matlab/mat/APA300ML_b_mat_K.CSV

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--1.8457235209690884e+02,1.7301918928302603e+05,2.5641571928068515e+01,2.6422589303900727e+03,2.7533572366421666e+00,5.8241979344293497e+02,1.4181952992388602e+02,1.7292474626467336e+05,2.6410792171231975e+01,-2.6407761935663261e+03,2.0991969789505553e+00,5.8076741626984233e+02,2.2993805653662037e+01,-1.5792309616018035e+03,2.6721298546068226e+00,-1.0652491749164028e-01,9.4702110566029507e-02,9.3113862533255549e+00,1.9759016387164593e+01,-3.4436470458608563e+05,-5.4724493886562414e+01,1.2681926200593807e+00,2.2402311984969856e+00,1.0482207507265615e+04,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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matlab/mat/APA300ML_b_mat_M.CSV

@@ -1,30 +0,0 @@
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--1.4855285726372427e-08,2.0847420748021692e-04,-1.0703604831706744e-08,3.6301015377558860e-06,2.0587064984584790e-10,1.3391110324094624e-07,-1.5836210111893560e-10,-1.6213862542735465e-06,-3.6324314208537155e-10,2.4992290780492576e-08,-9.8600361582237281e-12,-8.1380500810644834e-10,9.7322106506002676e-09,1.7625379220815372e-05,-1.9934307760184012e-09,-9.5310940836458449e-08,4.5362711505625478e-11,4.0782896626726310e-08,7.9371572391907361e-09,1.7327440296864877e-05,-3.8682870726350083e-09,-9.2653911707813300e-08,3.3849465985781987e-11,-3.6579826156812293e-08,-9.0534918685676973e-09,1.1311882648234729e-08,5.8933340674253114e-08,-7.7634106731750022e-08,-1.4292354704284731e-04,-1.5658481720818199e-04
--2.0371699072830736e-04,1.6673922315234365e-09,-3.2117269161997518e-05,2.0587064984584790e-10,3.4552285411925002e-06,5.3971411841053827e-09,6.8240588190787650e-06,-9.2424068051922275e-10,4.7928666595930285e-07,2.1973209408390766e-11,1.1809643885855493e-07,7.1489665528404756e-11,-2.5531130291525775e-05,4.8381081077140949e-08,2.1103568300205978e-05,-2.9337756459214897e-10,-2.6797591419335909e-07,1.3399594779051818e-11,-2.2084740069625680e-05,-4.4684545426033561e-08,-2.5658110211821661e-05,1.9810324568146908e-10,-2.6325304770016137e-07,-1.5242383565828687e-12,2.4047179038042549e-04,9.2642899181507004e-04,2.7385512250621057e-04,-3.9964156024956154e-04,-4.2607777441442843e-07,-3.8565168949155090e-07
--2.1745392833826402e-07,2.3321087279772923e-05,4.0227037214727572e-08,1.3391110324094624e-07,5.3971411841053827e-09,7.5277766095326578e-07,8.8646669428802092e-09,-3.7951879285763008e-08,1.0226785267385210e-09,8.1806577080346806e-10,1.5061018067429513e-10,-8.2232843690813518e-09,-1.1828236113200442e-08,-1.0731266550494226e-05,6.2697077978645651e-08,6.8425490988593457e-08,-3.3857021525737821e-10,-3.4427734484491376e-09,-1.7414734634783023e-08,1.1501926431063936e-05,-6.0952841206442293e-08,-8.5542667622825983e-08,-3.7279134675101884e-10,-1.1470471360021672e-08,6.3632327770373212e-07,2.6169654427495415e-06,5.3133258845425704e-07,-7.7033416935686729e-07,8.4549719379622244e-05,1.0103092517707942e-04
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--3.1932913354539853e-05,-3.1689495485744817e-08,1.3792882641993729e-05,-3.6324314208537155e-10,4.7928666595930285e-07,1.0226785267385210e-09,-7.1955727612052294e-04,-1.4554894065830701e-06,1.8500680585171864e-02,2.9651330646565552e-08,-3.2308451005118596e-05,6.6964762731386892e-08,-7.7653201252517873e-04,1.6177026519025475e-06,8.1289018390646648e-04,1.0914340968801451e-08,2.1513894996636448e-06,4.3218760601227906e-09,1.4948168001170080e-03,-4.3207128711837506e-07,9.2863281394679417e-04,-2.8084006507255753e-09,-6.9168244237829259e-06,-8.3166707579859840e-10,1.4815074388361563e-02,-3.4431229792968401e-03,3.1029076941670258e-02,2.1500078111474159e-02,-4.5308885812505270e-06,3.5503611386558879e-06
--1.6291624566999286e-09,1.6211520072552721e-06,-6.5901225271129960e-10,2.4992290780492576e-08,2.1973209408390766e-11,8.1806577080346806e-10,-2.4354396183705811e-08,-2.0846577155292590e-04,2.9651330646565552e-08,3.6300308429067821e-06,-1.3224245708382725e-10,-1.3355273985170506e-07,1.1919564185419764e-08,-1.7622675801844818e-05,7.5974471425170971e-09,-9.5250404047935082e-08,-1.3459526205199561e-10,-4.0810144457506839e-08,7.2040182809950229e-09,-1.7331658644641598e-05,9.5045176244506208e-10,-9.2678256399238610e-08,-4.1090109679646173e-11,3.6586482606985394e-08,1.5267738339093641e-07,-4.7256199419127589e-08,7.4848277785221044e-08,3.6822640676370892e-08,-1.4334890147197054e-04,1.5469671657942377e-04
--6.8417772679783104e-06,-4.4216105429561921e-11,4.7102412913508216e-07,-9.8600361582237281e-12,1.1809643885855493e-07,1.5061018067429513e-10,2.0254063814235466e-04,-3.5088438576853496e-09,-3.2308451005118596e-05,-1.3224245708382725e-10,3.4318807467887414e-06,1.7080365762476007e-09,2.5866368058626846e-05,2.6278001562175075e-08,2.0876081856622234e-05,9.3505853228806687e-11,-2.6922318766943660e-07,4.2350282748122511e-11,2.2426870486275633e-05,-1.8450243821782357e-08,-2.5464492326032117e-05,-9.5306237982905632e-11,-2.6459283381123206e-07,-4.0763279599020582e-12,9.3120519511358810e-04,-1.9473401058760291e-04,-3.9461713482364172e-04,-2.7455870283132184e-04,6.2156503452954828e-08,3.7770520946776815e-08
--3.8388998111583414e-09,-3.7803793314072381e-08,3.7517397524386865e-10,-8.1380500810644834e-10,7.1489665528404756e-11,-8.2232843690813518e-09,4.2982732373152850e-08,2.3313868178992241e-05,6.6964762731386892e-08,-1.3355273985170506e-07,1.7080365762476007e-09,7.5143276157053636e-07,3.3366161207082545e-09,-1.0705471261800232e-05,3.5502313872098743e-08,-6.8069505869524165e-08,-1.7868833429445421e-10,-3.3375385510527639e-09,1.6368400729117385e-08,1.1476899025139944e-05,-2.0565875284709919e-08,8.5181080433892891e-08,-2.1672347729229982e-10,-1.1358514173639934e-08,1.2913453140722295e-06,-2.8092123481064990e-07,-1.5357525597872957e-07,-1.1178408030701035e-07,-8.5923268713794567e-05,1.0094987357770084e-04
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--1.0034492266511058e-06,1.0931170994695402e-03,7.4823251352092058e-07,1.7625379220815372e-05,4.8381081077140949e-08,-1.0731266550494226e-05,3.2470614565074756e-07,1.0932497241376410e-03,1.6177026519025475e-06,-1.7622675801844818e-05,2.6278001562175075e-08,-1.0705471261800232e-05,-1.9360111494663364e-06,1.4291591380573638e-02,1.9384376587522461e-06,1.3684028511289494e-08,-1.2696482312759008e-08,-2.1614028574371046e-05,-8.7906144095018850e-07,-2.6564514179128217e-04,-9.0782965348417961e-07,-1.0782768144772890e-08,-2.2003585987316592e-08,5.3640807704353118e-07,3.9397010399357789e-05,3.7978965591001709e-05,7.8256140429005282e-06,-1.2679150965871501e-05,-5.3242764183186087e-05,1.0765247556630357e-02
--6.3126611914287982e-04,-2.1020044507387730e-07,8.1399178114214079e-04,-1.9934307760184012e-09,2.1103568300205978e-05,6.2697077978645651e-08,6.1796986986486135e-04,-4.8974848636588357e-07,8.1289018390646648e-04,7.5974471425170971e-09,2.0876081856622234e-05,3.5502313872098743e-08,4.7205080478775262e-06,1.9384376587522461e-06,1.5042497397507021e-02,-1.7418871911740445e-09,2.8907351863976703e-05,1.3153327396045632e-08,6.0382774207451070e-06,-9.7674329594195266e-07,2.5534244212013703e-04,3.4360706999119015e-09,-6.9501793669048047e-06,-7.4615851574839863e-10,4.2255211743104835e-02,2.6290635097006458e-02,4.5893706783715028e-03,2.4720490694272620e-02,-1.0881112921593950e-05,5.4436626454446008e-06
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-1.4313229820365255e-05,9.9008938313856144e-10,2.1871737790360525e-06,4.5362711505625478e-11,-2.6797591419335909e-07,-3.3857021525737821e-10,-1.4321363778190983e-05,3.6938113497197211e-09,2.1513894996636448e-06,-1.3459526205199561e-10,-2.6922318766943660e-07,-1.7868833429445421e-10,-4.6868173361840907e-08,-1.2696482312759008e-08,2.8907351863976703e-05,6.7442425336644724e-11,2.7984510510818298e-07,6.9524463388120750e-11,-6.1419246862805542e-08,1.6470096053092844e-08,3.9217366938157216e-06,-8.1588699300135691e-11,3.1957860413565765e-08,-2.7174943491167994e-11,-4.4239485804719126e-05,-2.6019431990559389e-05,1.5811473476354649e-05,8.5042080391325748e-05,-1.9643990516257122e-08,-1.5854567996781013e-07
-2.7835778708660203e-09,4.0446244313812347e-06,1.5886594278765330e-09,4.0782896626726310e-08,1.3399594779051818e-11,-3.4427734484491376e-09,3.8509086803468143e-10,4.0485273109107100e-06,4.3218760601227906e-09,-4.0810144457506839e-08,4.2350282748122511e-11,-3.3375385510527639e-09,-3.3306060871738000e-08,-2.1614028574371046e-05,1.3153327396045632e-08,1.0996589430279572e-10,6.9524463388120750e-11,3.5369369183140893e-07,-1.2122616095158942e-09,-9.4287993762330324e-07,-4.2336001202932914e-10,-2.6568064594903397e-11,-5.2959088148189155e-11,1.2070141377110959e-09,6.3985104041112299e-08,4.8715958722368958e-08,4.7388487095991299e-08,-2.2553881719432628e-08,-7.3800083697808571e-07,1.9346850933749053e-04
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--7.8368585089446264e-03,-9.7450161098053282e-07,3.5080195060233350e-03,-9.0534918685676973e-09,2.4047179038042549e-04,6.3632327770373212e-07,2.6986035757751169e-02,-1.0475098811573714e-05,1.4815074388361563e-02,1.5267738339093641e-07,9.3120519511358810e-04,1.2913453140722295e-06,-8.5654308645429517e-03,3.9397010399357789e-05,4.2255211743104835e-02,5.5746502142499671e-08,-4.4239485804719126e-05,6.3985104041112299e-08,5.6028256921109602e-03,-2.3449625632406611e-05,-1.6601470294411710e-02,-2.8147546014428653e-08,-1.1703100914871405e-04,1.3257296427331251e-09,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--2.6691741010441878e-02,-6.9674125063883316e-07,1.4877924065196259e-02,1.1311882648234729e-08,9.2642899181507004e-04,2.6169654427495415e-06,-4.7536931782869839e-03,3.2099899258691447e-06,-3.4431229792968401e-03,-4.7256199419127589e-08,-1.9473401058760291e-04,-2.8092123481064990e-07,1.4178346691946590e-02,3.7978965591001709e-05,2.6290635097006458e-02,-3.8437567332673447e-07,-2.6019431990559389e-05,4.8715958722368958e-08,-8.7266512276299724e-03,-3.9563812987916788e-05,-1.0272652773091639e-02,3.3506919589840966e-07,-7.1242566024660810e-05,4.1037725763543876e-08,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--1.0427386470714088e-02,1.9363345520680989e-06,-2.1382430604509124e-02,5.8933340674253114e-08,2.7385512250621057e-04,5.3133258845425704e-07,-1.5041053783048548e-02,-5.0828790146892040e-06,3.1029076941670258e-02,7.4848277785221044e-08,-3.9461713482364172e-04,-1.5357525597872957e-07,-2.3661256130655259e-02,7.8256140429005282e-06,4.5893706783715028e-03,-9.0889126615002546e-08,1.5811473476354649e-05,4.7388487095991299e-08,3.8957018025184406e-02,-5.1592053467100967e-06,9.6000877586945223e-03,1.4303033724950140e-07,-1.8670750304816238e-05,-1.6361580646079214e-08,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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matlab/mat/APA300ML_b_out_nodes_3D.txt

