id sid tid token lemma pos hjic-488 1 1 hungarian hungarian ADJ hjic-488 1 2 journal journal NOUN hjic-488 1 3 of of ADP hjic-488 1 4 industry industry NOUN hjic-488 1 5 and and CCONJ hjic-488 1 6 chemistry chemistry NOUN hjic-488 1 7 veszprém veszprém NOUN hjic-488 1 8 vol vol NOUN hjic-488 1 9 . . PUNCT hjic-488 2 1 42(2 42(2 NUM hjic-488 2 2 ) ) PUNCT hjic-488 3 1 pp pp ADV hjic-488 3 2 . . PUNCT hjic-488 4 1 71–77 71–77 NUM hjic-488 4 2 ( ( PUNCT hjic-488 4 3 2014 2014 NUM hjic-488 4 4 ) ) PUNCT hjic-488 5 1 the the DET hjic-488 5 2 application application NOUN hjic-488 5 3 of of ADP hjic-488 5 4 unknown unknown ADJ hjic-488 5 5 input input NOUN hjic-488 5 6 estimators estimator NOUN hjic-488 5 7 to to PART hjic-488 5 8 damp damp VERB hjic-488 5 9 load load NOUN hjic-488 5 10 oscillations oscillation NOUN hjic-488 5 11 of of ADP hjic-488 5 12 overhead overhead ADJ hjic-488 5 13 cranes crane NOUN hjic-488 5 14 bálint bálint NOUN hjic-488 5 15 patarticsb patarticsb NOUN hjic-488 5 16 and and CCONJ hjic-488 5 17 bálint bálint NOUN hjic-488 5 18 kiss kiss PROPN hjic-488 5 19 department department PROPN hjic-488 5 20 of of ADP hjic-488 5 21 control control PROPN hjic-488 5 22 engineering engineering NOUN hjic-488 5 23 and and CCONJ hjic-488 5 24 information information NOUN hjic-488 5 25 technology technology NOUN hjic-488 5 26 , , PUNCT hjic-488 5 27 budapest budapest PROPN hjic-488 5 28 university university PROPN hjic-488 5 29 of of ADP hjic-488 5 30 technology technology NOUN hjic-488 5 31 and and CCONJ hjic-488 5 32 economics economic NOUN hjic-488 5 33 , , PUNCT hjic-488 5 34 magyar magyar PROPN hjic-488 5 35 tudósok tudósok PROPN hjic-488 5 36 krt krt PROPN hjic-488 5 37 . . PUNCT hjic-488 5 38 2 2 NUM hjic-488 5 39 , , PUNCT hjic-488 5 40 budapest budapest NOUN hjic-488 5 41 , , PUNCT hjic-488 5 42 1111 1111 NUM hjic-488 5 43 , , PUNCT hjic-488 5 44 hungary hungary PROPN hjic-488 5 45 be be NOUN hjic-488 5 46 - - PUNCT hjic-488 5 47 mail mail NOUN hjic-488 5 48 : : PUNCT hjic-488 6 1 patarticsbalint@gmail.com patarticsbalint@gmail.com X hjic-488 6 2 this this DET hjic-488 6 3 paper paper NOUN hjic-488 6 4 focuses focus VERB hjic-488 6 5 on on ADP hjic-488 6 6 the the DET hjic-488 6 7 development development NOUN hjic-488 6 8 of of ADP hjic-488 6 9 state state NOUN hjic-488 6 10 estimation estimation NOUN hjic-488 6 11 methods method NOUN hjic-488 6 12 for for ADP hjic-488 6 13 mechanical mechanical ADJ hjic-488 6 14 systems system NOUN hjic-488 6 15 with with ADP hjic-488 6 16 uncertain uncertain ADJ hjic-488 6 17 frictional frictional ADJ hjic-488 6 18 parameters parameter NOUN hjic-488 6 19 . . PUNCT hjic-488 7 1 the the DET hjic-488 7 2 goal goal NOUN hjic-488 7 3 of of ADP hjic-488 7 4 the the DET hjic-488 7 5 study study NOUN hjic-488 7 6 is be AUX hjic-488 7 7 to to PART hjic-488 7 8 provide provide VERB hjic-488 7 9 reliable reliable ADJ hjic-488 7 10 angle angle NOUN hjic-488 7 11 estimation estimation NOUN hjic-488 7 12 for for ADP hjic-488 7 13 state state NOUN hjic-488 7 14 - - PUNCT hjic-488 7 15 feedback feedback NOUN hjic-488 7 16 - - PUNCT hjic-488 7 17 based base VERB hjic-488 7 18 crane crane NOUN hjic-488 7 19 control control NOUN hjic-488 7 20 solutions solution NOUN hjic-488 7 21 , , PUNCT hjic-488 7 22 designed design VERB hjic-488 7 23 to to PART hjic-488 7 24 reduce reduce VERB hjic-488 7 25 load load NOUN hjic-488 7 26 sway sway NOUN hjic-488 7 27 . . PUNCT hjic-488 8 1 cranes crane NOUN hjic-488 8 2 are be AUX hjic-488 8 3 underactuated underactuated ADJ hjic-488 8 4 systems system NOUN hjic-488 8 5 , , PUNCT hjic-488 8 6 usually usually ADV hjic-488 8 7 unequipped unequipped ADJ hjic-488 8 8 with with ADP hjic-488 8 9 the the DET hjic-488 8 10 sensors sensor NOUN hjic-488 8 11 necessary necessary ADJ hjic-488 8 12 to to PART hjic-488 8 13 measure measure VERB hjic-488 8 14 the the DET hjic-488 8 15 swinging swinge VERB hjic-488 8 16 angle angle NOUN hjic-488 8 17 , , PUNCT hjic-488 8 18 therefore therefore ADV hjic-488 8 19 the the DET hjic-488 8 20 damping damping NOUN hjic-488 8 21 of of ADP hjic-488 8 22 their their PRON hjic-488 8 23 oscillatory oscillatory ADJ hjic-488 8 24 behaviour behaviour NOUN hjic-488 8 25 is be AUX hjic-488 8 26 a a DET hjic-488 8 27 challenging challenging ADJ hjic-488 8 28 task task NOUN hjic-488 8 29 . . PUNCT hjic-488 9 1 two two NUM hjic-488 9 2 estimators estimator NOUN hjic-488 9 3 are be AUX hjic-488 9 4 proposed propose VERB hjic-488 9 5 for for ADP hjic-488 9 6 the the DET hjic-488 9 7 calculation calculation NOUN hjic-488 9 8 of of ADP hjic-488 9 9 the the DET hjic-488 9 10 unmeasured unmeasured ADJ hjic-488 9 11 states state NOUN hjic-488 9 12 . . PUNCT hjic-488 10 1 one one NUM hjic-488 10 2 is be AUX hjic-488 10 3 based base VERB hjic-488 10 4 on on ADP hjic-488 10 5 an an DET hjic-488 10 6 ’ ' PUNCT hjic-488 10 7 unknown unknown ADJ hjic-488 10 8 input input NOUN hjic-488 10 9 kalman kalman PROPN hjic-488 10 10 filter filter NOUN hjic-488 10 11 ’ ' PUNCT hjic-488 10 12 ( ( PUNCT hjic-488 10 13 uikf uikf NOUN hjic-488 10 14 ) ) PUNCT hjic-488 10 15 , , PUNCT hjic-488 10 16 the the DET hjic-488 10 17 other other ADJ hjic-488 10 18 applies apply VERB hjic-488 10 19 the the DET hjic-488 10 20 ’ ' PUNCT hjic-488 10 21 unscented unscente VERB hjic-488 10 22 kalman kalman PROPN hjic-488 10 23 filter filter NOUN hjic-488 10 24 ’ ' PUNCT hjic-488 10 25 ( ( PUNCT hjic-488 10 26 ukf ukf NOUN hjic-488 10 27 ) ) PUNCT hjic-488 10 28 with with ADP hjic-488 10 29 load load NOUN hjic-488 10 30 prediction prediction NOUN hjic-488 10 31 . . PUNCT hjic-488 11 1 simulation simulation NOUN hjic-488 11 2 results result NOUN hjic-488 11 3 are be AUX hjic-488 11 4 provided provide VERB hjic-488 11 5 to to PART hjic-488 11 6 demonstrate demonstrate VERB hjic-488 11 7 the the DET hjic-488 11 8 accuracy accuracy NOUN hjic-488 11 9 of of ADP hjic-488 11 10 the the DET hjic-488 11 11 algorithms algorithm NOUN hjic-488 11 12 . . PUNCT hjic-488 12 1 keywords keyword NOUN hjic-488 12 2 : : PUNCT hjic-488 12 3 overhead overhead ADJ hjic-488 12 4 crane crane NOUN hjic-488 12 5 , , PUNCT hjic-488 12 6 state state NOUN hjic-488 12 7 estimation estimation NOUN hjic-488 12 8 , , PUNCT hjic-488 12 9 nonlinear nonlinear ADJ hjic-488 12 10 systems system NOUN hjic-488 12 11 , , PUNCT hjic-488 12 12 unknown unknown ADJ hjic-488 12 13 inputs input NOUN hjic-488 12 14 , , PUNCT hjic-488 12 15 kalman kalman NOUN hjic-488 12 16 filter filter NOUN hjic-488 12 17 introduction introduction NOUN hjic-488 12 18 the the DET hjic-488 12 19 sway sway NOUN hjic-488 12 20 of of ADP hjic-488 12 21 the the DET hjic-488 12 22 load load NOUN hjic-488 12 23 carried carry VERB hjic-488 12 24 by by ADP hjic-488 12 25 cranes crane NOUN hjic-488 12 26 is be AUX hjic-488 12 27 an an DET hjic-488 12 28 unwanted unwanted ADJ hjic-488 12 29 phenomenon phenomenon NOUN hjic-488 12 30 . . PUNCT hjic-488 13 1 friction friction NOUN hjic-488 13 2 may may AUX hjic-488 13 3 decouple decouple VERB hjic-488 13 4 load load NOUN hjic-488 13 5 motion motion NOUN hjic-488 13 6 from from ADP hjic-488 13 7 the the DET hjic-488 13 8 remaining remain VERB hjic-488 13 9 crane crane NOUN hjic-488 13 10 mechanism mechanism NOUN hjic-488 13 11 . . PUNCT hjic-488 14 1 this this PRON hjic-488 14 2 causes cause VERB hjic-488 14 3 difficulty difficulty NOUN hjic-488 14 4 for for ADP hjic-488 14 5 inexperienced inexperienced ADJ hjic-488 14 6 operators operator NOUN hjic-488 14 7 , , PUNCT hjic-488 14 8 especially especially ADV hjic-488 14 9 when when SCONJ hjic-488 14 10 they they PRON hjic-488 14 11 try try VERB hjic-488 14 12 to to PART hjic-488 14 13 land land VERB hjic-488 14 14 the the DET hjic-488 14 15 cargo cargo NOUN hjic-488 14 16 . . PUNCT hjic-488 15 1 the the DET hjic-488 15 2 friction friction NOUN hjic-488 15 3 present present ADJ hjic-488 15 4 in in ADP hjic-488 15 5 the the DET hjic-488 15 6 crane crane NOUN hjic-488 15 7 mechanism mechanism NOUN hjic-488 15 8 makes make VERB hjic-488 15 9 the the DET hjic-488 15 10 reduction reduction NOUN hjic-488 15 11 of of ADP hjic-488 15 12 the the DET hjic-488 15 13 swinging swinging NOUN hjic-488 15 14 particularly particularly ADV hjic-488 15 15 demanding demanding ADJ hjic-488 15 16 . . PUNCT hjic-488 16 1 therefore therefore ADV hjic-488 16 2 the the DET hjic-488 16 3 goal goal NOUN hjic-488 16 4 of of ADP hjic-488 16 5 the the DET hjic-488 16 6 design design NOUN hjic-488 16 7 of of ADP hjic-488 16 8 crane crane NOUN hjic-488 16 9 control control NOUN hjic-488 16 10 systems system NOUN hjic-488 16 11 is be AUX hjic-488 16 12 often often ADV hjic-488 16 13 to to PART hjic-488 16 14 ensure ensure VERB hjic-488 16 15 minimal minimal ADJ hjic-488 16 16 swinging swinging NOUN hjic-488 16 17 along along ADP hjic-488 16 18 a a DET hjic-488 16 19 specified specified ADJ hjic-488 16 20 trajectory trajectory NOUN hjic-488 16 21 [ [ X hjic-488 16 22 1–6 1–6 NUM hjic-488 16 23 ] ] X hjic-488 16 24 . . PUNCT hjic-488 17 1 there there PRON hjic-488 17 2 are be VERB hjic-488 17 3 numerous numerous ADJ hjic-488 17 4 algorithms algorithm NOUN hjic-488 17 5 available available ADJ hjic-488 17 6 in in ADP hjic-488 17 7 the the DET hjic-488 17 8 literature literature NOUN hjic-488 17 9 for for ADP hjic-488 17 10 the the DET hjic-488 17 11 solution solution NOUN hjic-488 17 12 to to ADP hjic-488 17 13 this this DET hjic-488 17 14 problem problem NOUN hjic-488 17 15 . . PUNCT hjic-488 18 1 the the DET hjic-488 18 2 design design NOUN hjic-488 18 3 of of ADP hjic-488 18 4 such such DET hjic-488 18 5 a a DET hjic-488 18 6 control control NOUN hjic-488 18 7 system system NOUN hjic-488 18 8 can can AUX hjic-488 18 9 be be AUX hjic-488 18 10 addressed address VERB hjic-488 18 11 using use VERB hjic-488 18 12 soft soft ADJ hjic-488 18 13 computing computing NOUN hjic-488 18 14 methods method NOUN hjic-488 18 15 such such ADJ hjic-488 18 16 as as ADP hjic-488 18 17 fuzzy fuzzy ADJ hjic-488 18 18 logic logic NOUN hjic-488 18 19 and and CCONJ hjic-488 18 20 neural neural ADJ hjic-488 18 21 network network NOUN hjic-488 18 22 with with ADP hjic-488 18 23 genetic genetic ADJ hjic-488 18 24 algorithm algorithm NOUN hjic-488 18 25 . . PUNCT hjic-488 19 1 these these DET hjic-488 19 2 solutions solution NOUN hjic-488 19 3 require require VERB hjic-488 19 4 however however ADV hjic-488 19 5 the the DET hjic-488 19 6 measurement measurement NOUN hjic-488 19 7 of of ADP hjic-488 19 8 the the DET hjic-488 19 9 load load NOUN hjic-488 19 10 position position NOUN hjic-488 19 11 , , PUNCT hjic-488 19 12 which which PRON hjic-488 19 13 is be AUX hjic-488 19 14 often often ADV hjic-488 19 15 based base VERB hjic-488 19 16 on on ADP hjic-488 19 17 workspace workspace NOUN hjic-488 19 18 visualization visualization NOUN hjic-488 19 19 [ [ X hjic-488 19 20 1 1 NUM hjic-488 19 21 ] ] PUNCT hjic-488 19 22 . . PUNCT hjic-488 20 1 hard hard ADJ hjic-488 20 2 commuting commuting NOUN hjic-488 20 3 techniques technique NOUN hjic-488 20 4 are be AUX hjic-488 20 5 also also ADV hjic-488 20 6 widely widely ADV hjic-488 20 7 applied apply VERB hjic-488 20 8 for for ADP hjic-488 20 9 sway sway NOUN hjic-488 20 10 reduction reduction NOUN hjic-488 20 11 . . PUNCT hjic-488 21 1 an an DET hjic-488 21 2 h2 h2 NOUN hjic-488 21 3 optimal optimal ADJ hjic-488 21 4 solution solution NOUN hjic-488 21 5 is be AUX hjic-488 21 6 described describe VERB hjic-488 21 7 in in ADP hjic-488 21 8 ref.[2 ref.