / span > , < span class = "org-string" > "dz"< / span > , < span class = "org-string" > "dry"< / span > , < span class = "org-string" > "drx"< / span > , < span class = "org-string" > "fjur"< / span > , < span class = "org-string" > "fjuh"< / span > , < span class = "org-string" > "fjd"< / span > , < span class = "org-string" > "bragg"< / span > }, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
[1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 180]);
< span class = "org-matlab-cellbreak" > %% Actuator Jacobian< / span >
J_a_111 = [1, 0.14, < span class = "org-builtin" > -< / span > 0.0675
1, 0.14, 0.1525
1, < span class = "org-builtin" > -< / span > 0.14, 0.0425];
data_70_10_deg.ddz = 10.5e< span class = "org-builtin" > -< / span > 3< span class = "org-builtin" > ./< / span > (2< span class = "org-builtin" > *< / span > cos(data_70_10_deg.bragg)) < span class = "org-builtin" > -< / span > data_70_10_deg.dz;
< span class = "org-matlab-cellbreak" > %% Computation of the position of the FJ as measured by the interferometers< / span >
error = J_a_111 < span class = "org-builtin" > *< / span > [data_70_10_deg.ddz, data_70_10_deg.dry, data_70_10_deg.drx]< span class = "org-builtin" > '< / span > ;
data_70_10_deg.fjur_e = error(1,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
data_70_10_deg.fjuh_e = error(2,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
data_70_10_deg.fjd_e = error(3,< span class = "org-builtin" > :< / span > )< span class = "org-builtin" > '< / span > ; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > [m]< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
[pxx_10_70_ur, f] = pwelch(data_10_70_deg.fjur_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_10_ur, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_10_deg.fjur_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_70_uh, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_70_deg.fjuh_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_10_uh, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_10_deg.fjuh_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_10_70_d, < span class = "org-builtin" > ~< / span > ] = pwelch(data_10_70_deg.fjd_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_70_10_d, < span class = "org-builtin" > ~< / span > ] = pwelch(data_70_10_deg.fjd_e(t< span class = "org-builtin" > < < / span > 100), win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > CPS_10_70_ur = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_70_ur)));
CPS_10_70_uh = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_70_uh)));
CPS_10_70_d = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_10_70_d)));
CPS_70_10_ur = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_10_ur)));
CPS_70_10_uh = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_10_uh)));
CPS_70_10_d = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_70_10_d)));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, 1e9< span class = "org-builtin" > *< / span > sqrt(CPS_10_70_ur))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_10_70_ur))
< span class = "org-builtin" > plot< / span > (f, sqrt(pxx_70_10_ur))
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-builtin" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Frequency [Hz]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'ASD [$\frac{nrad}{\sqrt{Hz}}$]'< / span > );
< span class = "org-builtin" > legend< / span > (< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northwest'< / span > );
< span class = "org-builtin" > xlim< / span > ([1, 1e3]);
< / pre >
< / div >
< / div >
< / div >
2022-06-02 18:23:48 +02:00
< div id = "outline-container-org26d025b" class = "outline-3" >
< h3 id = "org26d025b" > < span class = "section-number-3" > 3.3.< / span > Noise budgeting - No rotation< / h3 >
2022-02-15 14:16:10 +01:00
< div class = "outline-text-3" id = "text-3-3" >
< p >
First, we look at the position errors when the bragg axis is not moving
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Load Measurement Data< / span >
ol_data = load(< span class = "org-string" > 'FJPUR_step.mat'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Pre-processing< / span >
ol_time = ol_data.time < span class = "org-builtin" > -< / span > ol_data.time(1);
ol_drx = ol_data.allValues(ol_time < span class = "org-builtin" > < < / span > 45, 6);
ol_dry = ol_data.allValues(ol_time < span class = "org-builtin" > < < / span > 45, 5);
ol_dz = ol_data.allValues(ol_time < span class = "org-builtin" > < < / span > 45, 4);
ol_drx = ol_drx < span class = "org-builtin" > -< / span > mean(ol_drx);
ol_dry = ol_dry < span class = "org-builtin" > -< / span > mean(ol_dry);
ol_dz = ol_dz < span class = "org-builtin" > -< / span > mean(ol_dz);
ol_time = ol_time(ol_time < span class = "org-builtin" > < < / span > 45);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > plot< / span > (ol_time, ol_drx)
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Parameters for Spectral Analysis< / span >
Ts = 1e< span class = "org-builtin" > -< / span > 4;
win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Computation of the PSD< / span >
[pxx_ol_drx, f] = pwelch(ol_drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_ol_dry, < span class = "org-builtin" > ~< / span > ] = pwelch(ol_dry, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_ol_dz, < span class = "org-builtin" > ~< / span > ] = pwelch(ol_dz, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
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< div id = "org7fb6c81" class = "figure" >
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< p > < img src = "figs/noise_budget_no_mov_asd.png" alt = "noise_budget_no_mov_asd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 23: < / span > Amplitude Spectral Density< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Cumulative Spectral Density< / span >