@@ -1,54 +0,0 @@
-
- LIST ALL SELECTED NODES.   DSYS=      0
-
- *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
- DISTRIBUTED ANSYS Mechanical Enterprise                       
-
- 00208316  VERSION=WINDOWS x64   11:07:02  MAR 25, 2021 CP=      2.062
-
- Unknown                                                                       
-
-
-
-    NODE        X             Y             Z           THXY     THYZ     THZX
-   840914   0.0000        0.0000       0.28000E-001     0.00     0.00     0.00
-   840915   0.0000        0.0000      -0.28000E-001     0.00     0.00     0.00
-   840916 -0.34000E-001   0.0000        0.0000          0.00     0.00     0.00
-   840917  0.34000E-001   0.0000        0.0000          0.00     0.00     0.00
-
- LIST MASTERS ON ALL SELECTED NODES.
- CURRENT DOF SET= UX   UY   UZ   ROTX ROTY ROTZ
-
- *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
- DISTRIBUTED ANSYS Mechanical Enterprise                       
-
- 00208316  VERSION=WINDOWS x64   11:07:02  MAR 25, 2021 CP=      2.188
-
- Unknown                                                                       
-
-
-     NODE  LABEL     SUPPORT
-    840914  UX  
-    840914  UY  
-    840914  UZ  
-    840914  ROTX
-    840914  ROTY
-    840914  ROTZ
-    840915  UX  
-    840915  UY  
-    840915  UZ  
-    840915  ROTX
-    840915  ROTY
-    840915  ROTZ
-    840916  UX  
-    840916  UY  
-    840916  UZ  
-    840916  ROTX
-    840916  ROTY
-    840916  ROTZ
-    840917  UX  
-    840917  UY  
-    840917  UZ  
-    840917  ROTX
-    840917  ROTY
-    840917  ROTZ

matlab/mat/full_APA300ML_K.CSV

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matlab/mat/full_APA300ML_M.CSV

@@ -1,36 +0,0 @@
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-0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,2.4226386986399002e-10,-4.1355618793143265e-05,-2.7764914499663005e-10,1.8960235911998903e-14,3.2305945952911957e-12,-3.9148639119402698e-07,-5.9706090517186022e-10,-4.9375767802099400e-05,-9.9396440298130193e-10,-2.3576555754302375e-12,-9.9015023481763857e-12,5.8193477585627729e-07,9.2213137191309433e-12,1.1973839422768796e-05,-2.7580916873239485e-11,-2.6428344165305951e-13,-1.6830176894599173e-13,-5.3653882225437740e-08,2.4728530947840425e-17,1.6751746635333189e-17,-2.6752289572637881e-17,-5.7499315552852813e-17,-6.8917232252527251e-15,7.6185318466825709e-15
-1.7588310237202792e-03,-1.5946142842221646e-07,-8.0289711729186752e-04,-1.9662990459606614e-08,-2.7531349874821373e-05,-1.8601654381262720e-08,1.7667748075557634e-03,-1.7703626949991876e-07,8.0073592354441240e-04,-4.4801316747056921e-10,2.7746838303401700e-05,3.7669541453423736e-09,-2.2280927891340011e-04,-1.9897246566788684e-06,1.6738427761483978e-06,2.6600611610123000e-08,-2.6190556977141870e-08,3.8899405831883296e-09,2.4775576487408605e-03,9.0387718997323417e-09,1.3699147297410155e-08,-4.8210859079293268e-11,-1.8223239883418740e-11,9.2213137191309433e-12,2.3844843740275984e-02,-5.3980517851666643e-07,-1.8508557580562050e-06,-2.8124976762155787e-08,-2.3613744949676837e-08,-3.9956704099087598e-08,5.1400833644824669e-03,-1.5558684622866895e-02,-9.6814722815906265e-04,2.3919535133556782e-02,3.0804109352445127e-05,2.3913388184361028e-05
-4.0473919133306971e-06,1.1133585922969182e-03,2.9516953113228149e-06,1.8604997224757686e-05,-1.3215923073995517e-07,1.3894025678912365e-05,-5.4819133618285368e-07,1.1168555280145966e-03,-2.4195740347652436e-07,-1.8684539128456464e-05,-7.6442767326631317e-09,1.3894536402242100e-05,3.5228761620069934e-06,-3.3831914736732951e-04,-1.1288307556597044e-06,5.1672913276929128e-09,2.6368390135037619e-08,7.2747473427265298e-07,1.3055495124542592e-08,2.1415008885718018e-03,4.9699685811851590e-09,3.7022181812964561e-11,-4.3179555216183687e-11,1.1973839422768796e-05,-5.3980517851666643e-07,2.6227343649495510e-02,1.8954425943683126e-06,9.0946404389049521e-09,1.6569734329975856e-09,6.9200247432634862e-05,4.3233606789047737e-05,9.0249102014144009e-05,-2.0760469627625316e-05,1.1528043443648827e-05,-3.4886283215487736e-04,1.0855537718400844e-02
--8.4558635740781293e-05,-1.1903131302821071e-06,9.6769358026596152e-04,-2.4277560657754693e-08,-1.0547021838479215e-05,-7.9625845047835227e-08,9.4215092581346660e-05,-2.8090478191373935e-09,9.6702570622137125e-04,-1.7312066406894035e-09,-1.0387048457562033e-05,-4.0871573450819118e-09,-6.4071842708615851e-06,-1.7973104305694709e-07,1.9098974082736459e-04,-1.1857938513011843e-09,6.1432046612156366e-06,3.6780358620406335e-09,-1.5486603538505326e-08,-6.5479155755539340e-09,2.1399832958746813e-03,2.1377115976110194e-11,-1.1977394054433592e-05,-2.7580916873239485e-11,-1.8508557580562050e-06,1.8954425943683126e-06,2.6308944024227086e-02,-2.0813984774814473e-10,-7.1417682966145034e-05,1.5643254887016203e-08,4.7274882017703149e-02,1.5963605116052819e-02,2.4542545638085618e-02,1.0323207797784809e-03,7.1066892489960303e-06,2.5591847524782320e-06
--9.2804884781376160e-10,-9.9176308427033486e-06,-2.2030882961226875e-08,-1.2794363402458843e-07,4.8637277703907580e-10,-9.1808942751358736e-08,7.1669501117728774e-09,9.9466907193319597e-06,-1.7264584136738321e-09,-1.2858507492534756e-07,1.0746858886167557e-10,9.1847805211491326e-08,-2.5636867082473507e-08,1.2132194952007389e-10,6.9883018200074241e-09,-2.9680455181253399e-08,-1.3443466396538433e-10,2.5763832486765300e-11,9.0434715350633260e-12,6.6832417733352129e-11,2.1093863558312420e-11,4.2663118169011185e-08,9.5342702851480413e-14,-2.6428344165305951e-13,-2.8124976762155787e-08,9.0946404389049521e-09,-2.0813984774814473e-10,1.1134104737899188e-06,-2.6770657790971538e-10,-9.1549075245360975e-11,-2.2746595471083301e-07,-5.5440105502280843e-07,1.0644559644311949e-07,-1.2727795977359786e-07,-4.0087268452467515e-04,-1.3726013554048109e-05
-1.6343982920173760e-05,-8.9790911190861651e-10,-5.8193109905064128e-06,-1.2174372459054723e-10,-2.5164931481923190e-07,-2.3333252770135892e-10,-1.6373895730074586e-05,-7.5798124308786279e-11,-5.8032587878764967e-06,1.7891374247785721e-11,-2.5273735484222652e-07,-6.3748730241823205e-11,-2.7315354575856875e-08,-1.8976108568854482e-08,-3.4365284155697740e-06,1.2208865688358232e-10,5.6025084077921977e-10,2.9628576318016861e-11,-6.9046718060170632e-11,-3.5053911013654051e-11,1.1928513482238625e-05,1.3615930920763346e-13,-5.3683229492860376e-08,-1.6830176894599173e-13,-2.3613744949676837e-08,1.6569734329975856e-09,-7.1417682966145034e-05,-2.6770657790971538e-10,7.0750152731787393e-07,-2.0276161487202595e-10,-1.2094497818069785e-04,-4.1545474024475742e-05,-1.6185862173618542e-04,-6.9731489837877039e-06,1.6791991440856165e-07,1.7732917063774981e-07
-1.7828026365384081e-08,-2.4491820723842003e-07,4.8077311716313397e-10,2.6012824175730070e-08,-3.5780709150316614e-10,5.6432011340062909e-08,-1.3160457495372054e-10,-2.5969121980411849e-07,7.8416166288207537e-10,-2.5779443973740474e-08,-1.0073277922273370e-11,5.6366196180689756e-08,1.1643532467258393e-08,-2.6744192499979445e-07,-8.9211460899106898e-10,2.8100830753871640e-11,6.8744841896691323e-11,2.7627234437565930e-10,-7.3851264192454854e-12,-1.1936193963848113e-05,-5.5858578368626676e-12,2.6830981552151709e-14,1.6602468379509925e-13,-5.3653882225437740e-08,-3.9956704099087598e-08,6.9200247432634862e-05,1.5643254887016203e-08,-9.1549075245360975e-11,-2.0276161487202595e-10,9.5752606365202938e-07,8.1652766316775640e-08,1.8338734344352090e-07,-2.3414727196993738e-08,2.9607839458613745e-09,5.8192164593301554e-06,-1.5917184658560470e-04
-1.2443642889233273e-02,-2.2643886423869724e-05,7.3014689962518399e-03,-4.3414578938503394e-07,-4.2555343598068418e-04,-1.7218986433125755e-06,-2.3889520659404521e-02,6.7836178728686985e-06,1.4203654857645194e-02,-1.3285138021445834e-07,-8.4160580990647028e-04,-2.5096760682066648e-07,-3.5216199283537994e-03,-2.2534462134192864e-05,-1.8241686655288705e-02,1.4434270917625216e-08,5.3628479941231250e-05,9.8683889189486147e-08,4.9438528515937297e-15,8.5337456866444873e-15,-2.0386174888479484e-15,-2.3773042040314455e-17,1.3647281594365435e-18,2.4728530947840425e-17,5.1400833644824669e-03,4.3233606789047737e-05,4.7274882017703149e-02,-2.2746595471083301e-07,-1.2094497818069785e-04,8.1652766316775640e-08,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
-2.3674999813816777e-02,-4.6463671672752870e-05,1.3829548038409705e-02,-8.8819978178299776e-07,-8.3920678929678375e-04,-3.4380302439433343e-06,1.1176595390426626e-02,-6.6783238233488808e-06,-6.5940698325439176e-03,1.1923842887080725e-07,4.0810143801751122e-04,8.3815465610236449e-08,9.7467035325089785e-03,-2.0578419948292292e-05,-6.1887544718480245e-03,2.1098552250521460e-07,1.6568605125362163e-05,1.4100571342910795e-07,1.3610321938035977e-15,5.1074558077970226e-15,3.6536175488511800e-16,-1.4506508102878551e-17,1.3847487421315232e-18,1.6751746635333189e-17,-1.5558684622866895e-02,9.0249102014144009e-05,1.5963605116052819e-02,-5.5440105502280843e-07,-4.1545474024475742e-05,1.8338734344352090e-07,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--1.2665814760891294e-02,1.4929863741048841e-06,2.8550602200522721e-02,2.5774124427060330e-08,3.4451743146389919e-04,8.9412622862594666e-07,1.1517387162601905e-02,-7.0450284360939704e-07,2.6324082796649471e-02,-1.8717415093643504e-08,3.1514819424967918e-04,2.1621817296699036e-07,1.6906857532482836e-03,1.9265376581661267e-05,5.3358689150398465e-02,-9.2523181038276382e-08,2.7846239084985009e-04,-4.1434277942299052e-08,-4.1357329724553186e-15,-9.0495997073290111e-15,1.7237953511911040e-15,2.2928517333650290e-17,-2.4518395459434443e-18,-2.6752289572637881e-17,-9.6814722815906265e-04,-2.0760469627625316e-05,2.4542545638085618e-02,1.0644559644311949e-07,-1.6185862173618542e-04,-2.3414727196993738e-08,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
-1.2392503509052711e-02,-1.3743410251703281e-07,-2.5513651731172409e-02,-1.7688582760618006e-09,-3.2518160080507547e-04,-8.3345933502319242e-07,1.3339549888966882e-02,1.6739977008106364e-07,2.7809119115105248e-02,-3.8359469805443676e-08,3.5179661055869099e-04,2.2514785285960931e-07,-3.9339196972392070e-02,-1.0354996039260608e-05,2.2225778688082982e-03,1.1829265269312945e-07,1.1305939844471519e-05,3.3876137309898650e-08,-7.6970165626223539e-15,-1.6844224714733814e-14,-2.4443150616442523e-15,6.5520581181426056e-17,1.7542881376587629e-18,-5.7499315552852813e-17,2.3919535133556782e-02,1.1528043443648827e-05,1.0323207797784809e-03,-1.2727795977359786e-07,-6.9731489837877039e-06,2.9607839458613745e-09,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--1.5877997525629387e-05,-1.4825615960744499e-03,-1.3684696973552163e-05,-1.2250482029118142e-04,2.0333629489585635e-07,-6.7368153553254133e-05,-6.9763994143242040e-06,1.7046317853673409e-03,3.0822636920965325e-08,-1.3503500869595041e-04,-1.3154249441709622e-07,7.4155141157064021e-05,1.3723632457380850e-06,2.1256445770437125e-04,-6.6920089040385829e-06,1.3338369972974633e-04,-1.0440932326420343e-07,2.5893198656537459e-07,-2.4258848831309949e-12,-2.1109127182877665e-12,1.0511624056904027e-12,1.0055631250783132e-14,1.1918708608799692e-15,-6.8917232252527251e-15,3.0804109352445127e-05,-3.4886283215487736e-04,7.1066892489960303e-06,-4.0087268452467515e-04,1.6791991440856165e-07,5.8192164593301554e-06,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00
--4.6812045940282448e-06,-3.1025104691272919e-03,-1.5377698713734422e-05,-1.6353201310745618e-04,2.5623725204854869e-08,-1.0685663395275263e-04,7.6080554131145197e-06,-2.9982630133594734e-03,-6.8311288952693023e-07,1.5652172827044340e-04,1.4050703116567984e-07,-1.0149600219414910e-04,-2.2532949574989803e-05,-6.4121834046156857e-03,-3.5374676331005905e-06,6.6709676252477444e-06,-3.8462217010480574e-08,-2.6782154632106800e-05,5.4339287700903742e-12,4.4210887013055602e-12,-5.0324569727524429e-12,-8.2525429972158425e-15,-7.6662395153113809e-16,7.6185318466825709e-15,2.3913388184361028e-05,1.0855537718400844e-02,2.5591847524782320e-06,-1.3726013554048109e-05,1.7732917063774981e-07,-1.5917184658560470e-04,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00