[2 NOUN hjic-488 21 9 ] ] PUNCT hjic-488 21 10 , , PUNCT hjic-488 21 11 which which PRON hjic-488 21 12 also also ADV hjic-488 21 13 relies rely VERB hjic-488 21 14 on on ADP hjic-488 21 15 image image NOUN hjic-488 21 16 processing processing NOUN hjic-488 21 17 for for ADP hjic-488 21 18 the the DET hjic-488 21 19 measurement measurement NOUN hjic-488 21 20 of of ADP hjic-488 21 21 the the DET hjic-488 21 22 load load NOUN hjic-488 21 23 coordinates coordinate NOUN hjic-488 21 24 . . PUNCT hjic-488 22 1 there there PRON hjic-488 22 2 are be VERB hjic-488 22 3 a a DET hjic-488 22 4 variety variety NOUN hjic-488 22 5 of of ADP hjic-488 22 6 algorithms algorithm NOUN hjic-488 22 7 taking take VERB hjic-488 22 8 advantage advantage NOUN hjic-488 22 9 of of ADP hjic-488 22 10 the the DET hjic-488 22 11 flatness flatness NOUN hjic-488 22 12 property property NOUN hjic-488 22 13 ( ( PUNCT hjic-488 22 14 or or CCONJ hjic-488 22 15 exact exact ADJ hjic-488 22 16 linearizability linearizability NOUN hjic-488 22 17 ) ) PUNCT hjic-488 22 18 of of ADP hjic-488 22 19 overhead overhead ADJ hjic-488 22 20 cranes crane NOUN hjic-488 23 1 [ [ X hjic-488 23 2 7 7 NUM hjic-488 23 3 ] ] PUNCT hjic-488 23 4 . . PUNCT hjic-488 24 1 the the DET hjic-488 24 2 control control NOUN hjic-488 24 3 systems system NOUN hjic-488 24 4 in in ADP hjic-488 24 5 refs.[3 refs.[3 NOUN hjic-488 24 6 ] ] PUNCT hjic-488 24 7 and and CCONJ hjic-488 24 8 [ [ X hjic-488 24 9 4 4 X hjic-488 24 10 ] ] PUNCT hjic-488 24 11 consider consider VERB hjic-488 24 12 all all DET hjic-488 24 13 the the DET hjic-488 24 14 states state NOUN hjic-488 24 15 measurable measurable ADJ hjic-488 24 16 , , PUNCT hjic-488 24 17 however however ADV hjic-488 24 18 an an DET hjic-488 24 19 estimator estimator NOUN hjic-488 24 20 is be AUX hjic-488 24 21 proposed propose VERB hjic-488 24 22 in in ADP hjic-488 24 23 ref.[3 ref.[3 NOUN hjic-488 24 24 ] ] PUNCT hjic-488 24 25 for for ADP hjic-488 24 26 the the DET hjic-488 24 27 computation computation NOUN hjic-488 24 28 of of ADP hjic-488 24 29 the the DET hjic-488 24 30 uncertain uncertain ADJ hjic-488 24 31 parameters parameter NOUN hjic-488 24 32 . . PUNCT hjic-488 25 1 in in ADP hjic-488 25 2 the the DET hjic-488 25 3 case case NOUN hjic-488 25 4 of of ADP hjic-488 25 5 navy navy PROPN hjic-488 25 6 cranes crane NOUN hjic-488 25 7 , , PUNCT hjic-488 25 8 local local ADJ hjic-488 25 9 asymptotic asymptotic ADJ hjic-488 25 10 stability stability NOUN hjic-488 25 11 can can AUX hjic-488 25 12 be be AUX hjic-488 25 13 achieved achieve VERB hjic-488 25 14 without without ADP hjic-488 25 15 the the DET hjic-488 25 16 measurement measurement NOUN hjic-488 25 17 of of ADP hjic-488 25 18 the the DET hjic-488 25 19 swinging swinge VERB hjic-488 25 20 angle angle NOUN hjic-488 25 21 , , PUNCT hjic-488 25 22 if if SCONJ hjic-488 25 23 trajectory trajectory NOUN hjic-488 25 24 planning planning NOUN hjic-488 25 25 exploits exploit VERB hjic-488 25 26 the the DET hjic-488 25 27 flatness flatness NOUN hjic-488 25 28 property property NOUN hjic-488 25 29 of of ADP hjic-488 25 30 the the DET hjic-488 25 31 system system NOUN hjic-488 26 1 [ [ X hjic-488 26 2 6 6 NUM hjic-488 26 3 ] ] PUNCT hjic-488 26 4 . . PUNCT hjic-488 27 1 there there PRON hjic-488 27 2 is be VERB hjic-488 27 3 also also ADV hjic-488 27 4 a a DET hjic-488 27 5 tracking tracking NOUN hjic-488 27 6 control control NOUN hjic-488 27 7 algorithm algorithm NOUN hjic-488 27 8 specifically specifically ADV hjic-488 27 9 designed design VERB hjic-488 27 10 for for ADP hjic-488 27 11 overhead overhead ADJ hjic-488 27 12 cranes crane NOUN hjic-488 27 13 , , PUNCT hjic-488 27 14 that that PRON hjic-488 27 15 is be AUX hjic-488 27 16 capable capable ADJ hjic-488 27 17 of of ADP hjic-488 27 18 effectively effectively ADV hjic-488 27 19 reducing reduce VERB hjic-488 27 20 the the DET hjic-488 27 21 sway sway NOUN hjic-488 27 22 despite despite SCONJ hjic-488 27 23 the the DET hjic-488 27 24 friction friction NOUN hjic-488 27 25 [ [ X hjic-488 27 26 5 5 NUM hjic-488 27 27 ] ] PUNCT hjic-488 27 28 . . PUNCT hjic-488 28 1 for for ADP hjic-488 28 2 the the DET hjic-488 28 3 calculation calculation NOUN hjic-488 28 4 of of ADP hjic-488 28 5 the the DET hjic-488 28 6 unmeasured unmeasured ADJ hjic-488 28 7 states state NOUN hjic-488 28 8 , , PUNCT hjic-488 28 9 this this DET hjic-488 28 10 controller controller NOUN hjic-488 28 11 uses use VERB hjic-488 28 12 a a DET hjic-488 28 13 linear linear ADJ hjic-488 28 14 observer observer NOUN hjic-488 28 15 . . PUNCT hjic-488 29 1 in in ADP hjic-488 29 2 this this DET hjic-488 29 3 paper paper NOUN hjic-488 29 4 we we PRON hjic-488 29 5 propose propose VERB hjic-488 29 6 new new ADJ hjic-488 29 7 methods method NOUN hjic-488 29 8 of of ADP hjic-488 29 9 state state NOUN hjic-488 29 10 observation observation NOUN hjic-488 29 11 for for ADP hjic-488 29 12 systems system NOUN hjic-488 29 13 that that PRON hjic-488 29 14 take take VERB hjic-488 29 15 into into ADP hjic-488 29 16 account account NOUN hjic-488 29 17 friction friction NOUN hjic-488 29 18 , , PUNCT hjic-488 29 19 and and CCONJ hjic-488 29 20 are be AUX hjic-488 29 21 applicable applicable ADJ hjic-488 29 22 to to ADP hjic-488 29 23 overhead overhead ADJ hjic-488 29 24 cranes crane NOUN hjic-488 29 25 . . PUNCT hjic-488 30 1 these these DET hjic-488 30 2 estimators estimator NOUN hjic-488 30 3 can can AUX hjic-488 30 4 replace replace VERB hjic-488 30 5 the the DET hjic-488 30 6 linear linear ADJ hjic-488 30 7 observer observer NOUN hjic-488 30 8 in in ADP hjic-488 30 9 ref.[5 ref.[5 NOUN hjic-488 30 10 ] ] X hjic-488 30 11 or or CCONJ hjic-488 30 12 the the DET hjic-488 30 13 need need NOUN hjic-488 30 14 to to PART hjic-488 30 15 measure measure VERB hjic-488 30 16 the the DET hjic-488 30 17 load load NOUN hjic-488 30 18 coordinates coordinate NOUN hjic-488 30 19 in in ADP hjic-488 30 20 any any DET hjic-488 30 21 other other ADJ hjic-488 30 22 state state NOUN hjic-488 30 23 - - PUNCT hjic-488 30 24 feedback feedback NOUN hjic-488 30 25 - - PUNCT hjic-488 30 26 based base VERB hjic-488 30 27 method method NOUN hjic-488 30 28 to to PART hjic-488 30 29 enhance enhance VERB hjic-488 30 30 the the DET hjic-488 30 31 precision precision NOUN hjic-488 30 32 of of ADP hjic-488 30 33 the the DET hjic-488 30 34 control control NOUN hjic-488 30 35 . . PUNCT hjic-488 31 1 our our PRON hjic-488 31 2 estimation estimation NOUN hjic-488 31 3 methods method NOUN hjic-488 31 4 are be AUX hjic-488 31 5 based base VERB hjic-488 31 6 on on ADP hjic-488 31 7 the the DET hjic-488 31 8 assumption assumption NOUN hjic-488 31 9 that that SCONJ hjic-488 31 10 the the DET hjic-488 31 11 effect effect NOUN hjic-488 31 12 of of ADP hjic-488 31 13 the the DET hjic-488 31 14 friction friction NOUN hjic-488 31 15 on on ADP hjic-488 31 16 the the DET hjic-488 31 17 inputs input NOUN hjic-488 31 18 can can AUX hjic-488 31 19 be be AUX hjic-488 31 20 reduced reduce VERB hjic-488 31 21 . . PUNCT hjic-488 32 1 this this PRON hjic-488 32 2 is be AUX hjic-488 32 3 true true ADJ hjic-488 32 4 for for ADP hjic-488 32 5 most most ADJ hjic-488 32 6 mechanical mechanical ADJ hjic-488 32 7 systems system NOUN hjic-488 32 8 ( ( PUNCT hjic-488 32 9 including include VERB hjic-488 32 10 overhead overhead ADJ hjic-488 32 11 cranes crane NOUN hjic-488 32 12 ) ) PUNCT hjic-488 32 13 , , PUNCT hjic-488 32 14 where where SCONJ hjic-488 32 15 the the DET hjic-488 32 16 actuating actuate VERB hjic-488 32 17 signals signal NOUN hjic-488 32 18 are be AUX hjic-488 32 19 usually usually ADV hjic-488 32 20 forces force NOUN hjic-488 32 21 and and CCONJ hjic-488 32 22 torques torque NOUN hjic-488 32 23 . . PUNCT hjic-488 33 1 in in ADP hjic-488 33 2 the the DET hjic-488 33 3 following follow VERB hjic-488 33 4 section section NOUN hjic-488 33 5 , , PUNCT hjic-488 33 6 the the DET hjic-488 33 7 modelling modelling NOUN hjic-488 33 8 of of ADP hjic-488 33 9 lagrangian lagrangian ADJ hjic-488 33 10 mechanical mechanical ADJ hjic-488 33 11 systems system NOUN hjic-488 33 12 is be AUX hjic-488 33 13 overviewed overviewe VERB hjic-488 33 14 , , PUNCT hjic-488 33 15 and and CCONJ hjic-488 33 16 it it PRON hjic-488 33 17 is be AUX hjic-488 33 18 shown show VERB hjic-488 33 19 how how SCONJ hjic-488 33 20 the the DET hjic-488 33 21 friction friction NOUN hjic-488 33 22 can can AUX hjic-488 33 23 be be AUX hjic-488 33 24 handled handle VERB hjic-488 33 25 as as ADP hjic-488 33 26 an an DET hjic-488 33 27 input input NOUN hjic-488 33 28 disturbance disturbance NOUN hjic-488 33 29 . . PUNCT hjic-488 34 1 in in ADP hjic-488 34 2 the the DET hjic-488 34 3 next next ADJ hjic-488 34 4 section section NOUN hjic-488 34 5 the the DET hjic-488 34 6 state state NOUN hjic-488 34 7 estimation estimation NOUN hjic-488 34 8 techniques technique NOUN hjic-488 34 9 are be AUX hjic-488 34 10 presented present VERB hjic-488 34 11 based base VERB hjic-488 34 12 on on ADP hjic-488 34 13 the the DET hjic-488 34 14 possible possible ADJ hjic-488 34 15 approaches approach NOUN hjic-488 34 16 of of ADP hjic-488 34 17 interpreting interpret VERB hjic-488 34 18 the the DET hjic-488 34 19 friction friction NOUN hjic-488 34 20 . . PUNCT hjic-488 35 1 the the DET hjic-488 35 2 next next ADJ hjic-488 35 3 section section NOUN hjic-488 35 4 describes describe VERB hjic-488 35 5 the the DET hjic-488 35 6 results result NOUN hjic-488 35 7 of of ADP hjic-488 35 8 the the DET hjic-488 35 9 application application NOUN hjic-488 35 10 of of ADP hjic-488 35 11 these these DET hjic-488 35 12 methods method NOUN hjic-488 35 13 to to ADP hjic-488 35 14 the the DET hjic-488 35 15 state state NOUN hjic-488 35 16 estimation estimation NOUN hjic-488 35 17 problem problem NOUN hjic-488 35 18 of of ADP hjic-488 35 19 overhead overhead ADJ hjic-488 35 20 cranes crane NOUN hjic-488 35 21 and and CCONJ hjic-488 35 22 presents present VERB hjic-488 35 23 the the DET hjic-488 35 24 simulation simulation NOUN hjic-488 35 25 results result VERB hjic-488 35 26 . . PUNCT hjic-488 36 1 lagrangian lagrangian ADJ hjic-488 36 2 - - PUNCT hjic-488 36 3 based base VERB hjic-488 36 4 models model NOUN hjic-488 36 5 of of ADP hjic-488 36 6 mechanical mechanical ADJ hjic-488 36 7 systems system NOUN hjic-488 36 8 the the DET hjic-488 36 9 nonlinear nonlinear ADJ hjic-488 36 10 dynamics dynamic NOUN hjic-488 36 11 of of ADP hjic-488 36 12 the the DET hjic-488 36 13 controlled control VERB hjic-488 36 14 system system NOUN hjic-488 36 15 can can AUX hjic-488 36 16 be be AUX hjic-488 36 17 obtained obtain VERB hjic-488 36 18 using use VERB hjic-488 36 19 the the DET hjic-488 36 20 euler euler NOUN hjic-488 36 21 - - PUNCT hjic-488 36 22 lagrange lagrange NOUN hjic-488 36 23 equations equation NOUN hjic-488 36 24 . . PUNCT hjic-488 37 1 if if SCONJ hjic-488 37 2 the the DET hjic-488 37 3 generalized generalized ADJ hjic-488 37 4 coordinates coordinate NOUN hjic-488 37 5 are be AUX hjic-488 37 6 q q ADJ hjic-488 37 7 = = SYM hjic-488 37 8 ( ( PUNCT hjic-488 37 9 q1 q1 PROPN hjic-488 37 10 q2 q2 NOUN hjic-488 37 11 . . PUNCT hjic-488 37 12 . . PUNCT hjic-488 37 13 . . PUNCT hjic-488 38 1 qn qn INTJ hjic-488 38 2 ) ) PUNCT hjic-488 38 3 t t PROPN hjic-488 38 4 and and CCONJ hjic-488 38 5 the the DET hjic-488 38 6 generalized generalized ADJ hjic-488 38 7 forces force NOUN hjic-488 38 8 are be AUX hjic-488 38 9 τ τ X hjic-488 38 10 = = PUNCT hjic-488 38 11 ( ( PUNCT hjic-488 38 12 τ1 τ1 PROPN hjic-488 38 13 τ2 τ2 NOUN hjic-488 38 14 . . PUNCT hjic-488 38 15 . . PUNCT hjic-488 38 16 . . PUNCT hjic-488 39 1 τn τn X hjic-488 39 2 ) ) PUNCT hjic-488 39 3 t t PROPN hjic-488 39 4 , , PUNCT hjic-488 39 5 the the DET hjic-488 39 6 eulerlagrange eulerlagrange NOUN hjic-488 39 7 equations equation NOUN hjic-488 39 8 read read VERB hjic-488 39 9 d d NOUN hjic-488 39 10 dt dt PROPN hjic-488 39 11 ∂l ∂l PROPN hjic-488 39 12 ∂q̇i ∂q̇i VERB hjic-488 39 13 − − PROPN hjic-488 39 14 ∂l ∂l PROPN