CPS_drx = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_ol_drx)));
CPS_dry = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_ol_dry)));
CPS_dz = flip(< span class = "org-builtin" > -< / span > cumtrapz(flip(f), flip(pxx_ol_dz)));
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Cumulative Spectral Density< / span >
CPS_drx = cumtrapz(f, pxx_ol_drx);
CPS_dry = cumtrapz(f, pxx_ol_dry);
CPS_dz = cumtrapz(f, pxx_ol_dz);
< / pre >
< / div >
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< div id = "org2f67e0e" class = "figure" >
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< p > < img src = "figs/noise_budget_no_mov_cas.png" alt = "noise_budget_no_mov_cas.png" / >
< / p >
< p > < span class = "figure-number" > Figure 24: < / span > Cumulative Amplitude Spectrum< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org8945ee2" class = "outline-3" >
< h3 id = "org8945ee2" > < span class = "section-number-3" > 3.4.< / span > Noise budgeting - Bragg rotation< / h3 >
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< / div >
< / div >
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< div id = "outline-container-orgc0ab5d1" class = "outline-2" >
< h2 id = "orgc0ab5d1" > < span class = "section-number-2" > 4.< / span > Test Mode C< / h2 >
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< div class = "outline-text-2" id = "text-4" >
< / div >
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< div id = "outline-container-org9996dc6" class = "outline-3" >
< h3 id = "org9996dc6" > < span class = "section-number-3" > 4.1.< / span > Mode B and Mode C< / h3 >
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< div class = "outline-text-3" id = "text-4-1" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_B = extractDatData(sprintf(< span class = "org-string" > "/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s"< / span > ,< span class = "org-string" > "lut_const_fj_vel_19012022_1450.dat"< / span > ), < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
{< span class = "org-string" > "bragg"< / span > , < span class = "org-string" > "dz"< / span > , < span class = "org-string" > "dry"< / span > , < span class = "org-string" > "drx"< / span > , < span class = "org-string" > "fjur"< / span > , < span class = "org-string" > "fjuh"< / span > , < span class = "org-string" > "fjd"< / span > }, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
[< span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 180, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8]);
data_B = processMeasData(data_B);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data_C = extractDatData(sprintf(< span class = "org-string" > "/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s"< / span > ,< span class = "org-string" > "lut_const_fj_vel_19012022_1454.dat"< / span > ), < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
{< span class = "org-string" > "bragg"< / span > , < span class = "org-string" > "dz"< / span > , < span class = "org-string" > "dry"< / span > , < span class = "org-string" > "drx"< / span > , < span class = "org-string" > "fjur"< / span > , < span class = "org-string" > "fjuh"< / span > , < span class = "org-string" > "fjd"< / span > }, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > ..< / span >
[< span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 180, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 9, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8, 1e< span class = "org-builtin" > -< / span > 8]);
data_C = processMeasData(data_C);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_B.bragg, 1e9< span class = "org-builtin" > *< / span > data_B.drx)
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Bragg Angle [deg]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'DRX [nrad]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_B.bragg, 1e9< span class = "org-builtin" > *< / span > data_B.fjur_e_filt)
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_C.bragg, 1e9< span class = "org-builtin" > *< / span > data_C.fjur_e_filt)
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Bragg Angle [deg]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'FJUR Error [nm]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_B.bragg, 1e9< span class = "org-builtin" > *< / span > data_B.fjur_e)
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_C.bragg, 1e9< span class = "org-builtin" > *< / span > data_C.fjur_e)
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Bragg Angle [deg]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'FJUR Error [nm]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% FIR Filter< / span >
Fs = 1e4; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Sampling Frequency [Hz]< / span >
fir_order = 5000; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Filter's order< / span >
delay = fir_order< span class = "org-builtin" > /< / span > 2; < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Delay induced by the filter< / span >
B_fir = firls(5000, < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > .. % Filter's order< / span >
[0 5< span class = "org-builtin" > /< / span > (Fs< span class = "org-builtin" > /< / span > 2) 10< span class = "org-builtin" > /< / span > (Fs< span class = "org-builtin" > /< / span > 2) 1], < span class = "org-comment-delimiter" > .< / span > < span class = "org-comment" > .. % Frequencies [Hz]< / span >
[1 1 0 0]); < span class = "org-comment-delimiter" > % < / span > < span class = "org-comment" > Wanted Magnitudes< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > %% Filtering all measured Fast Jack Position using the FIR filter< / span >
data_B.drx_filter = filter(B_fir, 1, data_B.drx);