matlab/mat/full_APA300ML_out_nodes_3D.txt

@@ -1,61 +0,0 @@
-
- LIST ALL SELECTED NODES.   DSYS=      0
-
- *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
- DISTRIBUTED ANSYS Mechanical Enterprise                       
-
- 00208316  VERSION=WINDOWS x64   10:10:05  MAR 26, 2021 CP=      2.188
-
- Unknown                                                                       
-
-
-
-    NODE        X             Y             Z           THXY     THYZ     THZX
-        1   0.0000        0.0000       0.28000E-001     0.00     0.00     0.00
-  1228810   0.0000        0.0000      -0.28000E-001     0.00     0.00     0.00
-  1228811 -0.30000E-001   0.0000        0.0000          0.00     0.00     0.00
-  1228812  0.10000E-001   0.0000        0.0000          0.00     0.00     0.00
-  1228813  0.30000E-001   0.0000        0.0000          0.00     0.00     0.00
-
- LIST MASTERS ON ALL SELECTED NODES.
- CURRENT DOF SET= UX   UY   UZ   ROTX ROTY ROTZ
-
- *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
- DISTRIBUTED ANSYS Mechanical Enterprise                       
-
- 00208316  VERSION=WINDOWS x64   10:10:05  MAR 26, 2021 CP=      2.188
-
- Unknown                                                                       
-
-
-     NODE  LABEL     SUPPORT
-         1  UX  
-         1  UY  
-         1  UZ  
-         1  ROTX
-         1  ROTY
-         1  ROTZ
-   1228810  UX  
-   1228810  UY  
-   1228810  UZ  
-   1228810  ROTX
-   1228810  ROTY
-   1228810  ROTZ
-   1228811  UX  
-   1228811  UY  
-   1228811  UZ  
-   1228811  ROTX
-   1228811  ROTY
-   1228811  ROTZ
-   1228812  UX  
-   1228812  UY  
-   1228812  UZ  
-   1228812  ROTX
-   1228812  ROTY
-   1228812  ROTZ
-   1228813  UX  
-   1228813  UY  
-   1228813  UZ  
-   1228813  ROTX
-   1228813  ROTY
-   1228813  ROTZ

matlab/src/computeJacobian.m

@@ -0,0 +1,35 @@
+function [stewart] = computeJacobian(stewart)
+% computeJacobian -
+%
+% Syntax: [stewart] = computeJacobian(stewart)
+%
+% Inputs:
+%    - stewart - With at least the following fields:
+%      - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
+%      - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
+%      - actuators.K [6x1] - Total stiffness of the actuators
+%
+% Outputs:
+%    - stewart - With the 3 added field:
+%        - kinematics.J [6x6] - The Jacobian Matrix
+%        - kinematics.K [6x6] - The Stiffness Matrix
+%        - kinematics.C [6x6] - The Compliance Matrix
+
+assert(isfield(stewart.geometry, 'As'),   'stewart.geometry should have attribute As')
+As = stewart.geometry.As;
+
+assert(isfield(stewart.geometry, 'Ab'),   'stewart.geometry should have attribute Ab')
+Ab = stewart.geometry.Ab;
+
+assert(isfield(stewart.actuators, 'K'),   'stewart.actuators should have attribute K')
+Ki = stewart.actuators.K;
+
+J = [As' , cross(Ab, As)'];
+
+K = J'*diag(Ki)*J;
+
+C = inv(K);
+
+stewart.kinematics.J = J;
+stewart.kinematics.K = K;
+stewart.kinematics.C = C;

matlab/src/computeJointsPose.m

@@ -0,0 +1,78 @@
+function [stewart] = computeJointsPose(stewart)
+% computeJointsPose -
+%
+% Syntax: [stewart] = computeJointsPose(stewart)
+%
+% Inputs:
+%    - stewart - A structure with the following fields
+%        - platform_F.Fa   [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
+%        - platform_M.Mb   [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
+%        - platform_F.FO_A [3x1] - Position of {A} with respect to {F}
+%        - platform_M.MO_B [3x1] - Position of {B} with respect to {M}
+%        - geometry.FO_M   [3x1] - Position of {M} with respect to {F}
+%
+% Outputs:
+%    - stewart - A structure with the following added fields
+%        - geometry.Aa    [3x6]   - The i'th column is the position of ai with respect to {A}
+%        - geometry.Ab    [3x6]   - The i'th column is the position of bi with respect to {A}
+%        - geometry.Ba    [3x6]   - The i'th column is the position of ai with respect to {B}
+%        - geometry.Bb    [3x6]   - The i'th column is the position of bi with respect to {B}
+%        - geometry.l     [6x1]   - The i'th element is the initial length of strut i
+%        - geometry.As    [3x6]   - The i'th column is the unit vector of strut i expressed in {A}
+%        - geometry.Bs    [3x6]   - The i'th column is the unit vector of strut i expressed in {B}
+%        - struts_F.l     [6x1]   - Length of the Fixed part of the i'th strut
+%        - struts_M.l     [6x1]   - Length of the Mobile part of the i'th strut
+%        - platform_F.FRa [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the bottom of the i'th strut from {F}
+%        - platform_M.MRb [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the top of the i'th strut from {M}
+
+assert(isfield(stewart.platform_F, 'Fa'),   'stewart.platform_F should have attribute Fa')
+Fa = stewart.platform_F.Fa;
+
+assert(isfield(stewart.platform_M, 'Mb'),   'stewart.platform_M should have attribute Mb')
+Mb = stewart.platform_M.Mb;
+
+assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
+FO_A = stewart.platform_F.FO_A;
+
+assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
+MO_B = stewart.platform_M.MO_B;
+
+assert(isfield(stewart.geometry,   'FO_M'), 'stewart.geometry should have attribute FO_M')
+FO_M = stewart.geometry.FO_M;
+
+Aa = Fa - repmat(FO_A, [1, 6]);
+Bb = Mb - repmat(MO_B, [1, 6]);
+
+Ab = Bb - repmat(-MO_B-FO_M+FO_A, [1, 6]);
+Ba = Aa - repmat( MO_B+FO_M-FO_A, [1, 6]);
+
+As = (Ab - Aa)./vecnorm(Ab - Aa); % As_i is the i'th vector of As
+
+l = vecnorm(Ab - Aa)';
+
+Bs = (Bb - Ba)./vecnorm(Bb - Ba);
+
+FRa = zeros(3,3,6);
+MRb = zeros(3,3,6);
+
+for i = 1:6
+  FRa(:,:,i) = [cross([0;1;0], As(:,i)) , cross(As(:,i), cross([0;1;0], As(:,i))) , As(:,i)];
+  FRa(:,:,i) = FRa(:,:,i)./vecnorm(FRa(:,:,i));
+
+  MRb(:,:,i) = [cross([0;1;0], Bs(:,i)) , cross(Bs(:,i), cross([0;1;0], Bs(:,i))) , Bs(:,i)];
+  MRb(:,:,i) = MRb(:,:,i)./vecnorm(MRb(:,:,i));
+end
+
+stewart.geometry.Aa = Aa;
+stewart.geometry.Ab = Ab;
+stewart.geometry.Ba = Ba;
+stewart.geometry.Bb = Bb;
+stewart.geometry.As = As;
+stewart.geometry.Bs = Bs;
+stewart.geometry.l  = l;
+
+stewart.struts_F.l  = l/2;
+stewart.struts_M.l  = l/2;
+
+stewart.platform_F.FRa = FRa;
+stewart.platform_M.MRb = MRb;

matlab/src/computeReferencePose.m

@@ -0,0 +1,77 @@
+function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
+% computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample
+%
+% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
+%
+% Inputs:
+%    - Dy - Reference of the Translation Stage [m]
+%    - Ry - Reference of the Tilt Stage [rad]
+%    - Rz - Reference of the Spindle [rad]
+%    - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad]
+%    - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad]
+%
+% Outputs:
+%    - WTr -
+
+  %% Translation Stage
+  Rty = [1 0 0 0;
+         0 1 0 Dy;
+         0 0 1 0;
+         0 0 0 1];
+
+  %% Tilt Stage - Pure rotating aligned with Ob
+  Rry = [ cos(Ry) 0 sin(Ry) 0;
+          0       1 0       0;
+         -sin(Ry) 0 cos(Ry) 0;
+          0       0 0       1];
+
+  %% Spindle - Rotation along the Z axis
+  Rrz = [cos(Rz) -sin(Rz) 0 0 ;
+         sin(Rz)  cos(Rz) 0 0 ;
+         0        0       1 0 ;
+         0        0       0 1 ];
+
+
+  %% Micro-Hexapod
+  Rhx = [1 0           0;
+         0 cos(Dh(4)) -sin(Dh(4));
+         0 sin(Dh(4))  cos(Dh(4))];
+
+  Rhy = [ cos(Dh(5)) 0 sin(Dh(5));
+         0           1 0;
+         -sin(Dh(5)) 0 cos(Dh(5))];
+
+  Rhz = [cos(Dh(6)) -sin(Dh(6)) 0;
+         sin(Dh(6))  cos(Dh(6)) 0;
+         0           0          1];
+
+  Rh = [1 0 0 Dh(1) ;
+        0 1 0 Dh(2) ;
+        0 0 1 Dh(3) ;
+        0 0 0 1 ];
+
+  Rh(1:3, 1:3) = Rhz*Rhy*Rhx;
+
+  %% Nano-Hexapod
+  Rnx = [1 0           0;
+         0 cos(Dn(4)) -sin(Dn(4));
+         0 sin(Dn(4))  cos(Dn(4))];
+
+  Rny = [ cos(Dn(5)) 0 sin(Dn(5));
+         0           1 0;
+         -sin(Dn(5)) 0 cos(Dn(5))];
+
+  Rnz = [cos(Dn(6)) -sin(Dn(6)) 0;
+         sin(Dn(6))  cos(Dn(6)) 0;
+         0           0          1];
+
+  Rn = [1 0 0 Dn(1) ;
+        0 1 0 Dn(2) ;
+        0 0 1 Dn(3) ;
+        0 0 0 1 ];
+
+  Rn(1:3, 1:3) = Rnz*Rny*Rnx;
+
+  %% Total Homogeneous transformation
+  WTr = Rty*Rry*Rrz*Rh*Rn;
+end