hjic-488 39 15 ∂qi ∂qi PROPN hjic-488 39 16 = = SYM hjic-488 39 17 τi τi PROPN hjic-488 39 18 , , PUNCT hjic-488 39 19 ( ( PUNCT hjic-488 39 20 1 1 X hjic-488 39 21 ) ) PUNCT hjic-488 39 22 72 72 NUM hjic-488 39 23 where where SCONJ hjic-488 39 24 l l NOUN hjic-488 39 25 is be AUX hjic-488 39 26 the the DET hjic-488 39 27 so so ADV hjic-488 39 28 - - PUNCT hjic-488 39 29 called call VERB hjic-488 39 30 lagrangian lagrangian ADJ hjic-488 39 31 , , PUNCT hjic-488 39 32 the the DET hjic-488 39 33 difference difference NOUN hjic-488 39 34 between between ADP hjic-488 39 35 the the DET hjic-488 39 36 kinetic kinetic ADJ hjic-488 39 37 and and CCONJ hjic-488 39 38 potential potential ADJ hjic-488 39 39 energy energy NOUN hjic-488 39 40 of of ADP hjic-488 39 41 the the DET hjic-488 39 42 system system NOUN hjic-488 39 43 , , PUNCT hjic-488 39 44 q̇i q̇i PROPN hjic-488 39 45 = = PUNCT hjic-488 40 1 dqi dqi ADP hjic-488 40 2 dt dt INTJ hjic-488 41 1 and and CCONJ hjic-488 41 2 i i PRON hjic-488 41 3 = = NOUN hjic-488 41 4 1 1 NUM hjic-488 41 5 , , PUNCT hjic-488 41 6 2 2 NUM hjic-488 41 7 , , PUNCT hjic-488 41 8 . . PUNCT hjic-488 41 9 . . PUNCT hjic-488 41 10 . . PUNCT hjic-488 42 1 n. n. NOUN hjic-488 42 2 using use VERB hjic-488 42 3 these these DET hjic-488 42 4 equations equation NOUN hjic-488 42 5 , , PUNCT hjic-488 42 6 under under ADP hjic-488 42 7 some some DET hjic-488 42 8 conditions condition NOUN hjic-488 42 9 the the DET hjic-488 42 10 controlled control VERB hjic-488 42 11 system system NOUN hjic-488 42 12 ’s ’s PART hjic-488 42 13 model model NOUN hjic-488 42 14 can can AUX hjic-488 42 15 be be AUX hjic-488 42 16 written write VERB hjic-488 42 17 in in ADP hjic-488 42 18 the the DET hjic-488 42 19 form form NOUN hjic-488 42 20 h(q)q̈ h(q)q̈ NOUN hjic-488 42 21 + + CCONJ hjic-488 42 22 h(q h(q ADV hjic-488 42 23 , , PUNCT hjic-488 42 24 q̇ q̇ ADV hjic-488 42 25 ) ) PUNCT hjic-488 42 26 + + NUM hjic-488 42 27 hs(s hs( NOUN hjic-488 42 28 ) ) PUNCT hjic-488 43 1 = = SYM hjic-488 43 2 τ τ PROPN hjic-488 43 3 , , PUNCT hjic-488 43 4 ( ( PUNCT hjic-488 43 5 2 2 NUM hjic-488 43 6 ) ) PUNCT hjic-488 43 7 where where SCONJ hjic-488 43 8 h(q h(q ADV hjic-488 43 9 ) ) PUNCT hjic-488 43 10 is be AUX hjic-488 43 11 the the DET hjic-488 43 12 inertia inertia NOUN hjic-488 43 13 matrix matrix NOUN hjic-488 43 14 , , PUNCT hjic-488 43 15 h(q h(q ADV hjic-488 43 16 , , PUNCT hjic-488 43 17 q̇ q̇ ADV hjic-488 43 18 ) ) PUNCT hjic-488 43 19 comprises comprise VERB hjic-488 43 20 the the DET hjic-488 43 21 centrifugal centrifugal ADJ hjic-488 43 22 , , PUNCT hjic-488 43 23 coriolis corioli NOUN hjic-488 43 24 and and CCONJ hjic-488 43 25 gravitational gravitational ADJ hjic-488 43 26 terms term NOUN hjic-488 43 27 , , PUNCT hjic-488 43 28 and and CCONJ hjic-488 43 29 hs(s hs( NOUN hjic-488 43 30 ) ) PUNCT hjic-488 43 31 is be AUX hjic-488 43 32 the the DET hjic-488 43 33 frictional frictional ADJ hjic-488 43 34 term term NOUN hjic-488 43 35 with with ADP hjic-488 43 36 s s AUX hjic-488 43 37 being be AUX hjic-488 43 38 the the DET hjic-488 43 39 vector vector NOUN hjic-488 43 40 of of ADP hjic-488 43 41 the the DET hjic-488 43 42 frictional frictional ADJ hjic-488 43 43 forces force NOUN hjic-488 43 44 . . PUNCT hjic-488 44 1 in in ADP hjic-488 44 2 this this DET hjic-488 44 3 form form NOUN hjic-488 44 4 hs(s hs(s NOUN hjic-488 44 5 ) ) PUNCT hjic-488 44 6 can can AUX hjic-488 44 7 be be AUX hjic-488 44 8 reorganized reorganize VERB hjic-488 44 9 to to ADP hjic-488 44 10 the the DET hjic-488 44 11 right right ADJ hjic-488 44 12 - - PUNCT hjic-488 44 13 hand hand NOUN hjic-488 44 14 - - PUNCT hjic-488 44 15 side side NOUN hjic-488 44 16 of of ADP hjic-488 44 17 the the DET hjic-488 44 18 equation equation NOUN hjic-488 44 19 . . PUNCT hjic-488 45 1 introducing introduce VERB hjic-488 45 2 the the DET hjic-488 45 3 disturbance disturbance NOUN hjic-488 45 4 torques torque NOUN hjic-488 45 5 as as ADP hjic-488 45 6 τ̃ τ̃ PROPN hjic-488 45 7 = = SYM hjic-488 45 8 τ τ PROPN hjic-488 45 9 − − PROPN hjic-488 45 10 hs(s hs(s NOUN hjic-488 45 11 ) ) PUNCT hjic-488 45 12 , , PUNCT hjic-488 45 13 eq.(2 eq.(2 NOUN hjic-488 45 14 ) ) PUNCT hjic-488 45 15 yields yield VERB hjic-488 45 16 h(q)q̈ h(q)q̈ PROPN hjic-488 46 1 + + CCONJ hjic-488 46 2 h(q h(q ADV hjic-488 46 3 , , PUNCT hjic-488 46 4 q̇ q̇ ADV hjic-488 46 5 ) ) PUNCT hjic-488 47 1 = = SYM hjic-488 47 2 τ̃ τ̃ PROPN hjic-488 47 3 . . PUNCT hjic-488 48 1 ( ( PUNCT hjic-488 48 2 3 3 X hjic-488 48 3 ) ) PUNCT hjic-488 48 4 the the DET hjic-488 48 5 state state NOUN hjic-488 48 6 - - PUNCT hjic-488 48 7 space space NOUN hjic-488 48 8 representation representation NOUN hjic-488 48 9 of of ADP hjic-488 48 10 the the DET hjic-488 48 11 model model NOUN hjic-488 48 12 is be AUX hjic-488 48 13 ẋ ẋ PROPN hjic-488 48 14 = = SYM hjic-488 48 15 f(x f(x PROPN hjic-488 48 16 , , PUNCT hjic-488 48 17 u u NOUN hjic-488 48 18 ) ) PUNCT hjic-488 48 19 y y PROPN hjic-488 48 20 = = SYM hjic-488 48 21 g(x g(x PROPN hjic-488 48 22 ) ) PUNCT hjic-488 48 23 , , PUNCT hjic-488 48 24 ( ( PUNCT hjic-488 48 25 4 4 X hjic-488 48 26 ) ) PUNCT hjic-488 48 27 where where SCONJ hjic-488 48 28 x x PRON hjic-488 48 29 is be AUX hjic-488 48 30 the the DET hjic-488 48 31 state state NOUN hjic-488 48 32 , , PUNCT hjic-488 48 33 u u PROPN hjic-488 48 34 is be AUX hjic-488 48 35 the the DET hjic-488 48 36 input input NOUN hjic-488 48 37 , , PUNCT hjic-488 48 38 y y PROPN hjic-488 48 39 is be AUX hjic-488 48 40 the the DET hjic-488 48 41 output output NOUN hjic-488 48 42 of of ADP hjic-488 48 43 the the DET hjic-488 48 44 system system NOUN hjic-488 48 45 , , PUNCT hjic-488 48 46 and and CCONJ hjic-488 48 47 f f PROPN hjic-488 48 48 and and CCONJ hjic-488 48 49 g g PROPN hjic-488 48 50 are be AUX hjic-488 48 51 nonlinear nonlinear ADJ hjic-488 48 52 functions function NOUN hjic-488 48 53 . . PUNCT hjic-488 49 1 this this DET hjic-488 49 2 form form NOUN hjic-488 49 3 can can AUX hjic-488 49 4 be be AUX hjic-488 49 5 obtained obtain VERB hjic-488 49 6 from from ADP hjic-488 49 7 eq.(5 eq.(5 NOUN hjic-488 49 8 ) ) PUNCT hjic-488 49 9 assuming assume VERB hjic-488 49 10 that that SCONJ hjic-488 49 11 xt xt PROPN hjic-488 49 12 =( =( PROPN hjic-488 49 13 qt qt PROPN hjic-488 49 14 q̇t q̇t PROPN hjic-488 49 15 ) ) PUNCT hjic-488 49 16 , , PUNCT hjic-488 49 17 and and CCONJ hjic-488 49 18 the the DET hjic-488 49 19 output output NOUN hjic-488 49 20 is be AUX hjic-488 49 21 not not PART hjic-488 49 22 directly directly ADV hjic-488 49 23 dependent dependent ADJ hjic-488 49 24 on on ADP hjic-488 49 25 the the DET hjic-488 49 26 torques torque NOUN hjic-488 49 27 . . PUNCT hjic-488 50 1 the the DET hjic-488 50 2 state state NOUN hjic-488 50 3 - - PUNCT hjic-488 50 4 space space NOUN hjic-488 50 5 equations equation NOUN hjic-488 50 6 read read VERB hjic-488 50 7 ẋ ẋ PUNCT hjic-488 51 1 = = PRON hjic-488 51 2 ( ( PUNCT hjic-488 51 3 q̇ q̇ ADV hjic-488 51 4 −h−1(q)h(q −h−1(q)h(q NOUN hjic-488 51 5 , , PUNCT hjic-488 51 6 q̇ q̇ PROPN hjic-488 51 7 ) ) PUNCT hjic-488 51 8 ) ) PUNCT hjic-488 52 1 + + CCONJ hjic-488 52 2 ( ( PUNCT hjic-488 52 3 0 0 NUM hjic-488 52 4 h−1(q h−1(q PROPN hjic-488 52 5 ) ) PUNCT hjic-488 52 6 ) ) PUNCT hjic-488 53 1 τ̃ τ̃ PROPN hjic-488 53 2 y y NOUN hjic-488 53 3 = = PUNCT hjic-488 53 4 g(x g(x PROPN hjic-488 53 5 ) ) PUNCT hjic-488 53 6 . . PUNCT hjic-488 54 1 ( ( PUNCT hjic-488 54 2 5 5 X hjic-488 54 3 ) ) PUNCT hjic-488 54 4 the the DET hjic-488 54 5 inputs input NOUN hjic-488 54 6 of of ADP hjic-488 54 7 mechanical mechanical ADJ hjic-488 54 8 systems system NOUN hjic-488 54 9 are be AUX hjic-488 54 10 usually usually ADV hjic-488 54 11 forces force NOUN hjic-488 54 12 and and CCONJ hjic-488 54 13 torques torque NOUN hjic-488 54 14 , , PUNCT hjic-488 54 15 consequently consequently ADV hjic-488 54 16 they they PRON hjic-488 54 17 are be AUX hjic-488 54 18 only only ADV hjic-488 54 19 dependent dependent ADJ hjic-488 54 20 on on ADP hjic-488 54 21 τ̃ τ̃ PROPN hjic-488 54 22 . . PUNCT hjic-488 55 1 this this PRON hjic-488 55 2 means mean VERB hjic-488 55 3 , , PUNCT hjic-488 55 4 that that SCONJ hjic-488 55 5 the the DET hjic-488 55 6 effect effect NOUN hjic-488 55 7 of of ADP hjic-488 55 8 the the DET hjic-488 55 9 friction friction NOUN hjic-488 55 10 can can AUX hjic-488 55 11 be be AUX hjic-488 55 12 reduced reduce VERB hjic-488 55 13 to to ADP hjic-488 55 14 the the DET hjic-488 55 15 actuated actuate VERB hjic-488 55 16 degrees degree NOUN hjic-488 55 17 of of ADP hjic-488 55 18 freedom freedom NOUN hjic-488 55 19 of of ADP hjic-488 55 20 the the DET hjic-488 55 21 system system NOUN hjic-488 55 22 . . PUNCT hjic-488 56 1 if if SCONJ hjic-488 56 2 it it PRON hjic-488 56 3 is be AUX hjic-488 56 4 necessary necessary ADJ hjic-488 56 5 for for ADP hjic-488 56 6 the the DET hjic-488 56 7 design design NOUN hjic-488 56 8 of of ADP hjic-488 56 9 the the DET hjic-488 56 10 control control NOUN hjic-488 56 11 system system NOUN hjic-488 56 12 , , PUNCT hjic-488 56 13 the the DET hjic-488 56 14 nonlinear nonlinear ADJ hjic-488 56 15 dynamics dynamic NOUN hjic-488 56 16 can can AUX hjic-488 56 17 be be AUX hjic-488 56 18 approximated approximate VERB hjic-488 56 19 by by ADP hjic-488 56 20 a a DET hjic-488 56 21 first first ADJ hjic-488 56 22 order order NOUN hjic-488 56 23 taylor taylor PROPN hjic-488 56 24 series series PROPN hjic-488 56 25 expansion expansion NOUN hjic-488 56 26 around around ADP hjic-488 56 27 a a DET hjic-488 56 28 setpoint setpoint NOUN hjic-488 56 29 ( ( PUNCT hjic-488 56 30 x0 x0 PROPN hjic-488 56 31 , , PUNCT hjic-488 56 32 u0 u0 ADJ hjic-488 56 33 ) ) PUNCT hjic-488 56 34 . . PUNCT hjic-488 57 1 the the DET hjic-488 57 2 linear linear PROPN hjic-488 57 3 model model NOUN hjic-488 57 4 then then ADV hjic-488 57 5 becomes become VERB hjic-488 57 6 δẋ δẋ NOUN hjic-488 58 1 = = SYM hjic-488 58 2 aδx+bδu aδx+bδu PROPN hjic-488 58 3 δy δy NOUN hjic-488 58 4 = = SYM hjic-488 58 5 cδx cδx PROPN hjic-488 58 6 , , PUNCT hjic-488 58 7 ( ( PUNCT hjic-488 58 8 6 6 NUM hjic-488 58 9 ) ) PUNCT hjic-488 58 10 where where SCONJ hjic-488 58 11 the the DET hjic-488 58 12 quantities quantity NOUN hjic-488 58 13 prefixed prefix VERB hjic-488 58 14 with with ADP hjic-488 58 15 δ δ PROPN hjic-488 58 16 mean mean VERB hjic-488 58 17 the the DET hjic-488 58 18 distance distance NOUN hjic-488 58 19 from from ADP hjic-488 58 20 the the DET hjic-488 58 21 setpoint setpoint NOUN hjic-488 58 22 , , PUNCT hjic-488 58 23 e.g. e.g. ADV hjic-488 58 24 δx δx NOUN hjic-488 58 25 = = PROPN hjic-488 58 26 x− x− PROPN hjic-488 58 27 x0 x0 PROPN hjic-488 58 28 , , PUNCT hjic-488 58 29 and and CCONJ hjic-488 58 30 the the DET hjic-488 58 31 matrices matrix NOUN hjic-488 58 32 are be AUX hjic-488 58 33 jacobians jacobian NOUN hjic-488 58 34 [ [ X hjic-488 58 35 8 8 NUM hjic-488 58 36 ] ] PUNCT hjic-488 58 37 . . PUNCT hjic-488 59 1 state state NOUN hjic-488 59 2 estimation estimation NOUN hjic-488 59 3 methods method NOUN hjic-488 59 4 since since SCONJ hjic-488 59 5 the the DET hjic-488 59 6 friction friction NOUN hjic-488 59 7 can can AUX hjic-488 59 8 be be AUX hjic-488 59 9 interpreted interpret VERB hjic-488 59 10 in in ADP hjic-488 59 11 our our PRON hjic-488 59 12 setup setup NOUN hjic-488 59 13 as as ADP hjic-488 59 14 an an DET hjic-488 59 15 input input NOUN hjic-488 59 16 disturbance disturbance NOUN hjic-488 59 17 , , PUNCT hjic-488 59 18 we we PRON hjic-488 59 19 consider consider VERB hjic-488 59 20 two two NUM hjic-488 59 21 ways way NOUN hjic-488 59 22 for for ADP hjic-488 59 23 its its PRON hjic-488 59 24 compensation compensation NOUN hjic-488 59 25 in in ADP hjic-488 59 26 the the DET hjic-488 59 27 state state NOUN