data_B.drx_filter(1< span class = "org-builtin" > :< / span > end< span class = "org-builtin" > -< / span > delay) = data_B.drx_filter(delay< span class = "org-builtin" > +< / span > 1< span class = "org-builtin" > :< / span > end);
data_C.drx_filter = filter(B_fir, 1, data_C.drx);
data_C.drx_filter(1< span class = "org-builtin" > :< / span > end< span class = "org-builtin" > -< / span > delay) = data_C.drx_filter(delay< span class = "org-builtin" > +< / span > 1< span class = "org-builtin" > :< / span > end);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-builtin" > figure< / span > ;
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > on;< / span >
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_B.bragg, 1e9< span class = "org-builtin" > *< / span > data_B.drx_filter)
< span class = "org-builtin" > plot< / span > (180< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > *< / span > data_C.bragg, 1e9< span class = "org-builtin" > *< / span > data_C.drx_filter)
< span class = "org-builtin" > hold< / span > < span class = "org-matlab-commanddual-string" > off;< / span >
< span class = "org-builtin" > xlabel< / span > (< span class = "org-string" > 'Bragg Angle [deg]'< / span > ); < span class = "org-builtin" > ylabel< / span > (< span class = "org-string" > 'DRX [nrad]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Ts = 1e< span class = "org-builtin" > -< / span > 4;
win = hanning(ceil(1< span class = "org-builtin" > /< / span > Ts));
[pxx_B_drx, f] = pwelch(data_B.drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
[pxx_C_drx, < span class = "org-builtin" > ~< / span > ] = pwelch(data_C.drx, win, [], [], 1< span class = "org-builtin" > /< / span > Ts);
< / pre >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org1c0791b" class = "outline-2" >
< h2 id = "org1c0791b" > < span class = "section-number-2" > 5.< / span > Export numerator and denominator< / h2 >
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< div class = "outline-text-2" id = "text-5" >
< / div >
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< div id = "outline-container-org22487de" class = "outline-3" >
< h3 id = "org22487de" > < span class = "section-number-3" > 5.1.< / span > Export< / h3 >
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< div class = "outline-text-3" id = "text-5-1" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > K_order = 10;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'X_tal_cage_PID.mat'< / span > , < span class = "org-string" > 'K'< / span > );
K_order = order(K(1,1));
Kz = c2d(K(1,1)< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order)< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order), 1e< span class = "org-builtin" > -< / span > 4);
[num, den] = tfdata(Kz, < span class = "org-string" > 'v'< / span > );
formatSpec = < span class = "org-string" > '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'< / span > ;
fileID = fopen(< span class = "org-string" > 'X_tal_cage_PID.dat'< / span > , < span class = "org-string" > 'w'< / span > );
fprintf(fileID, formatSpec, [num; den]< span class = "org-builtin" > '< / span > );
fclose(fileID);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'X_tal_cage_PID_20Hz.mat'< / span > , < span class = "org-string" > 'K'< / span > );
K_order = order(K(1,1));
Kz = c2d(K(1,1)< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order)< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order), 1e< span class = "org-builtin" > -< / span > 4);
[num, den] = tfdata(Kz, < span class = "org-string" > 'v'< / span > );
formatSpec = < span class = "org-string" > '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'< / span > ;
fileID = fopen(< span class = "org-string" > 'X_tal_cage_PID_20Hz.dat'< / span > , < span class = "org-string" > 'w'< / span > );
fprintf(fileID, formatSpec, [num; den]< span class = "org-builtin" > '< / span > );
fclose(fileID);
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'X_tal_cage_PID_40Hz.mat'< / span > , < span class = "org-string" > 'K'< / span > );
K_order = order(K(1,1));
Kz = c2d(K(1,1)< span class = "org-builtin" > *< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order)< span class = "org-builtin" > /< / span > (1 < span class = "org-builtin" > +< / span > s< span class = "org-builtin" > /< / span > 2< span class = "org-builtin" > /< / span > < span class = "org-matlab-math" > pi< / span > < span class = "org-builtin" > /< / span > 2e3)< span class = "org-builtin" > ^< / span > (9< span class = "org-builtin" > -< / span > K_order), 1e< span class = "org-builtin" > -< / span > 4);
[num, den] = tfdata(Kz, < span class = "org-string" > 'v'< / span > );
formatSpec = < span class = "org-string" > '%.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e %.18e\n'< / span > ;
fileID = fopen(< span class = "org-string" > 'X_tal_cage_PID_40Hz.dat'< / span > , < span class = "org-string" > 'w'< / span > );
fprintf(fileID, formatSpec, [num; den]< span class = "org-builtin" > '< / span > );
fclose(fileID);
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org2b8461a" class = "outline-3" >
< h3 id = "org2b8461a" > < span class = "section-number-3" > 5.2.< / span > Verify< / h3 >
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< div class = "outline-text-3" id = "text-5-2" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > K_data = importdata(< span class = "org-string" > 'X_tal_cage_PID_20Hz.dat'< / span > );
K = tf(K_data(1,< span class = "org-builtin" > :< / span > ), K_data(2,< span class = "org-builtin" > :< / span > ), 1e< span class = "org-builtin" > -< / span > 4)
< / pre >
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2022-02-20 dim. 23:36< / p >
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< / div >
< / body >
< / html >