matlab/src/computeSampleError.m

@@ -0,0 +1,20 @@
+function [MTr] = computeSampleError(WTm, WTr)
+% computeSampleError -
+%
+% Syntax: [MTr] = computeSampleError(WTm, WTr)
+%
+% Inputs:
+%    - WTm - Homoegeneous transformation that represent the
+%            wanted pose of the sample with respect to the granite
+%    - WTr - Homoegeneous transformation that represent the
+%            measured pose of the sample with respect to the granite
+%
+% Outputs:
+%    - MTr - Homoegeneous transformation that represent the
+%            wanted pose of the sample expressed in a frame
+%            attached to the top platform of the nano-hexapod
+
+MTr = zeros(4,4);
+
+MTr = [WTm(1:3,1:3)', -WTm(1:3,1:3)'*WTm(1:3,4) ; 0 0 0 1]*WTr;
+end

matlab/src/describeNassSetup.m

@@ -0,0 +1,196 @@
+function [] = describeNassSetup()
+% describeNassSetup -
+%
+% Syntax: [] = describeNassSetup()
+%
+% Inputs:
+%    -  -
+%
+% Outputs:
+%    -  -
+
+load('./mat/conf_simscape.mat', 'conf_simscape');
+
+fprintf('Simscape Configuration:\n');
+
+if conf_simscape.type == 1
+    fprintf('- Gravity is included\n');
+else
+    fprintf('- Gravity is not included\n');
+end
+
+fprintf('\n');
+
+load('./mat/nass_disturbances.mat', 'args');
+
+fprintf('Disturbances:\n');
+if ~args.enable
+    fprintf('- No disturbance is included\n');
+else
+    if args.Dwx && args.Dwy && args.Dwz
+        fprintf('- Ground motion\n');
+    end
+    if args.Fty_x && args.Fty_z
+        fprintf('- Vibrations of the Translation Stage\n');
+    end
+    if args.Frz_z
+        fprintf('- Vibrations of the Spindle\n');
+    end
+end
+fprintf('\n');
+
+load('./mat/nass_references.mat', 'args');
+
+fprintf('Reference Tracking:\n');
+fprintf('- Translation Stage:\n');
+switch args.Dy_type
+  case 'constant'
+    fprintf('  - Constant Position\n');
+    fprintf('  - Dy = %.0f [mm]\n', args.Dy_amplitude*1e3);
+  case 'triangular'
+    fprintf('  - Triangular Path\n');
+    fprintf('  - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
+    fprintf('  - Period = %.0f [s]\n', args.Dy_period);
+  case 'sinusoidal'
+    fprintf('  - Sinusoidal Path\n');
+    fprintf('  - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
+    fprintf('  - Period = %.0f [s]\n', args.Dy_period);
+end
+
+fprintf('- Tilt Stage:\n');
+switch args.Ry_type
+  case 'constant'
+    fprintf('  - Constant Position\n');
+    fprintf('  - Ry = %.0f [mm]\n', args.Ry_amplitude*1e3);
+  case 'triangular'
+    fprintf('  - Triangular Path\n');
+    fprintf('  - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
+    fprintf('  - Period = %.0f [s]\n', args.Ry_period);
+  case 'sinusoidal'
+    fprintf('  - Sinusoidal Path\n');
+    fprintf('  - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
+    fprintf('  - Period = %.0f [s]\n', args.Ry_period);
+end
+
+fprintf('- Spindle:\n');
+switch args.Rz_type
+  case 'constant'
+    fprintf('  - Constant Position\n');
+    fprintf('  - Rz = %.0f [deg]\n', 180/pi*args.Rz_amplitude);
+  case { 'rotating', 'rotating-not-filtered' }
+    fprintf('  - Rotating\n');
+    fprintf('  - Speed = %.0f [rpm]\n', 60/args.Rz_period);
+end
+
+
+fprintf('- Micro Hexapod:\n');
+switch args.Dh_type
+  case 'constant'
+    fprintf('  - Constant Position\n');
+    fprintf('  - Dh = %.0f, %.0f, %.0f [mm]\n',  args.Dh_pos(1), args.Dh_pos(2), args.Dh_pos(3));
+    fprintf('  - Rh = %.0f, %.0f, %.0f [deg]\n', args.Dh_pos(4), args.Dh_pos(5), args.Dh_pos(6));
+end
+
+fprintf('\n');
+
+load('./mat/controller.mat', 'controller');
+
+fprintf('Controller:\n');
+fprintf('- %s\n', controller.name);
+fprintf('\n');
+
+load('./mat/stages.mat', 'ground', 'granite', 'ty', 'ry', 'rz', 'micro_hexapod', 'axisc');
+
+fprintf('Micro Station:\n');
+
+if granite.type == 1 && ...
+        ty.type == 1 && ...
+        ry.type == 1 && ...
+        rz.type == 1 && ...
+        micro_hexapod.type == 1;
+    fprintf('- All stages are rigid\n');
+elseif granite.type == 2 && ...
+        ty.type == 2 && ...
+        ry.type == 2 && ...
+        rz.type == 2 && ...
+        micro_hexapod.type == 2;
+    fprintf('- All stages are flexible\n');
+else
+    if granite.type == 1 || granite.type == 4
+        fprintf('- Granite is rigid\n');
+    else
+        fprintf('- Granite is flexible\n');
+    end
+    if ty.type == 1 || ty.type == 4
+        fprintf('- Translation Stage is rigid\n');
+    else
+        fprintf('- Translation Stage is flexible\n');
+    end
+    if ry.type == 1 || ry.type == 4
+        fprintf('- Tilt Stage is rigid\n');
+    else
+        fprintf('- Tilt Stage is flexible\n');
+    end
+    if rz.type == 1 || rz.type == 4
+        fprintf('- Spindle is rigid\n');
+    else
+        fprintf('- Spindle is flexible\n');
+    end
+    if micro_hexapod.type == 1 || micro_hexapod.type == 4
+        fprintf('- Micro Hexapod is rigid\n');
+    else
+        fprintf('- Micro Hexapod is flexible\n');
+    end
+
+end
+
+fprintf('\n');
+
+load('./mat/stages.mat', 'mirror');
+
+fprintf('Reference Mirror:\n');
+
+if mirror.type == 2;
+    fprintf('- flexible fixation\n');
+    fprintf('- w = %.0f [Hz]\n', mirror.freq(1));
+else
+    fprintf('- rigidly attached to the nano-hexapod\n');
+end
+fprintf('- m = %.0f [kg]\n', mirror.mass);
+fprintf('\n');
+
+load('./mat/stages.mat', 'nano_hexapod');
+
+fprintf('Nano Hexapod:\n');
+
+if nano_hexapod.type == 0;
+    fprintf('- no included\n');
+elseif nano_hexapod.type == 1 || nano_hexapod.type == 3;
+    fprintf('- rigid\n');
+elseif nano_hexapod.type == 2;
+    fprintf('- flexible\n');
+    fprintf('- Ki = %.0g [N/m]\n', nano_hexapod.actuators.K(1));
+end
+
+fprintf('\n');
+
+load('./mat/stages.mat', 'sample');
+
+fprintf('Sample:\n');
+
+if sample.type == 0;
+    fprintf('- no included\n');
+elseif sample.type == 1 || sample.type == 3;
+    fprintf('- rigid\n');
+    fprintf('- mass = %.0f [kg]\n', sample.mass);
+    fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
+elseif sample.type == 2;
+    fprintf('- flexible\n');
+    fprintf('- mass = %.0f [kg]\n', sample.mass);
+    fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
+    % fprintf('- Kt = %.0g, %.0g, %.0g [N/m]\n', sample.K(1), sample.K(2), sample.K(3));
+    % fprintf('- Kr = %.0g, %.0g, %.0g [Nm/rad]\n', sample.K(4), sample.K(5), sample.K(6));
+    fprintf('- wt(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass));
+    fprintf('- wr(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(4)/sample.inertia(1)), 1/2/pi*sqrt(sample.K(5)/sample.inertia(2)), 1/2/pi*sqrt(sample.K(6)/sample.inertia(3)));
+end
+fprintf('\n');

matlab/src/describeStewartPlatform.m

@@ -0,0 +1,83 @@
+function [] = describeStewartPlatform(stewart)
+% describeStewartPlatform - Display some text describing the current defined Stewart Platform
+%
+% Syntax: [] = describeStewartPlatform(args)
+%
+% Inputs:
+%    - stewart
+%
+% Outputs:
+
+arguments
+    stewart
+end
+
+fprintf('GEOMETRY:\n')
+fprintf('- The height between the fixed based and the top platform is %.3g [mm].\n', 1e3*stewart.geometry.H)
+
+if stewart.platform_M.MO_B(3) > 0
+  fprintf('- Frame {A} is located %.3g [mm] above the top platform.\n',  1e3*stewart.platform_M.MO_B(3))
+else
+  fprintf('- Frame {A} is located %.3g [mm] below the top platform.\n', - 1e3*stewart.platform_M.MO_B(3))
+end
+
+fprintf('- The initial length of the struts are:\n')
+fprintf('\t %.3g, %.3g, %.3g, %.3g, %.3g, %.3g [mm]\n', 1e3*stewart.geometry.l)
+fprintf('\n')
+
+fprintf('ACTUATORS:\n')
+if stewart.actuators.type == 1
+    fprintf('- The actuators are classical.\n')
+    fprintf('- The Stiffness and Damping of each actuators is:\n')
+    fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.K(1), stewart.actuators.C(1))
+elseif stewart.actuators.type == 2
+    fprintf('- The actuators are mechanicaly amplified.\n')
+    fprintf('- The vertical stiffness and damping contribution of the piezoelectric stack is:\n')
+    fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.Ka(1), stewart.actuators.Ca(1))
+    fprintf('- Vertical stiffness when the piezoelectric stack is removed is:\n')
+    fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.Kr(1), stewart.actuators.Cr(1))
+end
+fprintf('\n')
+
+fprintf('JOINTS:\n')
+
+switch stewart.joints_F.type
+  case 1
+    fprintf('- The joints on the fixed based are universal joints\n')
+  case 2
+    fprintf('- The joints on the fixed based are spherical joints\n')
+  case 3
+    fprintf('- The joints on the fixed based are perfect universal joints\n')
+  case 4
+    fprintf('- The joints on the fixed based are perfect spherical joints\n')
+end
+
+switch stewart.joints_M.type
+  case 1
+    fprintf('- The joints on the mobile based are universal joints\n')
+  case 2
+    fprintf('- The joints on the mobile based are spherical joints\n')
+  case 3
+    fprintf('- The joints on the mobile based are perfect universal joints\n')
+  case 4
+    fprintf('- The joints on the mobile based are perfect spherical joints\n')
+end
+
+fprintf('- The position of the joints on the fixed based with respect to {F} are (in [mm]):\n')
+fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_F.Fa)
+
+fprintf('- The position of the joints on the mobile based with respect to {M} are (in [mm]):\n')
+fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_M.Mb)
+fprintf('\n')
+
+fprintf('KINEMATICS:\n')
+
+if isfield(stewart.kinematics, 'K')
+  fprintf('- The Stiffness matrix K is (in [N/m]):\n')
+  fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.K)
+end
+
+if isfield(stewart.kinematics, 'C')
+  fprintf('- The Damping matrix C is (in [m/N]):\n')
+  fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.C)
+end