hjic-488 59 28 estimation estimation NOUN hjic-488 59 29 . . PUNCT hjic-488 60 1 either either CCONJ hjic-488 60 2 all all DET hjic-488 60 3 input input NOUN hjic-488 60 4 variables variable NOUN hjic-488 60 5 can can AUX hjic-488 60 6 be be AUX hjic-488 60 7 disregarded disregard VERB hjic-488 60 8 , , PUNCT hjic-488 60 9 or or CCONJ hjic-488 60 10 the the DET hjic-488 60 11 additive additive ADJ hjic-488 60 12 disturbance disturbance NOUN hjic-488 60 13 can can AUX hjic-488 60 14 be be AUX hjic-488 60 15 estimated estimate VERB hjic-488 60 16 using use VERB hjic-488 60 17 a a DET hjic-488 60 18 load load NOUN hjic-488 60 19 predictor predictor NOUN hjic-488 60 20 . . PUNCT hjic-488 61 1 these these DET hjic-488 61 2 ideas idea NOUN hjic-488 61 3 form form VERB hjic-488 61 4 the the DET hjic-488 61 5 basis basis NOUN hjic-488 61 6 of of ADP hjic-488 61 7 the the DET hjic-488 61 8 two two NUM hjic-488 61 9 estimator estimator NOUN hjic-488 61 10 design design NOUN hjic-488 61 11 techniques technique NOUN hjic-488 61 12 described describe VERB hjic-488 61 13 as as ADP hjic-488 61 14 follows follow VERB hjic-488 61 15 . . PUNCT hjic-488 62 1 the the DET hjic-488 62 2 computations computation NOUN hjic-488 62 3 of of ADP hjic-488 62 4 the the DET hjic-488 62 5 controllers controller NOUN hjic-488 62 6 implemented implement VERB hjic-488 62 7 in in ADP hjic-488 62 8 embedded embed VERB hjic-488 62 9 systems system NOUN hjic-488 62 10 are be AUX hjic-488 62 11 based base VERB hjic-488 62 12 on on ADP hjic-488 62 13 sampled sample VERB hjic-488 62 14 signals signal NOUN hjic-488 62 15 . . PUNCT hjic-488 63 1 hence hence ADV hjic-488 63 2 the the DET hjic-488 63 3 design design NOUN hjic-488 63 4 of of ADP hjic-488 63 5 the the DET hjic-488 63 6 estimators estimator NOUN hjic-488 63 7 is be AUX hjic-488 63 8 done do VERB hjic-488 63 9 in in ADP hjic-488 63 10 discrete discrete ADJ hjic-488 63 11 - - PUNCT hjic-488 63 12 time time NOUN hjic-488 63 13 . . PUNCT hjic-488 64 1 unknown unknown ADJ hjic-488 64 2 input input NOUN hjic-488 64 3 approach approach NOUN hjic-488 64 4 consider consider VERB hjic-488 64 5 the the DET hjic-488 64 6 discrete discrete ADJ hjic-488 64 7 - - PUNCT hjic-488 64 8 time time NOUN hjic-488 64 9 linear linear PROPN hjic-488 64 10 stochastic stochastic ADJ hjic-488 64 11 system system NOUN hjic-488 64 12 model model NOUN hjic-488 64 13 x[k x[k PROPN hjic-488 65 1 + + CCONJ hjic-488 65 2 1 1 NUM hjic-488 65 3 ] ] X hjic-488 65 4 = = PUNCT hjic-488 65 5 φx[k φx[k PROPN hjic-488 65 6 ] ] PUNCT hjic-488 66 1 + + CCONJ hjic-488 66 2 γdd[k γdd[k NUM hjic-488 66 3 ] ] PUNCT hjic-488 66 4 + + CCONJ hjic-488 66 5 ω[k ω[k NOUN hjic-488 66 6 ] ] PUNCT hjic-488 66 7 z[k z[k NUM hjic-488 66 8 ] ] X hjic-488 66 9 = = PUNCT hjic-488 66 10 cx[k cx[k NOUN hjic-488 66 11 ] ] PUNCT hjic-488 66 12 + + CCONJ hjic-488 66 13 v[k v[k ADJ hjic-488 66 14 ] ] X hjic-488 66 15 , , PUNCT hjic-488 66 16 ( ( PUNCT hjic-488 66 17 7 7 X hjic-488 66 18 ) ) PUNCT hjic-488 66 19 where where SCONJ hjic-488 66 20 x x PRON hjic-488 66 21 is be AUX hjic-488 66 22 the the DET hjic-488 66 23 state state NOUN hjic-488 66 24 , , PUNCT hjic-488 66 25 d d PROPN hjic-488 66 26 is be AUX hjic-488 66 27 the the DET hjic-488 66 28 unknown unknown ADJ hjic-488 66 29 input input NOUN hjic-488 66 30 ( ( PUNCT hjic-488 66 31 disturbance disturbance NOUN hjic-488 66 32 ) ) PUNCT hjic-488 66 33 of of ADP hjic-488 66 34 the the DET hjic-488 66 35 system system NOUN hjic-488 66 36 and and CCONJ hjic-488 66 37 z z NOUN hjic-488 66 38 is be AUX hjic-488 66 39 the the DET hjic-488 66 40 measurement measurement NOUN hjic-488 66 41 of of ADP hjic-488 66 42 the the DET hjic-488 66 43 output output NOUN hjic-488 66 44 y[k y[k PROPN hjic-488 66 45 ] ] X hjic-488 66 46 = = PUNCT hjic-488 66 47 cx[k cx[k PROPN hjic-488 66 48 ] ] PUNCT hjic-488 66 49 . . PUNCT hjic-488 67 1 φ φ PROPN hjic-488 67 2 and and CCONJ hjic-488 67 3 γd γd ADV hjic-488 67 4 are be AUX hjic-488 67 5 obtained obtain VERB hjic-488 67 6 from from ADP hjic-488 67 7 the the DET hjic-488 67 8 matrices matrix NOUN hjic-488 67 9 of of ADP hjic-488 67 10 eq.(6 eq.(6 NOUN hjic-488 67 11 ) ) PUNCT hjic-488 67 12 in in ADP hjic-488 67 13 the the DET hjic-488 67 14 form form NOUN hjic-488 67 15 of of ADP hjic-488 67 16 φ φ PROPN hjic-488 67 17 = = PUNCT hjic-488 67 18 eats eat NOUN hjic-488 67 19 , , PUNCT hjic-488 67 20 γd γd ADV hjic-488 67 21 = = PUNCT hjic-488 67 22 ∫ ∫ PROPN hjic-488 67 23 ts ts ADP hjic-488 67 24 0 0 NUM hjic-488 67 25 eatb eatb PROPN hjic-488 67 26 dt dt PROPN hjic-488 67 27 , , PUNCT hjic-488 67 28 ( ( PUNCT hjic-488 67 29 8) 8) NUM hjic-488 67 30 where where SCONJ hjic-488 67 31 ts ts PROPN hjic-488 67 32 is be AUX hjic-488 67 33 the the DET hjic-488 67 34 sample sample NOUN hjic-488 67 35 time time NOUN hjic-488 67 36 . . PUNCT hjic-488 68 1 the the DET hjic-488 68 2 measurement measurement NOUN hjic-488 68 3 and and CCONJ hjic-488 68 4 process process NOUN hjic-488 68 5 noise noise NOUN hjic-488 68 6 v v NOUN hjic-488 68 7 and and CCONJ hjic-488 68 8 ω ω PROPN hjic-488 68 9 are be AUX hjic-488 68 10 assumed assume VERB hjic-488 68 11 to to PART hjic-488 68 12 be be AUX hjic-488 68 13 additive additive ADJ hjic-488 68 14 , , PUNCT hjic-488 68 15 white white ADJ hjic-488 68 16 , , PUNCT hjic-488 68 17 and and CCONJ hjic-488 68 18 gaussian gaussian NOUN hjic-488 68 19 with with ADP hjic-488 68 20 mean mean NOUN hjic-488 68 21 of of ADP hjic-488 68 22 zero zero NUM hjic-488 68 23 . . PUNCT hjic-488 69 1 notice notice NOUN hjic-488 69 2 , , PUNCT hjic-488 69 3 that that SCONJ hjic-488 69 4 in in ADP hjic-488 69 5 eq.(7 eq.(7 NOUN hjic-488 69 6 ) ) PUNCT hjic-488 69 7 , , PUNCT hjic-488 69 8 all all PRON hjic-488 69 9 of of ADP hjic-488 69 10 the the DET hjic-488 69 11 system system NOUN hjic-488 69 12 inputs input NOUN hjic-488 69 13 are be AUX hjic-488 69 14 considered consider VERB hjic-488 69 15 to to PART hjic-488 69 16 be be AUX hjic-488 69 17 disturbances disturbance NOUN hjic-488 69 18 . . PUNCT hjic-488 70 1 the the DET hjic-488 70 2 state state NOUN hjic-488 70 3 and and CCONJ hjic-488 70 4 the the DET hjic-488 70 5 unknown unknown ADJ hjic-488 70 6 input input NOUN hjic-488 70 7 of of ADP hjic-488 70 8 such such DET hjic-488 70 9 a a DET hjic-488 70 10 system system NOUN hjic-488 70 11 can can AUX hjic-488 70 12 be be AUX hjic-488 70 13 estimated estimate VERB hjic-488 70 14 using use VERB hjic-488 70 15 an an DET hjic-488 70 16 ’ ' PUNCT hjic-488 70 17 unknown unknown ADJ hjic-488 70 18 input input NOUN hjic-488 70 19 kalman kalman PROPN hjic-488 70 20 filter filter NOUN hjic-488 70 21 ’ ' PUNCT hjic-488 70 22 ( ( PUNCT hjic-488 70 23 uikf uikf NOUN hjic-488 70 24 ) ) PUNCT hjic-488 71 1 [ [ X hjic-488 71 2 9 9 NUM hjic-488 71 3 ] ] PUNCT hjic-488 71 4 , , PUNCT hjic-488 71 5 if if SCONJ hjic-488 71 6 the the DET hjic-488 71 7 system system NOUN hjic-488 71 8 satisfies satisfy VERB hjic-488 71 9 the the DET hjic-488 71 10 conditions condition NOUN hjic-488 71 11 dim{d dim{d NOUN hjic-488 71 12 } } PUNCT hjic-488 71 13 ≤ ≤ NUM hjic-488 71 14 dim{y dim{y NOUN hjic-488 71 15 } } PUNCT hjic-488 71 16 ( ( PUNCT hjic-488 71 17 9 9 X hjic-488 71 18 ) ) PUNCT hjic-488 71 19 rank{c rank{c NOUN hjic-488 71 20 } } PUNCT hjic-488 71 21 = = SYM hjic-488 71 22 dim{y dim{y NOUN hjic-488 71 23 } } PUNCT hjic-488 71 24 ( ( PUNCT hjic-488 71 25 10 10 NUM hjic-488 71 26 ) ) PUNCT hjic-488 71 27 rank{γd rank{γd ADJ hjic-488 71 28 } } PUNCT hjic-488 71 29 = = SYM hjic-488 71 30 dim{d dim{d PROPN hjic-488 71 31 } } PUNCT hjic-488 71 32 ( ( PUNCT hjic-488 71 33 11 11 NUM hjic-488 71 34 ) ) PUNCT hjic-488 71 35 rank{cγd rank{cγd PROPN hjic-488 71 36 } } PUNCT hjic-488 71 37 = = SYM hjic-488 71 38 dim{d dim{d PROPN hjic-488 71 39 } } PUNCT hjic-488 71 40 . . PUNCT hjic-488 72 1 ( ( PUNCT hjic-488 72 2 12 12 NUM hjic-488 72 3 ) ) PUNCT hjic-488 72 4 additive additive ADJ hjic-488 72 5 disturbance disturbance NOUN hjic-488 72 6 approach approach NOUN hjic-488 72 7 in in ADP hjic-488 72 8 the the DET hjic-488 72 9 case case NOUN hjic-488 72 10 of of ADP hjic-488 72 11 input input NOUN hjic-488 72 12 disturbances disturbance NOUN hjic-488 72 13 , , PUNCT hjic-488 72 14 load load NOUN hjic-488 72 15 prediction prediction NOUN hjic-488 72 16 is be AUX hjic-488 72 17 often often ADV hjic-488 72 18 applied apply VERB hjic-488 72 19 . . PUNCT hjic-488 73 1 let let VERB hjic-488 73 2 us we PRON hjic-488 73 3 introduce introduce VERB hjic-488 73 4 the the DET hjic-488 73 5 discrete discrete ADJ hjic-488 73 6 - - PUNCT hjic-488 73 7 time time NOUN hjic-488 73 8 nonlinear nonlinear ADJ hjic-488 73 9 model model NOUN hjic-488 73 10 of of ADP hjic-488 73 11 a a DET hjic-488 73 12 system system NOUN hjic-488 73 13 in in ADP hjic-488 73 14 the the DET hjic-488 73 15 form form NOUN hjic-488 73 16 x[k x[k PUNCT hjic-488 74 1 + + CCONJ hjic-488 74 2 1 1 NUM hjic-488 74 3 ] ] X hjic-488 74 4 = = PUNCT hjic-488 74 5 φ(x[k φ(x[k NOUN hjic-488 74 6 ] ] PUNCT hjic-488 74 7 , , PUNCT hjic-488 74 8 ũ[k ũ[k PROPN hjic-488 74 9 ] ] PUNCT hjic-488 74 10 ) ) PUNCT hjic-488 75 1 + + CCONJ hjic-488 75 2 ω[k ω[k NUM hjic-488 75 3 ] ] PUNCT hjic-488 75 4 z[k z[k NUM hjic-488 75 5 ] ] X hjic-488 75 6 = = PUNCT hjic-488 75 7 g(x[k g(x[k X hjic-488 75 8 ] ] PUNCT hjic-488 75 9 ) ) PUNCT hjic-488 76 1 + + CCONJ hjic-488 76 2 v[k v[k ADJ hjic-488 76 3 ] ] X hjic-488 76 4 , , PUNCT hjic-488 76 5 ( ( PUNCT hjic-488 76 6 13 13 NUM hjic-488 76 7 ) ) PUNCT hjic-488 76 8 where where SCONJ hjic-488 76 9 ũ ũ PROPN hjic-488 76 10 is be AUX hjic-488 76 11 the the DET hjic-488 76 12 disturbed disturbed ADJ hjic-488 76 13 input input NOUN hjic-488 76 14 of of ADP hjic-488 76 15 the the DET hjic-488 76 16 system system NOUN hjic-488 76 17 , , PUNCT hjic-488 76 18 and and CCONJ hjic-488 76 19 φ φ PROPN hjic-488 76 20 and and CCONJ hjic-488 76 21 g g PROPN hjic-488 76 22 are be AUX hjic-488 76 23 nonlinear nonlinear ADJ hjic-488 76 24 functions function NOUN hjic-488 76 25 . . PUNCT hjic-488 77 1 we we PRON hjic-488 77 2 will will AUX hjic-488 77 3 follow follow VERB hjic-488 77 4 the the DET hjic-488 77 5 assumption assumption NOUN hjic-488 77 6 , , PUNCT hjic-488 77 7 that that SCONJ hjic-488 77 8 the the DET hjic-488 77 9 disturbance disturbance NOUN hjic-488 77 10 is be AUX hjic-488 77 11 additive additive ADJ hjic-488 77 12 to to ADP hjic-488 77 13 the the DET hjic-488 77 14 input input NOUN hjic-488 77 15 , , PUNCT hjic-488 77 16 thus thus ADV hjic-488 77 17 ũ[k ũ[k ADP hjic-488 77 18 ] ] X hjic-488 77 19 = = SYM hjic-488 77 20 u[k u[k PROPN hjic-488 77 21 ] ] X hjic-488 77 22 + + CCONJ hjic-488 77 23 λd[k λd[k PROPN hjic-488 77 24 ] ] PUNCT hjic-488 77 25 , , PUNCT hjic-488 77 26 where where SCONJ hjic-488 77 27 u u NOUN hjic-488 77 28 is be AUX hjic-488 77 29 the the DET hjic-488 77 30 vector vector NOUN hjic-488 77 31 of of ADP hjic-488 77 32 actuating actuate VERB hjic-488 77 33 signals signal NOUN hjic-488 77 34 , , PUNCT hjic-488 77 35 and and CCONJ hjic-488 77 36 λ λ PROPN hjic-488 77 37 is be AUX hjic-488 77 38 a a DET hjic-488 77 39 constant constant ADJ hjic-488 77 40 matrix matrix NOUN hjic-488 77 41 . . PUNCT hjic-488 78 1 we we PRON hjic-488 78 2 also also ADV hjic-488 78 3 assume assume VERB hjic-488 78 4 a a DET hjic-488 78 5 constant constant ADJ hjic-488 78 6 disturbance disturbance NOUN hjic-488 78 7 model model NOUN hjic-488 78 8 with with ADP hjic-488 78 9 process process NOUN hjic-488 78 10 noise noise NOUN hjic-488 78 11 ωd ωd ADP hjic-488 78 12 , , PUNCT hjic-488 78 13 d[k d[k PROPN hjic-488 79 1 + + CCONJ hjic-488 80 1 1 1 NUM hjic-488 80 2 ] ] X hjic-488 80 3 = = SYM hjic-488 80 4 d[k d[k NUM hjic-488 80 5 ] ] X hjic-488 80 6 + + CCONJ hjic-488 80 7 ωd[k ωd[k NOUN hjic-488 80 8 ] ] PUNCT hjic-488 80 9 , , PUNCT hjic-488 80 10 resulting result VERB hjic-488 80 11 in in ADP hjic-488 80 12 the the DET hjic-488 80 13 model model NOUN hjic-488 80 14 x̃[k x̃[k PUNCT hjic-488 81 1 + + CCONJ hjic-488 81 2 1 1 X hjic-488 81 3 ] ] X hjic-488 81 4 = = PUNCT hjic-488 81 5 φ̃(x̃[k φ̃(x̃[k ADP hjic-488 81 6 ] ] PUNCT hjic-488 81 7 , , PUNCT hjic-488 81 8 u[k u[k PROPN hjic-488 81 9 ] ] X hjic-488 81 10 ) ) PUNCT hjic-488 81 11 + + CCONJ hjic-488 81 12 ω̃[k ω̃[k NOUN hjic-488 81 13 ] ] X hjic-488 81 14 z[k z[k X hjic-488 81 15 ] ] X hjic-488 81 16 = = SYM hjic-488 81 17 g̃(x̃[k g̃(x̃[k NOUN hjic-488 81 18 ] ] X hjic-488 81 19 ) ) PUNCT hjic-488 82 1 + + CCONJ hjic-488 82 2 v[k v[k ADJ hjic-488 82 3 ] ] X hjic-488 82 4 . . PUNCT hjic-488 83 1 ( ( PUNCT hjic-488 83 2 14 14 NUM hjic-488 83 3 ) ) PUNCT hjic-488 83 4 in in ADP hjic-488 83 5 eq.