matlab/src/displayArchitecture.m

@@ -0,0 +1,240 @@
+function [] = displayArchitecture(stewart, args)
+% displayArchitecture - 3D plot of the Stewart platform architecture
+%
+% Syntax: [] = displayArchitecture(args)
+%
+% Inputs:
+%    - stewart
+%    - args - Structure with the following fields:
+%        - AP   [3x1] - The wanted position of {B} with respect to {A}
+%        - ARB  [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
+%        - ARB  [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
+%        - F_color [color] - Color used for the Fixed elements
+%        - M_color [color] - Color used for the Mobile elements
+%        - L_color [color] - Color used for the Legs elements
+%        - frames    [true/false] - Display the Frames
+%        - legs      [true/false] - Display the Legs
+%        - joints    [true/false] - Display the Joints
+%        - labels    [true/false] - Display the Labels
+%        - platforms [true/false] - Display the Platforms
+%        - views     ['all', 'xy', 'yz', 'xz', 'default'] -
+%
+% Outputs:
+
+arguments
+    stewart
+    args.AP  (3,1) double {mustBeNumeric} = zeros(3,1)
+    args.ARB (3,3) double {mustBeNumeric} = eye(3)
+    args.F_color = [0 0.4470 0.7410]
+    args.M_color = [0.8500 0.3250 0.0980]
+    args.L_color = [0 0 0]
+    args.frames    logical {mustBeNumericOrLogical} = true
+    args.legs      logical {mustBeNumericOrLogical} = true
+    args.joints    logical {mustBeNumericOrLogical} = true
+    args.labels    logical {mustBeNumericOrLogical} = true
+    args.platforms logical {mustBeNumericOrLogical} = true
+    args.views     char    {mustBeMember(args.views,{'all', 'xy', 'xz', 'yz', 'default'})} = 'default'
+end
+
+assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
+FO_A = stewart.platform_F.FO_A;
+
+assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
+MO_B = stewart.platform_M.MO_B;
+
+assert(isfield(stewart.geometry, 'H'),   'stewart.geometry should have attribute H')
+H = stewart.geometry.H;
+
+assert(isfield(stewart.platform_F, 'Fa'),   'stewart.platform_F should have attribute Fa')
+Fa = stewart.platform_F.Fa;
+
+assert(isfield(stewart.platform_M, 'Mb'),   'stewart.platform_M should have attribute Mb')
+Mb = stewart.platform_M.Mb;
+
+if ~strcmp(args.views, 'all')
+  figure;
+else
+  f = figure('visible', 'off');
+end
+
+hold on;
+
+FTa = [eye(3), FO_A; ...
+       zeros(1,3), 1];
+ATb = [args.ARB, args.AP; ...
+       zeros(1,3), 1];
+BTm = [eye(3), -MO_B; ...
+       zeros(1,3), 1];
+
+FTm = FTa*ATb*BTm;
+
+d_unit_vector = H/4;
+
+d_label = H/20;
+
+Ff = [0, 0, 0];
+if args.frames
+  quiver3(Ff(1)*ones(1,3), Ff(2)*ones(1,3), Ff(3)*ones(1,3), ...
+          [d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
+
+  if args.labels
+    text(Ff(1) + d_label, ...
+        Ff(2) + d_label, ...
+        Ff(3) + d_label, '$\{F\}$', 'Color', args.F_color);
+  end
+end
+
+if args.frames
+  quiver3(FO_A(1)*ones(1,3), FO_A(2)*ones(1,3), FO_A(3)*ones(1,3), ...
+          [d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
+
+  if args.labels
+    text(FO_A(1) + d_label, ...
+         FO_A(2) + d_label, ...
+         FO_A(3) + d_label, '$\{A\}$', 'Color', args.F_color);
+  end
+end
+
+if args.platforms && stewart.platform_F.type == 1
+  theta = [0:0.01:2*pi+0.01]; % Angles [rad]
+  v = null([0; 0; 1]'); % Two vectors that are perpendicular to the circle normal
+  center = [0; 0; 0]; % Center of the circle
+  radius = stewart.platform_F.R; % Radius of the circle [m]
+
+  points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
+
+  plot3(points(1,:), ...
+        points(2,:), ...
+        points(3,:), '-', 'Color', args.F_color);
+end
+
+if args.joints
+  scatter3(Fa(1,:), ...
+           Fa(2,:), ...
+           Fa(3,:), 'MarkerEdgeColor', args.F_color);
+  if args.labels
+    for i = 1:size(Fa,2)
+      text(Fa(1,i) + d_label, ...
+           Fa(2,i), ...
+           Fa(3,i), sprintf('$a_{%i}$', i), 'Color', args.F_color);
+    end
+  end
+end
+
+Fm = FTm*[0; 0; 0; 1]; % Get the position of frame {M} w.r.t. {F}
+
+if args.frames
+  FM_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
+  quiver3(Fm(1)*ones(1,3), Fm(2)*ones(1,3), Fm(3)*ones(1,3), ...
+          FM_uv(1,1:3), FM_uv(2,1:3), FM_uv(3,1:3), '-', 'Color', args.M_color)
+
+  if args.labels
+    text(Fm(1) + d_label, ...
+         Fm(2) + d_label, ...
+         Fm(3) + d_label, '$\{M\}$', 'Color', args.M_color);
+  end
+end
+
+FB = FO_A + args.AP;
+
+if args.frames
+  FB_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
+  quiver3(FB(1)*ones(1,3), FB(2)*ones(1,3), FB(3)*ones(1,3), ...
+          FB_uv(1,1:3), FB_uv(2,1:3), FB_uv(3,1:3), '-', 'Color', args.M_color)
+
+  if args.labels
+    text(FB(1) - d_label, ...
+         FB(2) + d_label, ...
+         FB(3) + d_label, '$\{B\}$', 'Color', args.M_color);
+  end
+end
+
+if args.platforms && stewart.platform_M.type == 1
+  theta = [0:0.01:2*pi+0.01]; % Angles [rad]
+  v = null((FTm(1:3,1:3)*[0;0;1])'); % Two vectors that are perpendicular to the circle normal
+  center = Fm(1:3); % Center of the circle
+  radius = stewart.platform_M.R; % Radius of the circle [m]
+
+  points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
+
+  plot3(points(1,:), ...
+        points(2,:), ...
+        points(3,:), '-', 'Color', args.M_color);
+end
+
+if args.joints
+  Fb = FTm*[Mb;ones(1,6)];
+
+  scatter3(Fb(1,:), ...
+           Fb(2,:), ...
+           Fb(3,:), 'MarkerEdgeColor', args.M_color);
+
+  if args.labels
+    for i = 1:size(Fb,2)
+      text(Fb(1,i) + d_label, ...
+           Fb(2,i), ...
+           Fb(3,i), sprintf('$b_{%i}$', i), 'Color', args.M_color);
+    end
+  end
+end
+
+if args.legs
+  for i = 1:6
+    plot3([Fa(1,i), Fb(1,i)], ...
+          [Fa(2,i), Fb(2,i)], ...
+          [Fa(3,i), Fb(3,i)], '-', 'Color', args.L_color);
+
+    if args.labels
+      text((Fa(1,i)+Fb(1,i))/2 + d_label, ...
+           (Fa(2,i)+Fb(2,i))/2, ...
+           (Fa(3,i)+Fb(3,i))/2, sprintf('$%i$', i), 'Color', args.L_color);
+    end
+  end
+end
+
+switch args.views
+  case 'default'
+      view([1 -0.6 0.4]);
+  case 'xy'
+      view([0 0 1]);
+  case 'xz'
+      view([0 -1 0]);
+  case 'yz'
+      view([1 0 0]);
+end
+axis equal;
+axis off;
+
+if strcmp(args.views, 'all')
+  hAx = findobj('type', 'axes');
+
+  figure;
+  s1 = subplot(2,2,1);
+  copyobj(get(hAx(1), 'Children'), s1);
+  view([0 0 1]);
+  axis equal;
+  axis off;
+  title('Top')
+
+  s2 = subplot(2,2,2);
+  copyobj(get(hAx(1), 'Children'), s2);
+  view([1 -0.6 0.4]);
+  axis equal;
+  axis off;
+
+  s3 = subplot(2,2,3);
+  copyobj(get(hAx(1), 'Children'), s3);
+  view([1 0 0]);
+  axis equal;
+  axis off;
+  title('Front')
+
+  s4 = subplot(2,2,4);
+  copyobj(get(hAx(1), 'Children'), s4);
+  view([0 -1 0]);
+  axis equal;
+  axis off;
+  title('Side')
+
+  close(f);
+end

matlab/src/forwardKinematicsApprox.m

@@ -0,0 +1,34 @@
+function [P, R] = forwardKinematicsApprox(stewart, args)
+% forwardKinematicsApprox - Computed the approximate pose of {B} with respect to {A} from the length of each strut and using
+%                           the Jacobian Matrix
+%
+% Syntax: [P, R] = forwardKinematicsApprox(stewart, args)
+%
+% Inputs:
+%    - stewart - A structure with the following fields
+%        - kinematics.J  [6x6] - The Jacobian Matrix
+%    - args - Can have the following fields:
+%        - dL [6x1] - Displacement of each strut [m]
+%
+% Outputs:
+%    - P  [3x1] - The estimated position of {B} with respect to {A}
+%    - R  [3x3] - The estimated rotation matrix that gives the orientation of {B} with respect to {A}
+
+arguments
+    stewart
+    args.dL (6,1) double {mustBeNumeric} = zeros(6,1)
+end
+
+assert(isfield(stewart.kinematics, 'J'),   'stewart.kinematics should have attribute J')
+J = stewart.kinematics.J;
+
+X = J\args.dL;
+
+P = X(1:3);
+
+theta = norm(X(4:6));
+s = X(4:6)/theta;
+
+R = [s(1)^2*(1-cos(theta)) + cos(theta) ,        s(1)*s(2)*(1-cos(theta)) - s(3)*sin(theta), s(1)*s(3)*(1-cos(theta)) + s(2)*sin(theta);
+     s(2)*s(1)*(1-cos(theta)) + s(3)*sin(theta), s(2)^2*(1-cos(theta)) + cos(theta),         s(2)*s(3)*(1-cos(theta)) - s(1)*sin(theta);
+     s(3)*s(1)*(1-cos(theta)) - s(2)*sin(theta), s(3)*s(2)*(1-cos(theta)) + s(1)*sin(theta), s(3)^2*(1-cos(theta)) + cos(theta)];

matlab/src/generateCubicConfiguration.m

@@ -0,0 +1,50 @@
+function [stewart] = generateCubicConfiguration(stewart, args)
+% generateCubicConfiguration - Generate a Cubic Configuration
+%
+% Syntax: [stewart] = generateCubicConfiguration(stewart, args)
+%
+% Inputs:
+%    - stewart - A structure with the following fields
+%        - geometry.H [1x1] - Total height of the platform [m]
+%    - args - Can have the following fields:
+%        - Hc  [1x1] - Height of the "useful" part of the cube [m]
+%        - FOc [1x1] - Height of the center of the cube with respect to {F} [m]
+%        - FHa [1x1] - Height of the plane joining the points ai with respect to the frame {F} [m]
+%        - MHb [1x1] - Height of the plane joining the points bi with respect to the frame {M} [m]
+%
+% Outputs:
+%    - stewart - updated Stewart structure with the added fields:
+%        - platform_F.Fa  [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
+%        - platform_M.Mb  [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
+
+arguments
+    stewart
+    args.Hc  (1,1) double {mustBeNumeric, mustBePositive} = 60e-3
+    args.FOc (1,1) double {mustBeNumeric} = 50e-3
+    args.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
+    args.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
+end
+
+assert(isfield(stewart.geometry, 'H'),   'stewart.geometry should have attribute H')
+H = stewart.geometry.H;
+
+sx = [ 2; -1; -1];
+sy = [ 0;  1; -1];
+sz = [ 1;  1;  1];
+
+R = [sx, sy, sz]./vecnorm([sx, sy, sz]);
+
+L = args.Hc*sqrt(3);
+
+Cc = R'*[[0;0;L],[L;0;L],[L;0;0],[L;L;0],[0;L;0],[0;L;L]] - [0;0;1.5*args.Hc];
+
+CCf = [Cc(:,1), Cc(:,3), Cc(:,3), Cc(:,5), Cc(:,5), Cc(:,1)]; % CCf(:,i) corresponds to the bottom cube's vertice corresponding to the i'th leg
+CCm = [Cc(:,2), Cc(:,2), Cc(:,4), Cc(:,4), Cc(:,6), Cc(:,6)]; % CCm(:,i) corresponds to the top cube's vertice corresponding to the i'th leg
+
+CSi = (CCm - CCf)./vecnorm(CCm - CCf);
+
+Fa = CCf + [0; 0; args.FOc] + ((args.FHa-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
+Mb = CCf + [0; 0; args.FOc-H] + ((H-args.MHb-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
+
+stewart.platform_F.Fa = Fa;
+stewart.platform_M.Mb = Mb;

matlab/src/generateDiagPidControl.m

@@ -0,0 +1,18 @@
+function [K] = generateDiagPidControl(G, fs)
+    %%
+    pid_opts = pidtuneOptions(...
+        'PhaseMargin', 50, ...
+        'DesignFocus', 'disturbance-rejection');
+
+    %%
+    K = tf(zeros(6));
+
+    for i = 1:6
+        input_name = G.InputName(i);
+        output_name = G.OutputName(i);
+        K(i, i) = tf(pidtune(minreal(G(output_name, input_name)), 'PIDF', 2*pi*fs, pid_opts));
+    end
+
+    K.InputName = G.OutputName;
+    K.OutputName = G.InputName;
+end

matlab/src/generateGeneralConfiguration.m

@@ -0,0 +1,39 @@
+function [stewart] = generateGeneralConfiguration(stewart, args)
+% generateGeneralConfiguration - Generate a Very General Configuration
+%
+% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
+%
+% Inputs:
+%    - args - Can have the following fields:
+%        - FH  [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
+%        - FR  [1x1] - Radius of the position of the fixed joints in the X-Y [m]
+%        - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
+%        - MH  [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
+%        - FR  [1x1] - Radius of the position of the mobile joints in the X-Y [m]
+%        - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
+%
+% Outputs:
+%    - stewart - updated Stewart structure with the added fields:
+%        - platform_F.Fa  [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
+%        - platform_M.Mb  [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
+
+arguments
+    stewart
+    args.FH  (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+    args.FR  (1,1) double {mustBeNumeric, mustBePositive} = 115e-3;
+    args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180);
+    args.MH  (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+    args.MR  (1,1) double {mustBeNumeric, mustBePositive} = 90e-3;
+    args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180);
+end
+
+Fa = zeros(3,6);
+Mb = zeros(3,6);
+
+for i = 1:6
+  Fa(:,i) = [args.FR*cos(args.FTh(i)); args.FR*sin(args.FTh(i));  args.FH];
+  Mb(:,i) = [args.MR*cos(args.MTh(i)); args.MR*sin(args.MTh(i)); -args.MH];
+end
+
+stewart.platform_F.Fa = Fa;
+stewart.platform_M.Mb = Mb;

matlab/src/generateShapedNoise.m

@@ -0,0 +1,53 @@
+function [U_exc] = generateShapedNoise(args)
+% generateShapedNoise - Generate a Shaped Noise excitation signal
+%
+% Syntax: [U_exc] = generateShapedNoise(args)
+%
+% Inputs:
+%    - args - Optinal arguments:
+%        - Ts              - Sampling Time                                              - [s]
+%        - V_mean          - Mean value of the excitation voltage                       - [V]
+%        - V_exc           - Excitation Amplitude, could be numeric or TF               - [V rms]
+%        - t_start         - Time at which the noise begins                             - [s]
+%        - exc_duration    - Duration of the noise                                      - [s]
+%        - smooth_ends     - 'true' or 'false': smooth transition between 0 and V_mean  - [-]
+
+arguments
+    args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
+    args.V_mean          (1,1) double  {mustBeNumeric} = 0
+    args.V_exc                                         = 1
+    args.t_start         (1,1) double  {mustBeNumeric, mustBePositive} = 5
+    args.exc_duration    (1,1) double  {mustBeNumeric, mustBePositive} = 10
+    args.smooth_ends           logical {mustBeNumericOrLogical} = true
+end
+
+t_noise = 0:args.Ts:args.exc_duration;
+
+if isnumeric(args.V_exc)
+    V_noise = args.V_mean + args.V_exc*sqrt(1/args.Ts/2)*randn(length(t_noise), 1)';
+elseif isct(args.V_exc)
+    V_noise = args.V_mean + lsim(args.V_exc, sqrt(1/args.Ts/2)*randn(length(t_noise), 1), t_noise)';
+end
+
+t_smooth_start = args.Ts:args.Ts:args.t_start;
+
+V_smooth_start = zeros(size(t_smooth_start));
+V_smooth_end   = zeros(size(t_smooth_start));
+
+if args.smooth_ends
+    Vd_max = args.V_mean/(0.7*args.t_start);
+
+    V_d = zeros(size(t_smooth_start));
+    V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
+    V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
+    V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
+
+    V_smooth_start = cumtrapz(V_d)*args.Ts;
+
+    V_smooth_end = args.V_mean - V_smooth_start;
+end
+
+V_exc = [V_smooth_start, V_noise, V_smooth_end];
+t_exc = args.Ts*[0:1:length(V_exc)-1];
+
+U_exc = [t_exc; V_exc];

matlab/src/generateSinIncreasingAmpl.m

@@ -0,0 +1,54 @@
+function [U_exc] = generateSinIncreasingAmpl(args)
+% generateSinIncreasingAmpl - Generate Sinus with increasing amplitude
+%
+% Syntax: [U_exc] = generateSinIncreasingAmpl(args)
+%
+% Inputs:
+%    - args - Optinal arguments:
+%        - Ts              - Sampling Time                                              - [s]
+%        - V_mean          - Mean value of the excitation voltage                       - [V]
+%        - sin_ampls       - Excitation Amplitudes                                      - [V]
+%        - sin_freq        - Excitation Frequency                                       - [Hz]
+%        - sin_num         - Number of period for each amplitude                        - [-]
+%        - t_start         - Time at which the excitation begins                        - [s]
+%        - smooth_ends     - 'true' or 'false': smooth transition between 0 and V_mean  - [-]
+
+arguments
+    args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
+    args.V_mean          (1,1) double  {mustBeNumeric} = 0
+    args.sin_ampls             double  {mustBeNumeric, mustBePositive} = [0.1, 0.2, 0.3]
+    args.sin_period      (1,1) double  {mustBeNumeric, mustBePositive} = 1
+    args.sin_num         (1,1) double  {mustBeNumeric, mustBePositive, mustBeInteger} = 3
+    args.t_start         (1,1) double  {mustBeNumeric, mustBePositive} = 5
+    args.smooth_ends           logical {mustBeNumericOrLogical} = true
+end
+
+t_noise = 0:args.Ts:args.sin_period*args.sin_num;
+sin_exc = [];
+
+for sin_ampl = args.sin_ampls
+    sin_exc = [sin_exc, args.V_mean + sin_ampl*sin(2*pi/args.sin_period*t_noise)];
+end
+
+t_smooth_start = args.Ts:args.Ts:args.t_start;
+
+V_smooth_start = zeros(size(t_smooth_start));
+V_smooth_end   = zeros(size(t_smooth_start));
+
+if args.smooth_ends
+    Vd_max = args.V_mean/(0.7*args.t_start);
+
+    V_d = zeros(size(t_smooth_start));
+    V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
+    V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
+    V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
+
+    V_smooth_start = cumtrapz(V_d)*args.Ts;
+
+    V_smooth_end = args.V_mean - V_smooth_start;
+end
+
+V_exc = [V_smooth_start, sin_exc, V_smooth_end];
+t_exc = args.Ts*[0:1:length(V_exc)-1];
+
+U_exc = [t_exc; V_exc];

matlab/src/generateSpiralAngleTrajectory.m

@@ -0,0 +1,35 @@
+function [ref] = generateSpiralAngleTrajectory(args)
+% generateSpiralAngleTrajectory -
+%
+% Syntax: [ref] = generateSpiralAngleTrajectory(args)
+%
+% Inputs:
+%    - args
+%
+% Outputs:
+%    - ref - Reference Signal
+
+arguments
+    args.R_tot  (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [rad]
+    args.n_turn (1,1) double {mustBeInteger, mustBePositive} = 5 % [-]
+    args.Ts     (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [s]
+    args.t_turn (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
+    args.t_end  (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
+end
+
+time_s = 0:args.Ts:args.n_turn*args.t_turn;
+time_e = 0:args.Ts:args.t_end;
+
+Rx = sin(2*pi*time_s/args.t_turn).*(args.R_tot*time_s/(args.n_turn*args.t_turn));
+Ry = cos(2*pi*time_s/args.t_turn).*(args.R_tot*time_s/(args.n_turn*args.t_turn));
+
+Rx = [Rx, 0*time_e];
+Ry = [Ry, Ry(end) - Ry(end)*time_e/args.t_end];
+
+t = 0:args.Ts:args.Ts*(length(Rx) - 1);
+
+ref = zeros(length(Rx), 7);
+
+ref(:, 1) = t;
+ref(:, 5) = Rx;
+ref(:, 6) = Ry;

matlab/src/generateSweepExc.m

@@ -0,0 +1,76 @@
+function [U_exc] = generateSweepExc(args)
+% generateSweepExc - Generate a Sweep Sine excitation signal
+%
+% Syntax: [U_exc] = generateSweepExc(args)
+%
+% Inputs:
+%    - args - Optinal arguments:
+%        - Ts              - Sampling Time                                              - [s]
+%        - f_start         - Start frequency of the sweep                               - [Hz]
+%        - f_end           - End frequency of the sweep                                 - [Hz]
+%        - V_mean          - Mean value of the excitation voltage                       - [V]
+%        - V_exc           - Excitation Amplitude for the Sweep, could be numeric or TF - [V]
+%        - t_start         - Time at which the sweep begins                             - [s]
+%        - exc_duration    - Duration of the sweep                                      - [s]
+%        - sweep_type      - 'logarithmic' or 'linear'                                  - [-]
+%        - smooth_ends     - 'true' or 'false': smooth transition between 0 and V_mean  - [-]
+
+arguments
+    args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
+    args.f_start         (1,1) double  {mustBeNumeric, mustBePositive} = 1
+    args.f_end           (1,1) double  {mustBeNumeric, mustBePositive} = 1e3
+    args.V_mean          (1,1) double  {mustBeNumeric} = 0
+    args.V_exc                                         = 1
+    args.t_start         (1,1) double  {mustBeNumeric, mustBeNonnegative} = 5
+    args.exc_duration    (1,1) double  {mustBeNumeric, mustBePositive} = 10
+    args.sweep_type            char    {mustBeMember(args.sweep_type,{'log', 'lin'})} = 'lin'
+    args.smooth_ends           logical {mustBeNumericOrLogical} = true
+end
+
+t_sweep = 0:args.Ts:args.exc_duration;
+
+if strcmp(args.sweep_type, 'log')
+    V_exc = sin(2*pi*args.f_start * args.exc_duration/log(args.f_end/args.f_start) * (exp(log(args.f_end/args.f_start)*t_sweep/args.exc_duration) - 1));
+elseif strcmp(args.sweep_type, 'lin')
+    V_exc = sin(2*pi*(args.f_start + (args.f_end - args.f_start)/2/args.exc_duration*t_sweep).*t_sweep);
+else
+    error('sweep_type should either be equal to "log" or to "lin"');
+end
+
+if isnumeric(args.V_exc)
+    V_sweep = args.V_mean + args.V_exc*V_exc;
+elseif isct(args.V_exc)
+    if strcmp(args.sweep_type, 'log')
+        V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start*(args.f_end/args.f_start).^(t_sweep/args.exc_duration), 'Hz')))'.*V_exc;
+    elseif strcmp(args.sweep_type, 'lin')
+        V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start+(args.f_end-args.f_start)/args.exc_duration*t_sweep, 'Hz')))'.*V_exc;
+    end
+end
+
+if args.t_start > 0
+    t_smooth_start = args.Ts:args.Ts:args.t_start;
+
+    V_smooth_start = zeros(size(t_smooth_start));
+    V_smooth_end   = zeros(size(t_smooth_start));
+
+    if args.smooth_ends
+        Vd_max = args.V_mean/(0.7*args.t_start);
+
+        V_d = zeros(size(t_smooth_start));
+        V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
+        V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
+        V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
+
+        V_smooth_start = cumtrapz(V_d)*args.Ts;
+
+        V_smooth_end = args.V_mean - V_smooth_start;
+    end
+else
+    V_smooth_start = [];
+    V_smooth_end = [];
+end
+
+V_exc = [V_smooth_start, V_sweep, V_smooth_end];
+t_exc = args.Ts*[0:1:length(V_exc)-1];
+
+U_exc = [t_exc; V_exc];