(14 eq.(14 NOUN hjic-488 83 6 ) ) PUNCT hjic-488 83 7 x̃t x̃t X hjic-488 83 8 = = PUNCT hjic-488 84 1 ( ( PUNCT hjic-488 84 2 xt xt NUM hjic-488 84 3 dt dt NOUN hjic-488 84 4 ) ) PUNCT hjic-488 84 5 is be AUX hjic-488 84 6 the the DET hjic-488 84 7 extended extended ADJ hjic-488 84 8 state state NOUN hjic-488 84 9 and and CCONJ hjic-488 84 10 ω̃t ω̃t NUM hjic-488 84 11 = = SYM hjic-488 84 12 ( ( PUNCT hjic-488 84 13 ωt ωt INTJ hjic-488 84 14 ωtd ωtd ADJ hjic-488 84 15 ) ) PUNCT hjic-488 84 16 is be AUX hjic-488 84 17 the the DET hjic-488 84 18 extended extended ADJ hjic-488 84 19 process process NOUN hjic-488 84 20 noise noise NOUN hjic-488 84 21 . . PUNCT hjic-488 85 1 the the DET hjic-488 85 2 extended extended ADJ hjic-488 85 3 nonlinear nonlinear ADJ hjic-488 85 4 mappings mapping NOUN hjic-488 85 5 of of ADP hjic-488 85 6 the the DET hjic-488 85 7 system system NOUN hjic-488 85 8 are be AUX hjic-488 85 9 given give VERB hjic-488 85 10 by by ADP hjic-488 85 11 g̃(x̃[k g̃(x̃[k NOUN hjic-488 85 12 ] ] X hjic-488 85 13 ) ) PUNCT hjic-488 85 14 = = PUNCT hjic-488 85 15 g(x[k g(x[k X hjic-488 85 16 ] ] PUNCT hjic-488 85 17 ) ) PUNCT hjic-488 85 18 and and CCONJ hjic-488 85 19 φ̃(x̃[k φ̃(x̃[k ADP hjic-488 85 20 ] ] PUNCT hjic-488 85 21 , , PUNCT hjic-488 85 22 u[k u[k PROPN hjic-488 85 23 ] ] X hjic-488 85 24 ) ) PUNCT hjic-488 86 1 = = SYM hjic-488 86 2 ( ( PUNCT hjic-488 86 3 φ(x[k φ(x[k NOUN hjic-488 86 4 ] ] PUNCT hjic-488 86 5 , , PUNCT hjic-488 86 6 u[k u[k PROPN hjic-488 86 7 ] ] X hjic-488 86 8 + + CCONJ hjic-488 86 9 λd[k λd[k PROPN hjic-488 86 10 ] ] SYM hjic-488 86 11 ) ) PUNCT hjic-488 86 12 d[k d[k NUM hjic-488 86 13 ] ] PUNCT hjic-488 86 14 ) ) PUNCT hjic-488 86 15 . . PUNCT hjic-488 87 1 ( ( PUNCT hjic-488 87 2 15 15 NUM hjic-488 87 3 ) ) PUNCT hjic-488 87 4 in in ADP hjic-488 87 5 most most ADJ hjic-488 87 6 cases case NOUN hjic-488 87 7 the the DET hjic-488 87 8 continuous continuous ADJ hjic-488 87 9 - - PUNCT hjic-488 87 10 time time NOUN hjic-488 87 11 differential differential ADJ hjic-488 87 12 equation equation NOUN hjic-488 87 13 of of ADP hjic-488 87 14 the the DET hjic-488 87 15 observed observe VERB hjic-488 87 16 system system NOUN hjic-488 87 17 is be AUX hjic-488 87 18 available available ADJ hjic-488 87 19 , , PUNCT hjic-488 87 20 in in ADP hjic-488 87 21 the the DET hjic-488 87 22 form form NOUN hjic-488 87 23 73 73 NUM hjic-488 87 24 m m NOUN hjic-488 87 25 uf uf NOUN hjic-488 88 1 uc uc ADJ hjic-488 88 2 r r NOUN hjic-488 88 3 ` ` PUNCT hjic-488 88 4 θ θ PROPN hjic-488 88 5 j j PROPN hjic-488 88 6 ρ ρ PROPN hjic-488 88 7 cartwinch cartwinch PROPN hjic-488 88 8 m m PROPN hjic-488 88 9 load load NOUN hjic-488 88 10 rail rail NOUN hjic-488 88 11 figure figure NOUN hjic-488 88 12 1 1 NUM hjic-488 88 13 : : PUNCT hjic-488 88 14 the the DET hjic-488 88 15 two two NUM hjic-488 88 16 - - PUNCT hjic-488 88 17 dimensional dimensional ADJ hjic-488 88 18 ovearhead ovearhead ADJ hjic-488 88 19 crane crane NOUN hjic-488 88 20 of of ADP hjic-488 88 21 eq.(4 eq.(4 ADJ hjic-488 88 22 ) ) PUNCT hjic-488 88 23 . . PUNCT hjic-488 89 1 the the DET hjic-488 89 2 discrete discrete ADJ hjic-488 89 3 - - PUNCT hjic-488 89 4 time time NOUN hjic-488 89 5 state state NOUN hjic-488 89 6 - - PUNCT hjic-488 89 7 transition transition NOUN hjic-488 89 8 equation equation NOUN hjic-488 89 9 can can AUX hjic-488 89 10 then then ADV hjic-488 89 11 be be AUX hjic-488 89 12 obtained obtain VERB hjic-488 89 13 by by ADP hjic-488 89 14 φ(x[k φ(x[k NOUN hjic-488 89 15 ] ] PUNCT hjic-488 89 16 , , PUNCT hjic-488 89 17 u[k u[k PROPN hjic-488 89 18 ] ] PUNCT hjic-488 89 19 ) ) PUNCT hjic-488 90 1 = = SYM hjic-488 90 2 x[k x[k NOUN hjic-488 90 3 ] ] X hjic-488 91 1 + + CCONJ hjic-488 91 2 ( ( PUNCT hjic-488 91 3 k+1)ts∫ k+1)ts∫ PROPN hjic-488 91 4 kts kts PROPN hjic-488 91 5 f(x f(x PROPN hjic-488 91 6 , , PUNCT hjic-488 91 7 u[k u[k NOUN hjic-488 91 8 ] ] PUNCT hjic-488 91 9 ) ) PUNCT hjic-488 91 10 dt dt X hjic-488 91 11 , , PUNCT hjic-488 91 12 ( ( PUNCT hjic-488 91 13 16 16 NUM hjic-488 91 14 ) ) PUNCT hjic-488 91 15 where where SCONJ hjic-488 91 16 the the DET hjic-488 91 17 input input NOUN hjic-488 91 18 is be AUX hjic-488 91 19 piecewise piecewise NOUN hjic-488 91 20 constant constant ADJ hjic-488 91 21 and and CCONJ hjic-488 91 22 u[k u[k NUM hjic-488 91 23 ] ] X hjic-488 91 24 = = SYM hjic-488 91 25 u(kts u(kts NOUN hjic-488 91 26 ) ) PUNCT hjic-488 91 27 . . PUNCT hjic-488 92 1 if if SCONJ hjic-488 92 2 the the DET hjic-488 92 3 integral integral ADJ hjic-488 92 4 in in ADP hjic-488 92 5 eq.(16 eq.(16 NOUN hjic-488 92 6 ) ) PUNCT hjic-488 92 7 can can AUX hjic-488 92 8 not not PART hjic-488 92 9 be be AUX hjic-488 92 10 given give VERB hjic-488 92 11 in in ADP hjic-488 92 12 closed closed ADJ hjic-488 92 13 form form NOUN hjic-488 92 14 and and CCONJ hjic-488 92 15 ts ts NOUN hjic-488 92 16 is be AUX hjic-488 92 17 sufficiently sufficiently ADV hjic-488 92 18 small small ADJ hjic-488 92 19 , , PUNCT hjic-488 92 20 the the DET hjic-488 92 21 left left ADJ hjic-488 92 22 rectangle rectangle NOUN hjic-488 92 23 rule rule NOUN hjic-488 92 24 approximation approximation NOUN hjic-488 92 25 ( ( PUNCT hjic-488 92 26 k+1)ts∫ k+1)ts∫ PROPN hjic-488 92 27 kts kts PROPN hjic-488 92 28 f(x f(x PROPN hjic-488 92 29 , , PUNCT hjic-488 92 30 u[k u[k PROPN hjic-488 92 31 ] ] PUNCT hjic-488 92 32 ) ) PUNCT hjic-488 92 33 dt dt PROPN hjic-488 93 1 ≈ ≈ PROPN hjic-488 93 2 tsf(x[k tsf(x[k ADP hjic-488 93 3 ] ] PUNCT hjic-488 93 4 , , PUNCT hjic-488 93 5 u[k u[k PROPN hjic-488 93 6 ] ] PUNCT hjic-488 93 7 ) ) PUNCT hjic-488 93 8 . . PUNCT hjic-488 94 1 ( ( PUNCT hjic-488 94 2 17 17 NUM hjic-488 94 3 ) ) PUNCT hjic-488 94 4 can can AUX hjic-488 94 5 be be AUX hjic-488 94 6 used use VERB hjic-488 94 7 . . PUNCT hjic-488 95 1 substituting substitute VERB hjic-488 95 2 this this PRON hjic-488 95 3 into into ADP hjic-488 95 4 eq.(15 eq.(15 NOUN hjic-488 95 5 ) ) PUNCT hjic-488 95 6 , , PUNCT hjic-488 95 7 the the DET hjic-488 95 8 expression expression NOUN hjic-488 95 9 reads read VERB hjic-488 95 10 φ̃(x̃[k φ̃(x̃[k ADV hjic-488 95 11 ] ] PUNCT hjic-488 95 12 , , PUNCT hjic-488 95 13 u[k u[k PROPN hjic-488 95 14 ] ] PUNCT hjic-488 95 15 ) ) PUNCT hjic-488 96 1 = = SYM hjic-488 96 2 ( ( PUNCT hjic-488 96 3 x[k x[k NOUN hjic-488 96 4 ] ] X hjic-488 96 5 + + CCONJ hjic-488 96 6 tsf(x[k tsf(x[k ADP hjic-488 96 7 ] ] PUNCT hjic-488 96 8 , , PUNCT hjic-488 96 9 u[k u[k PROPN hjic-488 96 10 ] ] X hjic-488 96 11 + + CCONJ hjic-488 96 12 λd[k λd[k PROPN hjic-488 96 13 ] ] SYM hjic-488 96 14 ) ) PUNCT hjic-488 96 15 d[k d[k NUM hjic-488 96 16 ] ] PUNCT hjic-488 96 17 ) ) PUNCT hjic-488 96 18 . . PUNCT hjic-488 97 1 ( ( PUNCT hjic-488 97 2 18 18 NUM hjic-488 97 3 ) ) PUNCT hjic-488 97 4 for for ADP hjic-488 97 5 the the DET hjic-488 97 6 observation observation NOUN hjic-488 97 7 of of ADP hjic-488 97 8 the the DET hjic-488 97 9 system system NOUN hjic-488 97 10 described describe VERB hjic-488 97 11 by by ADP hjic-488 97 12 eq.(14 eq.(14 NOUN hjic-488 97 13 ) ) PUNCT hjic-488 97 14 and and CCONJ hjic-488 97 15 eq.(18 eq.(18 NOUN hjic-488 97 16 ) ) PUNCT hjic-488 97 17 the the DET hjic-488 97 18 ’ ' PUNCT hjic-488 97 19 unscented unscente VERB hjic-488 97 20 kalman kalman PROPN hjic-488 97 21 filter filter NOUN hjic-488 97 22 ’ ' PUNCT hjic-488 97 23 ( ( PUNCT hjic-488 97 24 ukf ukf NOUN hjic-488 97 25 ) ) PUNCT hjic-488 98 1 [ [ X hjic-488 98 2 10 10 NUM hjic-488 98 3 ] ] PUNCT hjic-488 98 4 is be AUX hjic-488 98 5 applicable applicable ADJ hjic-488 98 6 . . PUNCT hjic-488 99 1 we we PRON hjic-488 99 2 chose choose VERB hjic-488 99 3 one one NUM hjic-488 99 4 of of ADP hjic-488 99 5 the the DET hjic-488 99 6 implementation implementation NOUN hjic-488 99 7 variants variant NOUN hjic-488 99 8 of of ADP hjic-488 99 9 this this DET hjic-488 99 10 filter filter NOUN hjic-488 99 11 from from ADP hjic-488 99 12 ref.[10 ref.[10 NOUN hjic-488 99 13 ] ] PUNCT hjic-488 99 14 . . PUNCT hjic-488 100 1 application application NOUN hjic-488 100 2 of of ADP hjic-488 100 3 the the DET hjic-488 100 4 methods method NOUN hjic-488 100 5 to to PART hjic-488 100 6 overhead overhead ADJ hjic-488 100 7 cranes crane NOUN hjic-488 100 8 system system NOUN hjic-488 100 9 dynamics dynamic NOUN hjic-488 100 10 we we PRON hjic-488 100 11 will will AUX hjic-488 100 12 now now ADV hjic-488 100 13 consider consider VERB hjic-488 100 14 the the DET hjic-488 100 15 state state NOUN hjic-488 100 16 estimation estimation NOUN hjic-488 100 17 problem problem NOUN hjic-488 100 18 of of ADP hjic-488 100 19 the the DET hjic-488 100 20 two two NUM hjic-488 100 21 - - PUNCT hjic-488 100 22 dimensional dimensional ADJ hjic-488 100 23 overhead overhead ADJ hjic-488 100 24 crane crane NOUN hjic-488 100 25 ( ( PUNCT hjic-488 100 26 fig.1 fig.1 PROPN hjic-488 100 27 ) ) PUNCT hjic-488 100 28 . . PUNCT hjic-488 101 1 let let VERB hjic-488 101 2 us we PRON hjic-488 101 3 denote denote VERB hjic-488 101 4 the the DET hjic-488 101 5 horizontal horizontal ADJ hjic-488 101 6 displacement displacement NOUN hjic-488 101 7 of of ADP hjic-488 101 8 the the DET hjic-488 101 9 cart cart NOUN hjic-488 101 10 by by ADP hjic-488 101 11 ` ` PUNCT hjic-488 101 12 , , PUNCT hjic-488 101 13 the the DET hjic-488 101 14 length length NOUN hjic-488 101 15 of of ADP hjic-488 101 16 the the DET hjic-488 101 17 rope rope NOUN hjic-488 101 18 by by ADP hjic-488 101 19 r r NOUN hjic-488 101 20 and and CCONJ hjic-488 101 21 the the DET hjic-488 101 22 angle angle NOUN hjic-488 101 23 between between ADP hjic-488 101 24 the the DET hjic-488 101 25 vertical vertical ADJ hjic-488 101 26 and and CCONJ hjic-488 101 27 the the DET hjic-488 101 28 rope rope NOUN hjic-488 101 29 by by ADP hjic-488 101 30 θ θ PROPN hjic-488 101 31 . . PUNCT hjic-488 102 1 the the DET hjic-488 102 2 generalized generalized ADJ hjic-488 102 3 coordinates coordinate NOUN hjic-488 102 4 of of ADP hjic-488 102 5 the the DET hjic-488 102 6 system system NOUN hjic-488 102 7 are be AUX hjic-488 102 8 chosen choose VERB hjic-488 102 9 to to PART hjic-488 102 10 be be AUX hjic-488 102 11 q q NOUN hjic-488 102 12 = = PUNCT hjic-488 102 13 ( ( PUNCT hjic-488 102 14 ` ` PUNCT hjic-488 102 15 r r NOUN hjic-488 102 16 θ θ PROPN hjic-488 102 17 ) ) PUNCT hjic-488 102 18 t t PROPN hjic-488 102 19 , , PUNCT hjic-488 102 20 and and CCONJ hjic-488 102 21 the the DET hjic-488 102 22 state state NOUN hjic-488 102 23 is be AUX hjic-488 102 24 x x X hjic-488 102 25 =( =( ADJ hjic-488 102 26 ` ` PUNCT hjic-488 102 27 r r NOUN hjic-488 102 28 θ θ PROPN hjic-488 102 29 ˙̀ ˙̀ AUX hjic-488 102 30 ṙ ṙ VERB hjic-488 102 31 θ̇ θ̇ PRON hjic-488 102 32 ) ) PUNCT hjic-488 102 33 t t NOUN hjic-488 102 34 . . PUNCT hjic-488 103 1 based base VERB hjic-488 103 2 on on ADP hjic-488 103 3 the