matlab/src/generateXYZTrajectory.m

@@ -0,0 +1,48 @@
+function [ref] = generateXYZTrajectory(args)
+% generateXYZTrajectory -
+%
+% Syntax: [ref] = generateXYZTrajectory(args)
+%
+% Inputs:
+%    - args
+%
+% Outputs:
+%    - ref - Reference Signal
+
+arguments
+    args.points double {mustBeNumeric} = zeros(2, 3) % [m]
+
+    args.ti    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % Time to go to first point and after last point [s]
+    args.tw    (1,1) double {mustBeNumeric, mustBeNonnegative} = 0.5 % Time wait between each point [s]
+    args.tm    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % Motion time between points [s]
+
+    args.Ts    (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % Sampling Time [s]
+end
+
+time_i = 0:args.Ts:args.ti;
+time_w = 0:args.Ts:args.tw;
+time_m = 0:args.Ts:args.tm;
+
+% Go to initial position
+xyz = (args.points(1,:))'*(time_i/args.ti);
+
+% Wait
+xyz = [xyz, xyz(:,end).*ones(size(time_w))];
+
+% Scans
+for i = 2:size(args.points, 1)
+    % Go to next point
+    xyz = [xyz, xyz(:,end) + (args.points(i,:)' - xyz(:,end))*(time_m/args.tm)];
+    % Wait a litle bit
+    xyz = [xyz, xyz(:,end).*ones(size(time_w))];
+end
+
+% End motion
+xyz = [xyz, xyz(:,end) - xyz(:,end)*(time_i/args.ti)];
+
+t = 0:args.Ts:args.Ts*(length(xyz) - 1);
+
+ref = zeros(length(xyz), 7);
+
+ref(:, 1) = t;
+ref(:, 2:4) = xyz';

matlab/src/generateYZScanTrajectory.m

@@ -0,0 +1,83 @@
+function [ref] = generateYZScanTrajectory(args)
+% generateYZScanTrajectory -
+%
+% Syntax: [ref] = generateYZScanTrajectory(args)
+%
+% Inputs:
+%    - args
+%
+% Outputs:
+%    - ref - Reference Signal
+
+arguments
+    args.y_tot (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [m]
+    args.z_tot (1,1) double {mustBeNumeric, mustBePositive} = 10e-6 % [m]
+
+    args.n     (1,1) double {mustBeInteger, mustBePositive} = 10 % [-]
+
+    args.Ts    (1,1) double {mustBeNumeric, mustBePositive} = 1e-4 % [s]
+
+    args.ti    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
+    args.tw    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
+    args.ty    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
+    args.tz    (1,1) double {mustBeNumeric, mustBeNonnegative} = 1 % [s]
+end
+
+time_i = 0:args.Ts:args.ti;
+time_w = 0:args.Ts:args.tw;
+time_y = 0:args.Ts:args.ty;
+time_z = 0:args.Ts:args.tz;
+
+% Go to initial position
+y = (time_i/args.ti)*(args.y_tot/2);
+
+% Wait
+y = [y, y(end)*ones(size(time_w))];
+
+% Scans
+for i = 1:args.n
+    if mod(i,2) == 0
+        y = [y, -(args.y_tot/2) + (time_y/args.ty)*args.y_tot];
+    else
+        y = [y,  (args.y_tot/2) - (time_y/args.ty)*args.y_tot];
+    end
+
+    if i < args.n
+        y = [y, y(end)*ones(size(time_z))];
+    end
+end
+
+% Wait a litle bit
+y = [y, y(end)*ones(size(time_w))];
+
+% End motion
+y = [y, y(end) - y(end)*time_i/args.ti];
+
+% Go to initial position
+z = (time_i/args.ti)*(args.z_tot/2);
+
+% Wait
+z = [z, z(end)*ones(size(time_w))];
+
+% Scans
+for i = 1:args.n
+    z = [z, z(end)*ones(size(time_y))];
+
+    if i < args.n
+        z = [z, z(end) - (time_z/args.tz)*args.z_tot/(args.n-1)];
+    end
+end
+
+% Wait a litle bit
+z = [z, z(end)*ones(size(time_w))];
+
+% End motion
+z = [z, z(end) - z(end)*time_i/args.ti];
+
+t = 0:args.Ts:args.Ts*(length(y) - 1);
+
+ref = zeros(length(y), 7);
+
+ref(:, 1) = t;
+ref(:, 3) = y;
+ref(:, 4) = z;

matlab/src/getJacobianNanoHexapod.m

@@ -0,0 +1,34 @@
+function [J] = getJacobianNanoHexapod(Hbm)
+% getJacobianNanoHexapod -
+%
+% Syntax: [J] = getJacobianNanoHexapod(Hbm)
+%
+% Inputs:
+%    - Hbm - Height of {B} w.r.t. {M} [m]
+%
+% Outputs:
+%    - J - Jacobian Matrix
+
+Fa = [[-86.05,  -74.78, 22.49],
+      [ 86.05,  -74.78, 22.49],
+      [ 107.79, -37.13, 22.49],
+      [ 21.74,  111.91, 22.49],
+      [-21.74,  111.91, 22.49],
+      [-107.79, -37.13, 22.49]]'*1e-3; % Ai w.r.t. {F} [m]
+
+Mb = [[-28.47, -106.25, -22.50],
+      [ 28.47, -106.25, -22.50],
+      [ 106.25, 28.47,  -22.50],
+      [ 77.78,  77.78,  -22.50],
+      [-77.78,  77.78,  -22.50],
+      [-106.25, 28.47,  -22.50]]'*1e-3; % Bi w.r.t. {M} [m]
+
+H = 95e-3; % Stewart platform height [m]
+Fb = Mb + [0; 0; H]; % Bi w.r.t. {F} [m]
+
+si = Fb - Fa;
+si = si./vecnorm(si); % Normalize
+
+Bb = Mb - [0; 0; Hbm];
+
+J = [si', cross(Bb, si)'];

matlab/src/getTransformationMatrixAcc.m

@@ -0,0 +1,23 @@
+function [M] = getTransformationMatrixAcc(Opm, Osm)
+% getTransformationMatrixAcc -
+%
+% Syntax: [M] = getTransformationMatrixAcc(Opm, Osm)
+%
+% Inputs:
+%    - Opm - Nx3 (N = number of accelerometer measurements) X,Y,Z position of accelerometers
+%    - Opm - Nx3 (N = number of accelerometer measurements) Unit vectors representing the accelerometer orientation
+%
+% Outputs:
+%    - M - Transformation Matrix
+
+M = zeros(length(Opm), 6);
+
+for i = 1:length(Opm)
+    Ri = [0,         Opm(3,i), -Opm(2,i);
+         -Opm(3,i),  0,         Opm(1,i);
+          Opm(2,i), -Opm(1,i),  0];
+    M(i, 1:3) = Osm(:,i)';
+    M(i, 4:6) = Osm(:,i)'*Ri;
+end
+
+end

matlab/src/initializeAmplifiedStrutDynamics.m

@@ -0,0 +1,43 @@
+function [stewart] = initializeAmplifiedStrutDynamics(stewart, args)
+% initializeAmplifiedStrutDynamics - Add Stiffness and Damping properties of each strut
+%
+% Syntax: [stewart] = initializeAmplifiedStrutDynamics(args)
+%
+% Inputs:
+%    - args - Structure with the following fields:
+%        - Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
+%        - Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
+%        - Kr [6x1] - Vertical (residual) stiffness when the piezoelectric stack is removed [N/m]
+%        - Cr [6x1] - Vertical (residual) damping when the piezoelectric stack is removed [N/(m/s)]
+%
+% Outputs:
+%    - stewart - updated Stewart structure with the added fields:
+%      - actuators.type = 2
+%      - actuators.K   [6x1] - Total Stiffness of each strut [N/m]
+%      - actuators.C   [6x1] - Total Damping of each strut [N/(m/s)]
+%      - actuators.Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
+%      - actuators.Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
+%      - actuators.Kr [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
+%      - actuators.Cr [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
+
+arguments
+    stewart
+    args.Kr (6,1) double {mustBeNumeric, mustBeNonnegative} = 5e6*ones(6,1)
+    args.Cr (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+    args.Ka (6,1) double {mustBeNumeric, mustBeNonnegative} = 15e6*ones(6,1)
+    args.Ca (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+end
+
+K = args.Ka + args.Kr;
+C = args.Ca + args.Cr;
+
+stewart.actuators.type = 2;
+
+stewart.actuators.Ka = args.Ka;
+stewart.actuators.Ca = args.Ca;
+
+stewart.actuators.Kr = args.Kr;
+stewart.actuators.Cr = args.Cr;
+
+stewart.actuators.K = K;
+stewart.actuators.C = K;

matlab/src/initializeAxisc.m

@@ -0,0 +1,34 @@
+function [axisc] = initializeAxisc(args)
+
+arguments
+  args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
+end
+
+axisc = struct();
+
+switch args.type
+  case 'none'
+    axisc.type = 0;
+  case 'rigid'
+    axisc.type = 1;
+  case 'flexible'
+    axisc.type = 2;
+end
+
+% Structure
+axisc.structure.density = 3400; % [kg/m3]
+axisc.structure.STEP    = './STEPS/axisc/axisc_structure.STEP';
+
+% Wheel
+axisc.wheel.density     = 2700; % [kg/m3]
+axisc.wheel.STEP        = './STEPS/axisc/axisc_wheel.STEP';
+
+% Mass
+axisc.mass.density      = 7800; % [kg/m3]
+axisc.mass.STEP         = './STEPS/axisc/axisc_mass.STEP';
+
+% Gear
+axisc.gear.density      = 7800; % [kg/m3]
+axisc.gear.STEP         = './STEPS/axisc/axisc_gear.STEP';
+
+save('./mat/stages.mat', 'axisc', '-append');

matlab/src/initializeCedratPiezo.m

@@ -0,0 +1,17 @@
+function [cedrat] = initializeCedratPiezo()
+  %% Stewart Object
+  cedrat = struct();
+  cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]
+  cedrat.ka = 10e7; % Linear Stiffness of the stack [N/m]
+
+  cedrat.c = 0.1*sqrt(1*cedrat.k); % [N/(m/s)]
+  cedrat.ca = 0.1*sqrt(1*cedrat.ka); % [N/(m/s)]
+
+  cedrat.L = 80; % Total Width of the Actuator[mm]
+  cedrat.H = 45; % Total Height of the Actuator [mm]
+  cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
+  cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
+
+  %% Save
+  save('./mat/stages.mat', 'cedrat', '-append');
+end

matlab/src/initializeController.m

@@ -0,0 +1,39 @@
+function [] = initializeController(args)
+
+arguments
+  args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
+end
+
+controller = struct();
+
+switch args.type
+  case 'open-loop'
+    controller.type = 1;
+    controller.name = 'Open-Loop';
+  case 'dvf'
+    controller.type = 2;
+    controller.name = 'Decentralized Direct Velocity Feedback';
+  case 'iff'
+    controller.type = 3;
+    controller.name = 'Decentralized Integral Force Feedback';
+  case 'hac-dvf'
+    controller.type = 4;
+    controller.name = 'HAC-DVF';
+  case 'ref-track-L'
+    controller.type = 5;
+    controller.name = 'Reference Tracking in the frame of the legs';
+  case 'ref-track-iff-L'
+    controller.type = 6;
+    controller.name = 'Reference Tracking in the frame of the legs + IFF';
+  case 'cascade-hac-lac'
+    controller.type = 7;
+    controller.name = 'Cascade Control + HAC-LAC';
+  case 'hac-iff'
+    controller.type = 8;
+    controller.name = 'HAC-IFF';
+  case 'stabilizing'
+    controller.type = 9;
+    controller.name = 'Stabilizing Controller';
+end
+
+save('./mat/controller.mat', 'controller');

matlab/src/initializeCylindricalPlatforms.m

@@ -0,0 +1,59 @@
+function [stewart] = initializeCylindricalPlatforms(stewart, args)
+% initializeCylindricalPlatforms - Initialize the geometry of the Fixed and Mobile Platforms
+%
+% Syntax: [stewart] = initializeCylindricalPlatforms(args)
+%
+% Inputs:
+%    - args - Structure with the following fields:
+%        - Fpm [1x1] - Fixed Platform Mass [kg]
+%        - Fph [1x1] - Fixed Platform Height [m]
+%        - Fpr [1x1] - Fixed Platform Radius [m]
+%        - Mpm [1x1] - Mobile Platform Mass [kg]
+%        - Mph [1x1] - Mobile Platform Height [m]
+%        - Mpr [1x1] - Mobile Platform Radius [m]
+%
+% Outputs:
+%    - stewart - updated Stewart structure with the added fields:
+%      - platform_F [struct] - structure with the following fields:
+%        - type = 1
+%        - M [1x1] - Fixed Platform Mass [kg]
+%        - I [3x3] - Fixed Platform Inertia matrix [kg*m^2]
+%        - H [1x1] - Fixed Platform Height [m]
+%        - R [1x1] - Fixed Platform Radius [m]
+%      - platform_M [struct] - structure with the following fields:
+%        - M [1x1] - Mobile Platform Mass [kg]
+%        - I [3x3] - Mobile Platform Inertia matrix [kg*m^2]
+%        - H [1x1] - Mobile Platform Height [m]
+%        - R [1x1] - Mobile Platform Radius [m]
+
+arguments
+    stewart
+    args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
+    args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
+    args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 125e-3
+    args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
+    args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
+    args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
+end
+
+I_F = diag([1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
+            1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
+            1/2 *args.Fpm * args.Fpr^2]);
+
+I_M = diag([1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
+            1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
+            1/2 *args.Mpm * args.Mpr^2]);
+
+stewart.platform_F.type = 1;
+
+stewart.platform_F.I = I_F;
+stewart.platform_F.M = args.Fpm;
+stewart.platform_F.R = args.Fpr;
+stewart.platform_F.H = args.Fph;
+
+stewart.platform_M.type = 1;
+
+stewart.platform_M.I = I_M;
+stewart.platform_M.M = args.Mpm;
+stewart.platform_M.R = args.Mpr;
+stewart.platform_M.H = args.Mph;

matlab/src/initializeCylindricalStruts.m

@@ -0,0 +1,71 @@
+function [stewart] = initializeCylindricalStruts(stewart, args)
+% initializeCylindricalStruts - Define the mass and moment of inertia of cylindrical struts
+%
+% Syntax: [stewart] = initializeCylindricalStruts(args)
+%
+% Inputs:
+%    - args - Structure with the following fields:
+%        - Fsm [1x1] - Mass of the Fixed part of the struts [kg]
+%        - Fsh [1x1] - Height of cylinder for the Fixed part of the struts [m]
+%        - Fsr [1x1] - Radius of cylinder for the Fixed part of the struts [m]
+%        - Msm [1x1] - Mass of the Mobile part of the struts [kg]
+%        - Msh [1x1] - Height of cylinder for the Mobile part of the struts [m]
+%        - Msr [1x1] - Radius of cylinder for the Mobile part of the struts [m]
+%
+% Outputs:
+%    - stewart - updated Stewart structure with the added fields:
+%      - struts_F [struct] - structure with the following fields:
+%        - M [6x1]   - Mass of the Fixed part of the struts [kg]
+%        - I [3x3x6] - Moment of Inertia for the Fixed part of the struts [kg*m^2]
+%        - H [6x1]   - Height of cylinder for the Fixed part of the struts [m]
+%        - R [6x1]   - Radius of cylinder for the Fixed part of the struts [m]
+%      - struts_M [struct] - structure with the following fields:
+%        - M [6x1]   - Mass of the Mobile part of the struts [kg]
+%        - I [3x3x6] - Moment of Inertia for the Mobile part of the struts [kg*m^2]
+%        - H [6x1]   - Height of cylinder for the Mobile part of the struts [m]
+%        - R [6x1]   - Radius of cylinder for the Mobile part of the struts [m]
+
+arguments
+    stewart
+    args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
+    args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
+    args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
+    args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
+    args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
+    args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
+end
+
+Fsm = ones(6,1).*args.Fsm;
+Fsh = ones(6,1).*args.Fsh;
+Fsr = ones(6,1).*args.Fsr;
+
+Msm = ones(6,1).*args.Msm;
+Msh = ones(6,1).*args.Msh;
+Msr = ones(6,1).*args.Msr;
+
+I_F = zeros(3, 3, 6); % Inertia of the "fixed" part of the strut
+I_M = zeros(3, 3, 6); % Inertia of the "mobile" part of the strut
+
+for i = 1:6
+  I_F(:,:,i) = diag([1/12 * Fsm(i) * (3*Fsr(i)^2 + Fsh(i)^2), ...
+                     1/12 * Fsm(i) * (3*Fsr(i)^2 + Fsh(i)^2), ...
+                     1/2  * Fsm(i) * Fsr(i)^2]);
+
+  I_M(:,:,i) = diag([1/12 * Msm(i) * (3*Msr(i)^2 + Msh(i)^2), ...
+                     1/12 * Msm(i) * (3*Msr(i)^2 + Msh(i)^2), ...
+                     1/2  * Msm(i) * Msr(i)^2]);
+end
+
+stewart.struts_M.type = 1;
+
+stewart.struts_M.I = I_M;
+stewart.struts_M.M = Msm;
+stewart.struts_M.R = Msr;
+stewart.struts_M.H = Msh;
+
+stewart.struts_F.type = 1;
+
+stewart.struts_F.I = I_F;
+stewart.struts_F.M = Fsm;
+stewart.struts_F.R = Fsr;
+stewart.struts_F.H = Fsh;

matlab/src/initializeDisturbances.m

@@ -0,0 +1,135 @@
+function [] = initializeDisturbances(args)
+% initializeDisturbances - Initialize the disturbances
+%
+% Syntax: [] = initializeDisturbances(args)
+%
+% Inputs:
+%    - args -
+
+arguments
+    % Global parameter to enable or disable the disturbances
+    args.enable logical {mustBeNumericOrLogical} = true
+    % Ground Motion - X direction
+    args.Dwx logical {mustBeNumericOrLogical} = true
+    % Ground Motion - Y direction
+    args.Dwy logical {mustBeNumericOrLogical} = true
+    % Ground Motion - Z direction
+    args.Dwz logical {mustBeNumericOrLogical} = true
+    % Translation Stage - X direction
+    args.Fty_x logical {mustBeNumericOrLogical} = true
+    % Translation Stage - Z direction
+    args.Fty_z logical {mustBeNumericOrLogical} = true
+    % Spindle - Z direction
+    args.Frz_z logical {mustBeNumericOrLogical} = true
+end
+
+load('./mat/dist_psd.mat', 'dist_f');
+
+dist_f.f = dist_f.f(2:end);
+dist_f.psd_gm = dist_f.psd_gm(2:end);
+dist_f.psd_ty = dist_f.psd_ty(2:end);
+dist_f.psd_rz = dist_f.psd_rz(2:end);
+
+Fs = 2*dist_f.f(end);      % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz]
+N  = 2*length(dist_f.f);   % Number of Samples match the one of the wanted PSD
+T0 = N/Fs;                 % Signal Duration [s]
+df = 1/T0;                 % Frequency resolution of the DFT [Hz]
+                           % Also equal to (dist_f.f(2)-dist_f.f(1))
+t = linspace(0, T0, N+1)'; % Time Vector [s]
+Ts = 1/Fs;                 % Sampling Time [s]
+
+phi = dist_f.psd_gm;
+C = zeros(N/2,1);
+for i = 1:N/2
+  C(i) = sqrt(phi(i)*df);
+end
+
+if args.Dwx && args.enable
+  rng(111);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  Dwx = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m]
+else
+  Dwx = zeros(length(t), 1);
+end
+
+if args.Dwy && args.enable
+  rng(112);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  Dwy = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m]
+else
+  Dwy = zeros(length(t), 1);
+end
+
+if args.Dwy && args.enable
+  rng(113);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  Dwz = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m]
+else
+  Dwz = zeros(length(t), 1);
+end
+
+if args.Fty_x && args.enable
+  phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate
+  C = zeros(N/2,1);
+  for i = 1:N/2
+    C(i) = sqrt(phi(i)*df);
+  end
+  rng(121);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty x [N]
+  Fty_x = u;
+else
+  Fty_x = zeros(length(t), 1);
+end
+
+if args.Fty_z && args.enable
+  phi = dist_f.psd_ty;
+  C = zeros(N/2,1);
+  for i = 1:N/2
+    C(i) = sqrt(phi(i)*df);
+  end
+  rng(122);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty z [N]
+  Fty_z = u;
+else
+  Fty_z = zeros(length(t), 1);
+end
+
+if args.Frz_z && args.enable
+  phi = dist_f.psd_rz;
+  C = zeros(N/2,1);
+  for i = 1:N/2
+    C(i) = sqrt(phi(i)*df);
+  end
+  rng(131);
+  theta = 2*pi*rand(N/2,1); % Generate random phase [rad]
+  Cx = [0 ; C.*complex(cos(theta),sin(theta))];
+  Cx = [Cx; flipud(conj(Cx(2:end)))];;
+  u = N/sqrt(2)*ifft(Cx); % Disturbance Force Rz z [N]
+  Frz_z = u;
+else
+  Frz_z = zeros(length(t), 1);
+end
+
+u = zeros(length(t), 6);
+Fd = u;
+
+Dwx    = Dwx   - Dwx(1);
+Dwy    = Dwy   - Dwy(1);
+Dwz    = Dwz   - Dwz(1);
+Fty_x  = Fty_x - Fty_x(1);
+Fty_z  = Fty_z - Fty_z(1);
+Frz_z  = Frz_z - Frz_z(1);
+
+save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't', 'args');

matlab/src/initializeFramesPositions.m

@@ -0,0 +1,35 @@
+function [stewart] = initializeFramesPositions(stewart, args)
+% initializeFramesPositions - Initialize the positions of frames {A}, {B}, {F} and {M}
+%
+% Syntax: [stewart] = initializeFramesPositions(stewart, args)
+%
+% Inputs:
+%    - args - Can have the following fields:
+%        - H    [1x1] - Total Height of the Stewart Platform (height from {F} to {M}) [m]
+%        - MO_B [1x1] - Height of the frame {B} with respect to {M} [m]
+%
+% Outputs:
+%    - stewart - A structure with the following fields:
+%        - geometry.H      [1x1] - Total Height of the Stewart Platform [m]
+%        - geometry.FO_M   [3x1] - Position of {M} with respect to {F} [m]
+%        - platform_M.MO_B [3x1] - Position of {B} with respect to {M} [m]
+%        - platform_F.FO_A [3x1] - Position of {A} with respect to {F} [m]
+
+arguments
+    stewart
+    args.H    (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
+    args.MO_B (1,1) double {mustBeNumeric} = 50e-3
+end
+
+H = args.H; % Total Height of the Stewart Platform [m]
+
+FO_M = [0; 0; H]; % Position of {M} with respect to {F} [m]
+
+MO_B = [0; 0; args.MO_B]; % Position of {B} with respect to {M} [m]
+
+FO_A = MO_B + FO_M; % Position of {A} with respect to {F} [m]
+
+stewart.geometry.H      = H;
+stewart.geometry.FO_M   = FO_M;
+stewart.platform_M.MO_B = MO_B;
+stewart.platform_F.FO_A = FO_A;

matlab/src/initializeGranite.m

@@ -0,0 +1,45 @@
+function [granite] = initializeGranite(args)
+
+arguments
+  args.type          char    {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible'
+  args.Foffset       logical {mustBeNumericOrLogical} = false
+  args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
+  args.K  (3,1) double {mustBeNumeric, mustBeNonnegative} = [4e9; 3e8; 8e8] % [N/m]
+  args.C  (3,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5] % [N/(m/s)]
+  args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m]
+  args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m]
+  args.z0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Z direction [m]
+  args.sample_pos (1,1) double {mustBeNumeric} = 0.8 % Height of the measurment point [m]
+end
+
+granite = struct();
+
+switch args.type
+  case 'none'
+    granite.type = 0;
+  case 'rigid'
+    granite.type = 1;
+  case 'flexible'
+    granite.type = 2;
+  case 'modal-analysis'
+    granite.type = 3;
+  case 'init'
+    granite.type = 4;
+end
+
+granite.density = args.density; % [kg/m3]
+granite.STEP    = './STEPS/granite/granite.STEP';
+
+granite.sample_pos = args.sample_pos; % [m]
+
+granite.K = args.K; % [N/m]
+granite.C = args.C; % [N/(m/s)]
+
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+  load('mat/Foffset.mat', 'Fgm');
+  granite.Deq = -Fgm'./granite.K;
+else
+  granite.Deq = zeros(6,1);
+end
+
+save('./mat/stages.mat', 'granite', '-append');

matlab/src/initializeGround.m

@@ -0,0 +1,22 @@
+function [ground] = initializeGround(args)
+
+arguments
+  args.type char {mustBeMember(args.type,{'none', 'rigid'})} = 'rigid'
+  args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) % Rotation point for the ground motion [m]
+end
+
+ground = struct();
+
+switch args.type
+  case 'none'
+    ground.type = 0;
+  case 'rigid'
+    ground.type = 1;
+end
+
+ground.shape   = [2, 2, 0.5]; % [m]
+ground.density = 2800;        % [kg/m3]
+
+ground.rot_point = args.rot_point;
+
+save('./mat/stages.mat', 'ground', '-append');