the DET hjic-488 103 4 sensors sensor NOUN hjic-488 103 5 available available ADJ hjic-488 103 6 , , PUNCT hjic-488 103 7 the the DET hjic-488 103 8 output output NOUN hjic-488 103 9 is be AUX hjic-488 103 10 y y NOUN hjic-488 103 11 = = PUNCT hjic-488 103 12 ( ( PUNCT hjic-488 103 13 ` ` PUNCT hjic-488 103 14 r r NOUN hjic-488 103 15 ˙̀ ˙̀ PROPN hjic-488 103 16 ṙ ṙ PROPN hjic-488 103 17 ) ) PUNCT hjic-488 103 18 t t PROPN hjic-488 103 19 . . PUNCT hjic-488 104 1 overhead overhead ADJ hjic-488 104 2 cranes crane NOUN hjic-488 104 3 is be AUX hjic-488 104 4 a a DET hjic-488 104 5 typical typical ADJ hjic-488 104 6 example example NOUN hjic-488 104 7 of of ADP hjic-488 104 8 underactuated underactuated ADJ hjic-488 104 9 systems system NOUN hjic-488 104 10 . . PUNCT hjic-488 105 1 it it PRON hjic-488 105 2 is be AUX hjic-488 105 3 actuated actuate VERB hjic-488 105 4 by by ADP hjic-488 105 5 two two NUM hjic-488 105 6 motors motor NOUN hjic-488 105 7 , , PUNCT hjic-488 105 8 one one NUM hjic-488 105 9 applying apply VERB hjic-488 105 10 the the DET hjic-488 105 11 force force NOUN hjic-488 105 12 uf uf PROPN hjic-488 105 13 on on ADP hjic-488 105 14 the the DET hjic-488 105 15 cart cart NOUN hjic-488 105 16 , , PUNCT hjic-488 105 17 and and CCONJ hjic-488 105 18 another another PRON hjic-488 105 19 delivering deliver VERB hjic-488 105 20 the the DET hjic-488 105 21 estimated estimate VERB hjic-488 105 22 system system NOUN hjic-488 105 23 s s PART hjic-488 105 24 λ λ NOUN hjic-488 105 25 + + PROPN hjic-488 105 26 + + CCONJ hjic-488 105 27 u u NOUN hjic-488 105 28 u u NOUN hjic-488 105 29 system system NOUN hjic-488 105 30 model model NOUN hjic-488 105 31 s s PART hjic-488 105 32 = = PUNCT hjic-488 105 33 η(x η(x PROPN hjic-488 105 34 , , PUNCT hjic-488 105 35 ẋ ẋ PROPN hjic-488 105 36 , , PUNCT hjic-488 105 37 u u NOUN hjic-488 105 38 ) ) PUNCT hjic-488 105 39 ẋ ẋ PUNCT hjic-488 106 1 = = SYM hjic-488 106 2 f(x f(x PROPN hjic-488 106 3 , , PUNCT hjic-488 106 4 ũ ũ PROPN hjic-488 106 5 ) ) PUNCT hjic-488 106 6 y y PROPN hjic-488 106 7 = = SYM hjic-488 106 8 g(x g(x PROPN hjic-488 106 9 ) ) PUNCT hjic-488 107 1 ũ ũ PROPN hjic-488 107 2 y∫ẋ y∫ẋ NOUN hjic-488 107 3 x x PUNCT hjic-488 107 4 figure figure NOUN hjic-488 107 5 2 2 NUM hjic-488 107 6 : : PUNCT hjic-488 107 7 dynamics dynamic NOUN hjic-488 107 8 of of ADP hjic-488 107 9 the the DET hjic-488 107 10 estimated estimate VERB hjic-488 107 11 system system NOUN hjic-488 107 12 torque torque NOUN hjic-488 107 13 uc uc INTJ hjic-488 107 14 to to ADP hjic-488 107 15 the the DET hjic-488 107 16 winch winch NOUN hjic-488 107 17 . . PUNCT hjic-488 108 1 the the DET hjic-488 108 2 system system NOUN hjic-488 108 3 input input NOUN hjic-488 108 4 consists consist VERB hjic-488 108 5 of of ADP hjic-488 108 6 these these PRON hjic-488 108 7 , , PUNCT hjic-488 108 8 u u NOUN hjic-488 108 9 = = PUNCT hjic-488 108 10 ( ( PUNCT hjic-488 108 11 uf uf NOUN hjic-488 108 12 uc uc PROPN hjic-488 108 13 ) ) PUNCT hjic-488 108 14 t t PROPN hjic-488 108 15 . . PUNCT hjic-488 109 1 the the DET hjic-488 109 2 parameters parameter NOUN hjic-488 109 3 of of ADP hjic-488 109 4 the the DET hjic-488 109 5 system system NOUN hjic-488 109 6 are be AUX hjic-488 109 7 the the DET hjic-488 109 8 mass mass NOUN hjic-488 109 9 of of ADP hjic-488 109 10 the the DET hjic-488 109 11 cart cart NOUN hjic-488 109 12 m m VERB hjic-488 109 13 , , PUNCT hjic-488 109 14 the the DET hjic-488 109 15 mass mass NOUN hjic-488 109 16 of of ADP hjic-488 109 17 the the DET hjic-488 109 18 load load NOUN hjic-488 109 19 m m PROPN hjic-488 109 20 , , PUNCT hjic-488 109 21 the the DET hjic-488 109 22 moment moment NOUN hjic-488 109 23 of of ADP hjic-488 109 24 inertia inertia NOUN hjic-488 109 25 of of ADP hjic-488 109 26 the the DET hjic-488 109 27 winch winch NOUN hjic-488 109 28 j j PROPN hjic-488 109 29 and and CCONJ hjic-488 109 30 the the DET hjic-488 109 31 radius radius NOUN hjic-488 109 32 of of ADP hjic-488 109 33 the the DET hjic-488 109 34 winch winch NOUN hjic-488 109 35 ρ ρ NOUN hjic-488 109 36 . . PUNCT hjic-488 110 1 the the DET hjic-488 110 2 acceleration acceleration NOUN hjic-488 110 3 in in ADP hjic-488 110 4 the the DET hjic-488 110 5 gravitational gravitational ADJ hjic-488 110 6 field field NOUN hjic-488 110 7 is be AUX hjic-488 110 8 denoted denote VERB hjic-488 110 9 by by ADP hjic-488 110 10 g. g. PROPN hjic-488 110 11 the the DET hjic-488 110 12 following follow VERB hjic-488 110 13 assumptions assumption NOUN hjic-488 110 14 are be AUX hjic-488 110 15 made make VERB hjic-488 110 16 of of ADP hjic-488 110 17 the the DET hjic-488 110 18 system system NOUN hjic-488 110 19 . . PUNCT hjic-488 111 1 • • NUM hjic-488 111 2 the the DET hjic-488 111 3 rope rope NOUN hjic-488 111 4 connecting connect VERB hjic-488 111 5 the the DET hjic-488 111 6 load load NOUN hjic-488 111 7 to to ADP hjic-488 111 8 the the DET hjic-488 111 9 winch winch NOUN hjic-488 111 10 is be AUX hjic-488 111 11 massless massless ADJ hjic-488 111 12 and and CCONJ hjic-488 111 13 behaves behave VERB hjic-488 111 14 as as ADP hjic-488 111 15 a a DET hjic-488 111 16 rigid rigid ADJ hjic-488 111 17 rod rod NOUN hjic-488 111 18 during during ADP hjic-488 111 19 the the DET hjic-488 111 20 motion motion NOUN hjic-488 111 21 . . PUNCT hjic-488 112 1 • • NOUN hjic-488 112 2 the the DET hjic-488 112 3 load load NOUN hjic-488 112 4 is be AUX hjic-488 112 5 a a DET hjic-488 112 6 point point NOUN hjic-488 112 7 mass mass NOUN hjic-488 112 8 . . PUNCT hjic-488 113 1 • • NUM hjic-488 113 2 m m PROPN hjic-488 113 3 , , PUNCT hjic-488 113 4 m m PROPN hjic-488 113 5 , , PUNCT hjic-488 113 6 j j PROPN hjic-488 113 7 and and CCONJ hjic-488 113 8 ρ ρ PROPN hjic-488 113 9 are be AUX hjic-488 113 10 known know VERB hjic-488 113 11 . . PUNCT hjic-488 114 1 • • NUM hjic-488 114 2 in in ADP hjic-488 114 3 the the DET hjic-488 114 4 initial initial ADJ hjic-488 114 5 state state NOUN hjic-488 114 6 of of ADP hjic-488 114 7 the the DET hjic-488 114 8 system system NOUN hjic-488 114 9 the the DET hjic-488 114 10 unmeasured unmeasured ADJ hjic-488 114 11 states state NOUN hjic-488 114 12 are be AUX hjic-488 114 13 zero zero NUM hjic-488 114 14 : : PUNCT hjic-488 115 1 θ θ X hjic-488 115 2 = = SYM hjic-488 115 3 0 0 NUM hjic-488 115 4 rad rad NOUN hjic-488 115 5 and and CCONJ hjic-488 115 6 θ̇ θ̇ NOUN hjic-488 115 7 = = SYM hjic-488 115 8 0 0 NUM hjic-488 115 9 rad rad PROPN hjic-488 115 10 / / SYM hjic-488 115 11 s. s. PROPN hjic-488 115 12 • • NUM hjic-488 115 13 the the DET hjic-488 115 14 effect effect NOUN hjic-488 115 15 of of ADP hjic-488 115 16 the the DET hjic-488 115 17 aerodynamic aerodynamic ADJ hjic-488 115 18 resistance resistance NOUN hjic-488 115 19 is be AUX hjic-488 115 20 negligible negligible ADJ hjic-488 115 21 . . PUNCT hjic-488 116 1 the the DET hjic-488 116 2 lagrangian lagrangian NOUN hjic-488 116 3 of of ADP hjic-488 116 4 overhead overhead ADJ hjic-488 116 5 cranes crane NOUN hjic-488 116 6 reads read VERB hjic-488 116 7 l l NOUN hjic-488 116 8 = = SYM hjic-488 116 9 1 1 NUM hjic-488 116 10 2 2 NUM hjic-488 116 11 ( ( PUNCT hjic-488 116 12 m m VERB hjic-488 116 13 + + NOUN hjic-488 116 14 m m X hjic-488 116 15 ) ) PUNCT hjic-488 116 16 ˙̀2 ˙̀2 NOUN hjic-488 117 1 + + CCONJ hjic-488 117 2 1 1 NUM hjic-488 117 3 2 2 NUM hjic-488 117 4 j j NOUN hjic-488 117 5 ρ2 ρ2 PROPN hjic-488 117 6 ṙ2 ṙ2 PROPN hjic-488 117 7 + + CCONJ hjic-488 117 8 + + NUM hjic-488 117 9 1 1 NUM hjic-488 117 10 2 2 NUM hjic-488 117 11 m m NOUN hjic-488 117 12 ( ( PUNCT hjic-488 117 13 ṙ2 ṙ2 PROPN hjic-488 117 14 + + NUM hjic-488 117 15 r2θ̇2 r2θ̇2 PROPN hjic-488 117 16 ) ) PUNCT hjic-488 118 1 + + PUNCT hjic-488 118 2 ml̇ṙ ml̇ṙ ADJ hjic-488 118 3 sin sin NOUN hjic-488 118 4 θ θ NOUN hjic-488 118 5 + + NOUN hjic-488 118 6 ml̇rθ̇ ml̇rθ̇ NOUN hjic-488 118 7 cos cos ADP hjic-488 118 8 θ θ PROPN hjic-488 118 9 + + PUNCT hjic-488 118 10 mgr mgr PROPN hjic-488 118 11 cos cos PROPN hjic-488 118 12 θ θ PROPN hjic-488 118 13 . . PUNCT hjic-488 118 14 ( ( PUNCT hjic-488 118 15 19 19 NUM hjic-488 118 16 ) ) PUNCT hjic-488 118 17 using use VERB hjic-488 118 18 eq.(1 eq.(1 ADJ hjic-488 118 19 ) ) PUNCT hjic-488 118 20 , , PUNCT hjic-488 118 21 the the DET hjic-488 118 22 model model NOUN hjic-488 118 23 can can AUX hjic-488 118 24 be be AUX hjic-488 118 25 written write VERB hjic-488 118 26 in in ADP hjic-488 118 27 the the DET hjic-488 118 28 form form NOUN hjic-488 118 29 of of ADP hjic-488 118 30 eq.(2 eq.(2 NOUN hjic-488 118 31 ) ) PUNCT hjic-488 118 32 , , PUNCT hjic-488 118 33 where where SCONJ hjic-488 118 34 the the DET hjic-488 118 35 expressions expression NOUN hjic-488 118 36 become become VERB hjic-488 118 37 h(q h(q ADV hjic-488 118 38 ) ) PUNCT hjic-488 119 1 = = PRON hjic-488 119 2   NOUN hjic-488 119 3 ( ( PUNCT hjic-488 119 4 m m VERB hjic-488 119 5 + + NOUN hjic-488 119 6 m m PROPN hjic-488 119 7 sin2 sin2 NOUN hjic-488 119 8 θ θ PROPN hjic-488 119 9 ) ) PUNCT hjic-488 119 10 m m VERB hjic-488 119 11 sin sin NOUN hjic-488 119 12 θ θ PROPN hjic-488 119 13 0 0 NUM hjic-488 119 14 m m VERB hjic-488 119 15 sin sin NOUN hjic-488 119 16 θ θ PROPN hjic-488 119 17 ( ( PUNCT hjic-488 119 18 j j PROPN hjic-488 119 19 ρ2 ρ2 PROPN hjic-488 119 20 + + NOUN hjic-488 119 21 m m PROPN hjic-488 119 22 ) ) PUNCT hjic-488 119 23 0 0 PUNCT hjic-488 120 1 cos cos PROPN hjic-488 120 2 θ θ PROPN hjic-488 120 3 0 0 NUM hjic-488 120 4 r r NOUN hjic-488 120 5   PROPN hjic-488 120 6 , , PUNCT hjic-488 120 7 ( ( PUNCT hjic-488 120 8 20 20 NUM hjic-488 120 9 ) ) PUNCT hjic-488 120 10 h(q h(q ADV hjic-488 120 11 , , PUNCT hjic-488 120 12 q̇ q̇ ADV hjic-488 120 13 ) ) PUNCT hjic-488 120 14 = = PUNCT hjic-488 121 1 − − PROPN hjic-488 121 2 m(rθ̇2 m(rθ̇2 PROPN hjic-488 122 1 + + CCONJ hjic-488 122 2 g g PROPN hjic-488 122 3 cos cos PROPN hjic-488 122 4 θ θ PROPN hjic-488 122 5 ) ) PUNCT hjic-488 122 6 sin sin NOUN hjic-488 122 7 θ θ PROPN hjic-488 122 8 mrθ̇2 mrθ̇2 PROPN hjic-488 123 1 + + NOUN hjic-488 123 2 mg mg PROPN hjic-488 123 3 cos cos PROPN hjic-488 123 4 θ θ PROPN hjic-488 123 5 −2ṙθ̇ −2ṙθ̇ NUM hjic-488 123 6 − − PROPN hjic-488 123 7 g g NOUN hjic-488 123 8 sin sin NOUN hjic-488 123 9 θ θ PROPN hjic-488 123 10   PROPN hjic-488 123 11 , , PUNCT hjic-488 124 1 ( ( PUNCT hjic-488 124 2 21 21 NUM hjic-488 124 3 ) ) PUNCT hjic-488 124 4 hs(s hs( NOUN hjic-488 124 5 ) ) PUNCT hjic-488 124 6 = = SYM hjic-488 125 1 − − PROPN hjic-488 125 2 sfsc sfsc NUM hjic-488 125 3 0 0 NUM hjic-488 126 1   PROPN hjic-488 126 2 , , PUNCT hjic-488 126 3 τ τ X hjic-488 126 4 = = SYM hjic-488 126 5   PROPN hjic-488 126 6 uf uf PROPN hjic-488 126 7 −uc −uc NOUN hjic-488 126 8 ρ ρ PROPN hjic-488 126 9 0 0 NUM hjic-488 127 1   PROPN hjic-488 127 2 , , PUNCT hjic-488 127 3 ( ( PUNCT hjic-488 127 4 22 22 NUM hjic-488 127 5 ) ) PUNCT hjic-488 127 6 where where SCONJ hjic-488 127 7 sf sf PROPN hjic-488 127 8 is be AUX hjic-488 127 9 the the DET hjic-488 127 10 frictional frictional ADJ hjic-488 127 11 force force NOUN hjic-488 127 12 between between ADP hjic-488 127 13 the the DET hjic-488 127 14 cart cart NOUN hjic-488 127 15 and and CCONJ hjic-488 127 16 the the DET hjic-488 127 17 rail rail NOUN hjic-488 127 18 and and CCONJ hjic-488 127 19 sc sc PROPN hjic-488 127 20 is be AUX hjic-488 127 21 the the DET hjic-488 127 22 frictional frictional ADJ hjic-488 127 23 force force NOUN hjic-488 127 24 applied apply VERB hjic-488 127 25 to to ADP hjic-488 127 26 the the DET hjic-488 127 27 winch winch NOUN hjic-488 127 28 . . PUNCT hjic-488 128 1 the the DET hjic-488 128 2 continuous continuous ADJ hjic-488 128 3 - - PUNCT hjic-488 128 4 time time NOUN hjic-488 128 5 linear linear PROPN hjic-488 128 6 model model NOUN hjic-488 128 7 of of ADP hjic-488 128 8 the the DET hjic-488 128 9 crane crane NOUN hjic-488 128 10 is be AUX hjic-488 128 11 computed compute VERB hjic-488 128 12 around around ADP hjic-488 128 13 the the DET hjic-488 128 14 setpoint setpoint NOUN hjic-488 128 15 x0 x0 NOUN hjic-488 128 16 = = PUNCT hjic-488 128 17 ( ( PUNCT hjic-488 128 18 0 0 NUM hjic-488 128 19 r0 r0 NOUN hjic-488 128 20 0 0 NUM hjic-488 128 21 0 0 NUM hjic-488 128 22 0 0 NUM hjic-488 128 23 0 0 NUM hjic-488 128 24 ) ) PUNCT hjic-488 128 25 t t NOUN hjic-488 128 26 , , PUNCT hjic-488 128 27 u0 u0 ADJ hjic-488 128 28 = = PUNCT hjic-488 128 29 ( ( PUNCT hjic-488 128 30 0 0 NUM hjic-488 128 31 mgρ mgρ NOUN hjic-488 128 32 ) ) PUNCT hjic-488 128 33 t t PROPN hjic-488 128 34 , , PUNCT hjic-488 128 35 and and CCONJ hjic-488 128 36 sf sf NOUN hjic-488 128 37 = = SYM hjic-488 128 38 sc sc PROPN hjic-488 128 39 = = NOUN hjic-488 128 40 0 0 NUM hjic-488 128 41 is be AUX hjic-488 128 42 substituted substitute VERB hjic-488 128 43 74 74 NUM hjic-488 128 44 table table NOUN hjic-488 128 45 1 1 NUM hjic-488 128 46 : : PUNCT hjic-488 128 47 numeric numeric ADJ hjic-488 128 48 values value NOUN hjic-488 128 49 of of ADP hjic-488 128 50 the the DET hjic-488 128 51 parameters parameter NOUN hjic-488 128 52 value value NOUN hjic-488 128 53 unit unit NOUN hjic-488 128 54 m m VERB hjic-488 128 55 5 5 NUM hjic-488 128 56 kg kg NOUN hjic-488 128 57 m m VERB hjic-488 128 58 0.05 0.05 NUM hjic-488 128 59 kg kg NOUN hjic-488 128 60 j j PROPN hjic-488 128 61 3.802 3.802 NUM hjic-488 128 62 · · SYM hjic-488 128 63 10−4 10−4 NUM hjic-488 128 64 kg kg NOUN hjic-488 128 65 m2 m2 PROPN hjic-488 128 66 ρ ρ PROPN hjic-488 128 67 0.02 0.02 NUM hjic-488 128 68 m m NOUN hjic-488 128 69 g g PROPN hjic-488 128 70 9.81 9.81 NUM hjic-488 128 71 m m NOUN hjic-488 129 1 s−2 s−2 NOUN hjic-488 129 2 ts ts ADP hjic-488 129 3 1 1 NUM hjic-488 129 4 ms ms NOUN hjic-488 129 5 r0 r0 NOUN hjic-488 129 6 0.47 0.47 NUM hjic-488 129 7 m m NOUN hjic-488 129 8 ` ` PUNCT hjic-488 129 9 d d PROPN hjic-488 129 10 0.5 0.5 NUM hjic-488 129 11 m m NOUN hjic-488 129 12 into into ADP hjic-488 129 13 eq.(5 eq.(5 NOUN hjic-488 129 14 ) ) PUNCT hjic-488 129 15 . . PUNCT hjic-488 130 1 the the DET hjic-488 130 2 resulting result VERB hjic-488 130 3 jacobians jacobian NOUN hjic-488 130 4 are be AUX hjic-488 130 5 a a DET hjic-488 130 6 = = ADJ hjic-488 130 7   NOUN hjic-488 130 8 0 0 NUM hjic-488 130 9 0 0 SYM hjic-488 130 10 0 0 NUM hjic-488 130 11 1 1 NUM hjic-488 130 12 0 0 NUM hjic-488 130 13 0 0 NUM hjic-488 130 14 0 0 NUM hjic-488 130 15 0 0 NUM hjic-488 130 16 0 0 NUM hjic-488 130 17 0 0 NUM hjic-488 130 18 1 1 NUM hjic-488 130 19 0 0 NUM hjic-488 130 20 0 0 NUM hjic-488 130 21 0 0 NUM hjic-488 130 22 0 0 NUM hjic-488 130 23 0 0 NUM hjic-488 130 24 0 0 NUM hjic-488 130 25 1 1 NUM hjic-488 130 26 0 0 NUM hjic-488 130 27 0 0 NUM hjic-488 130 28 m m NOUN hjic-488 130 29 m m VERB hjic-488 130 30 g g ADJ hjic-488 130 31 0 0 NUM hjic-488 130 32 0 0 NUM hjic-488 130 33 0 0 NUM hjic-488 130 34 0 0 NUM hjic-488 130 35 0 0 NUM hjic-488 130 36 0 0 NUM hjic-488 130 37 0 0 NUM hjic-488 130 38 0 0 NUM hjic-488 130 39 0 0 NUM hjic-488 130 40 0 0 NUM hjic-488 130 41 0 0 NUM hjic-488 131 1 −m+m −m+m NOUN hjic-488 131 2 mr0 mr0 VERB hjic-488 131 3 g g PROPN hjic-488 131 4 0 0 NUM hjic-488 131 5 0 0 NUM hjic-488 131 6 0 0 NUM hjic-488 131 7   PROPN hjic-488 131 8 , , PUNCT hjic-488 131 9 b b X hjic-488 131 10 = = SYM hjic-488 131 11   NOUN hjic-488 131 12 0 0 NUM hjic-488 131 13 0 0 NUM hjic-488 131 14 0 0 NUM hjic-488 131 15 0 0 NUM hjic-488 131 16 0 0 NUM hjic-488 131 17 0 0 NUM hjic-488 131 18 1 1 NUM hjic-488 131 19 m m NOUN hjic-488 131 20 0 0 NUM hjic-488 131 21 0 0 NUM hjic-488 131 22 − − PROPN hjic-488 131 23 ρ ρ PROPN hjic-488 131 24 mρ2+j mρ2+j NOUN hjic-488 131 25 − − NOUN hjic-488 131 26 1 1 NUM hjic-488 131 27 mr0 mr0 NOUN hjic-488 131 28 0 0 NUM hjic-488 131 29   NOUN hjic-488 131 30 , , PUNCT hjic-488 131 31 c c X hjic-488 131 32 = = SYM hjic-488 131 33   ADJ hjic-488 131 34 1 1 NUM hjic-488 131 35 0 0 NUM hjic-488 131 36 0 0 NUM hjic-488 131 37 0 0 NUM hjic-488 131 38 0 0 NUM hjic-488 131 39 0 0 NUM hjic-488 131 40 0 0 NUM hjic-488 131 41 1 1 NUM hjic-488 131 42 0 0 NUM hjic-488 131 43 0 0 NUM hjic-488 131 44 0 0 NUM hjic-488 131 45 0 0 NUM hjic-488 131 46 0 0 NUM hjic-488 131 47 0 0 NUM hjic-488 131 48 0 0 NUM hjic-488 131 49 1 1 NUM hjic-488 131 50 0 0 NUM hjic-488 131 51 0 0 NUM hjic-488 131 52 0 0 NUM hjic-488 131 53 0 0 NUM hjic-488 131 54 0 0 NUM hjic-488 131 55 0 0 NUM hjic-488 131 56 1 1 NUM hjic-488 131 57 0 0 NUM hjic-488 131 58   NOUN hjic-488 131 59 . . PUNCT hjic-488 132 1 ( ( PUNCT hjic-488 132 2 23 23 NUM hjic-488 132 3 ) ) PUNCT hjic-488 132 4 substituting substitute VERB hjic-488 132 5 eq.(22 eq.(22 NOUN hjic-488 132 6 ) ) PUNCT hjic-488 132 7 , , PUNCT hjic-488 132 8 the the DET hjic-488 132 9 disturbance disturbance NOUN hjic-488 132 10 torque torque NOUN hjic-488 132 11 term term NOUN hjic-488 132 12 in in ADP hjic-488 132 13 eq.(3 eq.(3 NOUN hjic-488 132 14 ) ) PUNCT hjic-488 132 15 reads read VERB hjic-488 132 16 τ̃ τ̃ PROPN hjic-488 133 1 = = SYM hjic-488 133 2   PROPN hjic-488 133 3 uf uf PROPN hjic-488 133 4 + + PROPN hjic-488 133 5 sf sf PROPN hjic-488 133 6 − − PROPN hjic-488 133 7 1 1 NUM hjic-488 133 8 ρ ρ NOUN hjic-488 133 9 ( ( PUNCT hjic-488 133 10 uc uc PROPN hjic-488 133 11 − − NUM hjic-488 133 12 ρsc ρsc ADJ hjic-488 133 13 ) ) PUNCT hjic-488 133 14 0 0 NUM hjic-488 134 1   PROPN hjic-488 134 2 . . PUNCT hjic-488 135 1 ( ( PUNCT hjic-488 135 2 24 24 NUM hjic-488 135 3 ) ) PUNCT hjic-488 135 4 eq.(24 eq.(24 PROPN hjic-488 135 5 ) ) PUNCT hjic-488 135 6 shows show NOUN hjic-488 135 7 , , PUNCT hjic-488 135 8 that that SCONJ hjic-488 135 9 the the DET hjic-488 135 10 disturbed disturbed ADJ hjic-488 135 11 input input NOUN hjic-488 135 12 of of ADP hjic-488 135 13 the the DET hjic-488 135 14 system system NOUN hjic-488 135 15 can can AUX hjic-488 135 16 be be AUX hjic-488 135 17 introduced introduce VERB hjic-488 135 18 in in ADP hjic-488 135 19 the the DET hjic-488 135 20 form form NOUN hjic-488 136 1 ũ ũ PROPN hjic-488 136 2 = = X hjic-488 136 3 u+ u+ NOUN hjic-488 136 4 λs λs PROPN hjic-488 136 5 , , PUNCT hjic-488 136 6 where where SCONJ hjic-488 136 7 λ λ X hjic-488 136 8 = = PRON hjic-488 136 9 ( ( PUNCT hjic-488 136 10 1 1 NUM hjic-488 136 11 0 0 NUM hjic-488 136 12 0 0 NUM hjic-488 136 13 −ρ −ρ NOUN hjic-488 136 14 ) ) PUNCT hjic-488 136 15 . . PUNCT hjic-488 137 1 ( ( PUNCT hjic-488 137 2 25 25 NUM hjic-488 137 3 ) ) PUNCT hjic-488 137 4 the the DET hjic-488 137 5 frictional frictional ADJ hjic-488 137 6 forces force NOUN hjic-488 137 7 usually usually ADV hjic-488 137 8 depend depend VERB hjic-488 137 9 on on ADP hjic-488 137 10 the the DET hjic-488 137 11 actuating actuate VERB hjic-488 137 12 signals signal NOUN hjic-488 137 13 , , PUNCT hjic-488 137 14 state state NOUN hjic-488 137 15 variables variable NOUN hjic-488 137 16 , , PUNCT hjic-488 137 17 and and CCONJ hjic-488 137 18 the the DET hjic-488 137 19 derivative derivative NOUN hjic-488 137 20 of of ADP hjic-488 137 21 the the DET hjic-488 137 22 state state NOUN hjic-488 137 23 as as ADV hjic-488 137 24 well well ADV hjic-488 137 25 . . PUNCT hjic-488 138 1 the the DET hjic-488 138 2 general general ADJ hjic-488 138 3 characteristics characteristic NOUN hjic-488 138 4 of of ADP hjic-488 138 5 the the DET hjic-488 138 6 friction friction NOUN hjic-488 138 7 reads read VERB hjic-488 138 8 as as ADP hjic-488 138 9 s s NOUN hjic-488 138 10 = = PUNCT hjic-488 138 11 η(x η(x PROPN hjic-488 138 12 , , PUNCT hjic-488 138 13 ẋ ẋ PROPN hjic-488 138 14 , , PUNCT hjic-488 138 15 u u NOUN hjic-488 138 16 ) ) PUNCT hjic-488 138 17 . . PUNCT hjic-488 139 1 the the DET hjic-488 139 2 block block NOUN hjic-488 139 3 diagram diagram NOUN hjic-488 139 4 of of ADP hjic-488 139 5 the the DET hjic-488 139 6 dynamics dynamic NOUN hjic-488 139 7 of of ADP hjic-488 139 8 the the DET hjic-488 139 9 system system NOUN hjic-488 139 10 is be AUX hjic-488 139 11 illustrated illustrate VERB hjic-488 139 12 in in ADP hjic-488 139 13 fig.2 fig.2 PROPN hjic-488 139 14 . . PUNCT hjic-488 140 1 only only ADV hjic-488 140 2 the the DET hjic-488 140 3 system system NOUN hjic-488 140 4 model model NOUN hjic-488 140 5 block block NOUN hjic-488 140 6 is be AUX hjic-488 140 7 used use VERB hjic-488 140 8 for for ADP hjic-488 140 9 estimator estimator NOUN hjic-488 140 10 design design NOUN hjic-488 140 11 , , PUNCT hjic-488 140 12 which which PRON hjic-488 140 13 is be AUX hjic-488 140 14 eq.(5 eq.(5 NOUN hjic-488 140 15 ) ) PUNCT hjic-488 140 16 if if SCONJ hjic-488 140 17 the the DET hjic-488 140 18 effect effect NOUN hjic-488 140 19 of of ADP hjic-488 140 20 the the DET hjic-488 140 21 friction friction NOUN hjic-488 140 22 is be AUX hjic-488 140 23 disregarded disregarded ADJ hjic-488 140 24 , , PUNCT hjic-488 140 25 hs(s hs( NOUN hjic-488 140 26 ) ) PUNCT hjic-488 141 1 = = SYM hjic-488 141 2 0 0 X hjic-488 141 3 . . PUNCT hjic-488 141 4 proposition proposition NOUN hjic-488 141 5 1 1 NUM hjic-488 141 6 . . PUNCT hjic-488 142 1 the the DET hjic-488 142 2 discrete discrete ADJ hjic-488 142 3 - - PUNCT hjic-488 142 4 time time NOUN hjic-488 142 5 linear linear PROPN hjic-488 142 6 crane crane NOUN hjic-488 142 7 model model NOUN hjic-488 142 8 obtained obtain VERB hjic-488 142 9 from from ADP hjic-488 142 10 the the DET hjic-488 142 11 matrices matrix NOUN hjic-488 142 12 in in ADP hjic-488 142 13 eq.(23 eq.(23 NOUN hjic-488 142 14 ) ) PUNCT hjic-488 142 15 and and CCONJ hjic-488 142 16 using use VERB hjic-488 142 17 eq.(8 eq.(8 ADV hjic-488 142 18 ) ) PUNCT hjic-488 142 19 satisfies satisfy VERB hjic-488 142 20 the the DET hjic-488 142 21 design design NOUN hjic-488 142 22 conditions condition NOUN hjic-488 142 23 of of ADP hjic-488 142 24 the the DET hjic-488 142 25 uikf uikf NOUN hjic-488 142 26 in in ADP hjic-488 142 27 eq.(9 eq.(9 ADV hjic-488 142 28 - - PUNCT hjic-488 142 29 12 12 NUM hjic-488 142 30 ) ) PUNCT hjic-488 142 31 . . PUNCT hjic-488 143 1 proof proof NOUN hjic-488 143 2 . . PUNCT hjic-488 144 1 it it PRON hjic-488 144 2 is be AUX hjic-488 144 3 clear clear ADJ hjic-488 144 4 that that SCONJ hjic-488 144 5 dim{y dim{y NOUN hjic-488 144 6 } } PUNCT hjic-488 144 7 = = SYM hjic-488 144 8 4 4 NUM hjic-488 144 9 , , PUNCT hjic-488 144 10 dim{d dim{d PROPN hjic-488 144 11 } } PUNCT hjic-488 144 12 = = SYM hjic-488 144 13 2 2 NUM hjic-488 144 14 and and CCONJ hjic-488 144 15 rank{c rank{c NOUN hjic-488 144 16 } } PUNCT hjic-488 144 17 = = SYM hjic-488 144 18 4 4 NUM hjic-488 144 19 , , PUNCT hjic-488 144 20 thus thus ADV hjic-488 144 21 eq.(9 eq.(9 ADJ hjic-488 144 22 ) ) PUNCT hjic-488 144 23 and and CCONJ hjic-488 144 24 ( ( PUNCT hjic-488 144 25 10 10 NUM hjic-488 144 26 ) ) PUNCT hjic-488 144 27 are be AUX hjic-488 144 28 satisfied satisfied ADJ hjic-488 144 29 . . PUNCT hjic-488 145 1 using use VERB hjic-488 145 2 eq.(8 eq.(8 ADV hjic-488 145 3 ) ) PUNCT hjic-488 146 1 and and CCONJ hjic-488 146 2 the the DET hjic-488 146 3 numerical numerical ADJ hjic-488 146 4 values value NOUN hjic-488 146 5 in in ADP hjic-488 146 6 table table NOUN hjic-488 146 7 1 1 NUM hjic-488 146 8 , , PUNCT hjic-488 146 9 γd γd ADP hjic-488 146 10 = = SYM hjic-488 146 11 10−2 10−2 NUM hjic-488 146 12   VERB hjic-488 146 13 0.0001 0.0001 NUM hjic-488 146 14 0 0 NUM hjic-488 146 15 0 0 NUM hjic-488 146 16 −0.025 −0.025 NOUN hjic-488 146 17 −0.0002 −0.0002 NUM hjic-488 146 18 0 0 NUM hjic-488 146 19 0.2 0.2 NUM hjic-488 146 20 0 0 NUM hjic-488 146 21 0 0 NUM hjic-488 146 22 −49.975 −49.975 NOUN hjic-488 146 23 −0.4255 −0.4255 PROPN hjic-488 146 24 0 0 NUM hjic-488 146 25   NOUN hjic-488 146 26 , , PUNCT hjic-488 146 27 cγd cγd NOUN hjic-488 146 28 = = SYM hjic-488 146 29 10−2 10−2 NUM hjic-488 146 30   NOUN hjic-488 146 31 0.0001 0.0001 NUM hjic-488 146 32 0 0 NUM hjic-488 146 33 0 0 NUM hjic-488 147 1 −0.025 −0.025 NOUN hjic-488 147 2 0.2 0.2 NUM hjic-488 147 3 0 0 NUM hjic-488 147 4 0 0 NUM hjic-488 147 5 −49.975 −49.975 NOUN hjic-488 147 6   NOUN hjic-488 147 7 . . PUNCT hjic-488 148 1 ( ( PUNCT hjic-488 148 2 26 26 NUM hjic-488 148 3 ) ) PUNCT hjic-488 148 4 we we PRON hjic-488 148 5 obtain obtain VERB hjic-488 148 6 rank{γd rank{γd ADV hjic-488 148 7 } } PUNCT hjic-488 148 8 = = SYM hjic-488 148 9 2 2 NUM hjic-488 148 10 and and CCONJ hjic-488 148 11 rank{cγd rank{cγd PROPN hjic-488 148 12 } } PUNCT hjic-488 148 13 = = SYM hjic-488 148 14 2 2 NUM hjic-488 148 15 , , PUNCT hjic-488 148 16 which which PRON hjic-488 148 17 are be AUX hjic-488 148 18 both both CCONJ hjic-488 148 19 equal equal ADJ hjic-488 148 20 to to ADP hjic-488 148 21 the the DET hjic-488 148 22 number number NOUN hjic-488 148 23 of of ADP hjic-488 148 24 unknown unknown ADJ hjic-488 148 25 inputs input NOUN hjic-488 148 26 . . PUNCT hjic-488 149 1 this this PRON hjic-488 149 2 satisfies satisfy VERB hjic-488 149 3 eqs.(11 eqs.(11 PROPN hjic-488 149 4 ) ) PUNCT hjic-488 149 5 and and CCONJ hjic-488 149 6 ( ( PUNCT hjic-488 149 7 12 12 NUM hjic-488 149 8 ) ) PUNCT hjic-488 149 9 . . PUNCT hjic-488 150 1 the the DET hjic-488 150 2 continuity continuity NOUN hjic-488 150 3 argument argument NOUN hjic-488 150 4 holds hold VERB hjic-488 150 5 for for ADP hjic-488 150 6 the the DET hjic-488 150 7 rank rank NOUN hjic-488 150 8 of of ADP hjic-488 150 9 the the DET hjic-488 150 10 matrices matrix NOUN hjic-488 150 11 in in ADP hjic-488 150 12 eq.(26 eq.(26 ADV hjic-488 150 13 ) ) PUNCT hjic-488 150 14 , , PUNCT hjic-488 150 15 therefore therefore ADV hjic-488 150 16 there there PRON hjic-488 150 17 exists exist VERB hjic-488 150 18 a a DET hjic-488 150 19 neighbourhood neighbourhood NOUN hjic-488 150 20 around around ADP hjic-488 150 21 our our PRON hjic-488 150 22 parameter parameter NOUN hjic-488 150 23 set set VERB hjic-488 150 24 where where SCONJ hjic-488 150 25 the the DET hjic-488 150 26 design design NOUN hjic-488 150 27 conditions condition NOUN hjic-488 150 28 are be AUX hjic-488 150 29 still still ADV hjic-488 150 30 satisfied satisfied ADJ hjic-488 150 31 . . PUNCT hjic-488 151 1 simulation simulation NOUN hjic-488 151 2 the the DET hjic-488 151 3 estimation estimation NOUN hjic-488 151 4 results result NOUN hjic-488 151 5 were be AUX hjic-488 151 6 obtained obtain VERB hjic-488 151 7 by by ADP hjic-488 151 8 simulation simulation NOUN hjic-488 151 9 of of ADP hjic-488 151 10 overhead overhead ADJ hjic-488 151 11 cranes crane NOUN hjic-488 151 12 in in ADP hjic-488 151 13 a a DET hjic-488 151 14 closed closed ADJ hjic-488 151 15 - - PUNCT hjic-488 151 16 loop loop NOUN hjic-488 151 17 scenario scenario NOUN hjic-488 151 18 using use VERB hjic-488 151 19 a a DET hjic-488 151 20 simple simple ADJ hjic-488 151 21 discrete discrete ADJ hjic-488 151 22 - - PUNCT hjic-488 151 23 time time NOUN hjic-488 151 24 pole pole NOUN hjic-488 151 25 - - PUNCT hjic-488 151 26 placement placement NOUN hjic-488 151 27 - - PUNCT hjic-488 151 28 based base VERB hjic-488 151 29 linear linear ADJ hjic-488 151 30 controller controller NOUN hjic-488 151 31 . . PUNCT hjic-488 152 1 the the DET hjic-488 152 2 simulation simulation NOUN hjic-488 152 3 also also ADV hjic-488 152 4 took take VERB hjic-488 152 5 into into ADP hjic-488 152 6 account account NOUN hjic-488 152 7 friction friction NOUN hjic-488 152 8 . . PUNCT hjic-488 153 1 there there PRON hjic-488 153 2 are be VERB hjic-488 153 3 various various ADJ hjic-488 153 4 models model NOUN hjic-488 153 5 of of ADP hjic-488 153 6 the the DET hjic-488 153 7 friction friction NOUN hjic-488 153 8 phenomenon phenomenon NOUN hjic-488 153 9 , , PUNCT hjic-488 153 10 ours ours PRON hjic-488 153 11 included include VERB hjic-488 153 12 coulomb coulomb NOUN hjic-488 153 13 , , PUNCT hjic-488 153 14 stribeck stribeck NOUN hjic-488 153 15 , , PUNCT hjic-488 153 16 viscous viscous ADJ hjic-488 153 17 friction friction NOUN hjic-488 153 18 , , PUNCT hjic-488 153 19 and and CCONJ hjic-488 153 20 stiction stiction NOUN hjic-488 153 21 [ [ X hjic-488 153 22 11 11 NUM hjic-488 153 23 ] ] PUNCT hjic-488 153 24 . . PUNCT hjic-488 154 1 the the DET hjic-488 154 2 numerical numerical ADJ hjic-488 154 3 values value NOUN hjic-488 154 4 of of ADP hjic-488 154 5 the the DET hjic-488 154 6 parameters parameter NOUN hjic-488 154 7 used use VERB hjic-488 154 8 in in ADP hjic-488 154 9 the the DET hjic-488 154 10 simulation simulation NOUN hjic-488 154 11 are be AUX hjic-488 154 12 given give VERB hjic-488 154 13 in in ADP hjic-488 154 14 table table NOUN hjic-488 154 15 1 1 NUM hjic-488 154 16 . . PUNCT hjic-488 154 17 because because SCONJ hjic-488 154 18 of of ADP hjic-488 154 19 friction friction NOUN hjic-488 154 20 , , PUNCT hjic-488 154 21 but but CCONJ hjic-488 154 22 mainly mainly ADV hjic-488 154 23 stiction stiction NOUN hjic-488 154 24 , , PUNCT hjic-488 154 25 the the DET hjic-488 154 26 position position NOUN hjic-488 154 27 of of ADP hjic-488 154 28 the the DET hjic-488 154 29 crane crane NOUN hjic-488 154 30 can can AUX hjic-488 154 31 not not PART hjic-488 154 32 be be AUX hjic-488 154 33 accurately accurately ADV hjic-488 154 34 controlled control VERB hjic-488 154 35 without without ADP hjic-488 154 36 integrators integrator NOUN hjic-488 154 37 in in ADP hjic-488 154 38 the the DET hjic-488 154 39 controller controller NOUN hjic-488 154 40 . . PUNCT hjic-488 155 1 consequently consequently ADV hjic-488 155 2 we we PRON hjic-488 155 3 included include VERB hjic-488 155 4 the the DET hjic-488 155 5 integral integral NOUN hjic-488 155 6 of of ADP hjic-488 155 7 the the DET hjic-488 155 8 measurable measurable ADJ hjic-488 155 9 positions position NOUN hjic-488 155 10 in in ADP hjic-488 155 11 the the DET hjic-488 155 12 controller controller NOUN hjic-488 155 13 design design NOUN hjic-488 155 14 as as SCONJ hjic-488 155 15 proposed propose VERB hjic-488 155 16 on on ADP hjic-488 155 17 page page NOUN hjic-488 155 18 309 309 NUM hjic-488 155 19 of of ADP hjic-488 155 20 ref ref NOUN hjic-488 155 21 . . PUNCT hjic-488 156 1 [ [ X hjic-488 156 2 8 8 NUM hjic-488 156 3 ] ] PUNCT hjic-488 156 4 . . PUNCT hjic-488 157 1 the the DET hjic-488 157 2 outputs output NOUN hjic-488 157 3 to to PART hjic-488 157 4 be be AUX hjic-488 157 5 integrated integrate VERB hjic-488 157 6 are be AUX hjic-488 157 7 yi yi NOUN hjic-488 157 8 = = PUNCT hjic-488 157 9 ( ( PUNCT hjic-488 157 10 ` ` PUNCT hjic-488 157 11 r r NOUN hjic-488 157 12 ) ) PUNCT hjic-488 157 13 t t NOUN hjic-488 157 14 . . PUNCT hjic-488 158 1 integrals integral NOUN hjic-488 158 2 of of ADP hjic-488 158 3 these these DET hjic-488 158 4 quantities quantity NOUN hjic-488 158 5 are be AUX hjic-488 158 6 approximated approximate VERB hjic-488 158 7 by by ADP hjic-488 158 8 the the DET hjic-488 158 9 left left ADJ hjic-488 158 10 rectangle rectangle NOUN hjic-488 158 11 rule rule NOUN hjic-488 158 12 as as ADP hjic-488 158 13 xi xi ADP hjic-488 158 14 [ [ X hjic-488 158 15 k+ k+ NOUN hjic-488 158 16 1 1 NUM hjic-488 158 17 ] ] PUNCT hjic-488 158 18 = = PUNCT hjic-488 158 19 xi xi X hjic-488 159 1 [ [ X hjic-488 159 2 k k X hjic-488 159 3 ] ] X hjic-488 159 4 + + ADJ hjic-488 159 5 tsyi tsyi NOUN hjic-488 159 6 [ [ X hjic-488 159 7 k k X hjic-488 159 8 ] ] X hjic-488 159 9 = = PUNCT hjic-488 159 10 xi xi X hjic-488 160 1 [ [ X hjic-488 160 2 k k X hjic-488 160 3 ] ] X hjic-488 160 4 + + NOUN hjic-488 160 5 tscix[k tscix[k NOUN hjic-488 160 6 ] ] X hjic-488 160 7 , , PUNCT hjic-488 160 8 ( ( PUNCT hjic-488 160 9 27 27 NUM hjic-488 160 10 ) ) PUNCT hjic-488 160 11 where where SCONJ hjic-488 160 12 ci ci PROPN hjic-488 160 13 is be AUX hjic-488 160 14 defined define VERB hjic-488 160 15 so so SCONJ hjic-488 160 16 that that SCONJ hjic-488 160 17 yi yi PROPN hjic-488 161 1 [ [ X hjic-488 161 2 k k X hjic-488 161 3 ] ] X hjic-488 161 4 = = PUNCT hjic-488 161 5 cix[k cix[k NOUN hjic-488 161 6 ] ] PUNCT hjic-488 161 7 . . PUNCT hjic-488 162 1 in in ADP hjic-488 162 2 our our PRON hjic-488 162 3 case case NOUN hjic-488 162 4 ci ci NOUN hjic-488 162 5 is be AUX hjic-488 162 6 the the DET hjic-488 162 7 first first ADJ hjic-488 162 8 two two NUM hjic-488 162 9 rows row NOUN hjic-488 162 10 of of ADP hjic-488 162 11 c c NOUN hjic-488 162 12 in in ADP hjic-488 162 13 eq.(23 eq.(23 NOUN hjic-488 162 14 ) ) PUNCT hjic-488 162 15 . . PUNCT hjic-488 163 1 using use VERB hjic-488 163 2 eq.(27 eq.(27 PROPN hjic-488 163 3 ) ) PUNCT hjic-488 163 4 and and CCONJ hjic-488 163 5 eq.(7 eq.(7 VERB hjic-488 163 6 ) ) PUNCT hjic-488 163 7 a a DET hjic-488 163 8 new new ADJ hjic-488 163 9 system system NOUN hjic-488 163 10 model model NOUN hjic-488 163 11 is be AUX hjic-488 163 12 introduced introduce VERB hjic-488 163 13 in in ADP hjic-488 163 14 the the DET hjic-488 163 15 form form NOUN hjic-488 163 16 x̃[k x̃[k PUNCT hjic-488 164 1 + + NOUN hjic-488 164 2 1 1 X hjic-488 164 3 ] ] X hjic-488 164 4 = = PUNCT hjic-488 164 5 φ̃x̃[k φ̃x̃[k PROPN hjic-488 164 6 ] ] X hjic-488 164 7 + + CCONJ hjic-488 164 8 γ̃u[k γ̃u[k ADV hjic-488 164 9 ] ] X hjic-488 164 10 y[k y[k ADJ hjic-488 164 11 ] ] X hjic-488 164 12 = = PUNCT hjic-488 164 13 c̃x̃[k c̃x̃[k PROPN hjic-488 164 14 ] ] PUNCT hjic-488 164 15 . . PUNCT hjic-488 165 1 ( ( PUNCT hjic-488 165 2 28 28 NUM hjic-488 165 3 ) ) PUNCT hjic-488 165 4 where where SCONJ hjic-488 165 5 the the DET hjic-488 165 6 expanded expand VERB hjic-488 165 7 state state NOUN hjic-488 165 8 is be AUX hjic-488 165 9 x̃t x̃t ADJ hjic-488 165 10 = = PUNCT hjic-488 165 11 ( ( PUNCT hjic-488 165 12 xt xt PROPN hjic-488 165 13 xti xti PROPN hjic-488 165 14 ) ) PUNCT hjic-488 166 1 and and CCONJ hjic-488 166 2 the the DET hjic-488 166 3 matrices matrix NOUN hjic-488 166 4 are be AUX hjic-488 166 5 φ̃ φ̃ PROPN hjic-488 166 6 = = SYM hjic-488 166 7 ( ( PUNCT hjic-488 166 8 φ φ PROPN hjic-488 166 9 0 0 X hjic-488 166 10 tsci tsci PROPN hjic-488 166 11 i i PROPN hjic-488 166 12 ) ) PUNCT hjic-488 166 13 , , PUNCT hjic-488 166 14 γ̃ γ̃ PROPN hjic-488 166 15 = = PUNCT hjic-488 166 16 ( ( PUNCT hjic-488 166 17 γd γd ADV hjic-488 166 18 0 0 NUM hjic-488 166 19 ) ) PUNCT hjic-488 166 20 , , PUNCT hjic-488 166 21 and and CCONJ hjic-488 166 22 c̃ c̃ PROPN hjic-488 167 1 = = PRON hjic-488 167 2 ( ( PUNCT hjic-488 167 3 c c NOUN hjic-488 167 4 0 0 NUM hjic-488 167 5 ) ) PUNCT hjic-488 167 6 . . PUNCT hjic-488 168 1 ( ( PUNCT hjic-488 168 2 29 29 NUM hjic-488 168 3 ) ) PUNCT hjic-488 168 4 for for ADP hjic-488 168 5 the the DET hjic-488 168 6 controller controller NOUN hjic-488 168 7 design design VERB hjic-488 168 8 the the DET hjic-488 168 9 process process NOUN hjic-488 168 10 and and CCONJ hjic-488 168 11 measurement measurement NOUN hjic-488 168 12 noises noise NOUN hjic-488 168 13 are be AUX hjic-488 168 14 omitted omit VERB hjic-488 168 15 . . PUNCT hjic-488 169 1 75 75 NUM hjic-488 169 2 ∫ ∫ PROPN hjic-488 169 3 dac dac NOUN hjic-488 169 4 system system NOUN hjic-488 169 5 in in ADP hjic-488 169 6 fig fig NOUN hjic-488 169 7 . . PUNCT hjic-488 170 1 2 2 NUM hjic-488 170 2 adc adc PROPN hjic-488 170 3 ukf ukf PROPN hjic-488 170 4 k k PROPN hjic-488 170 5 ki ki PROPN hjic-488 170 6 u[k u[k PROPN hjic-488 170 7 ] ] X hjic-488 171 1 y y PROPN hjic-488 171 2 y[k]u y[k]u PROPN hjic-488 171 3 u0 u0 PROPN hjic-488 171 4 + + PROPN hjic-488 172 1 + + ADJ hjic-488 172 2 + + X hjic-488 172 3 yid yid ADJ hjic-488 172 4 + + NOUN hjic-488 172 5 xd xd NUM hjic-488 172 6 adc adc PROPN hjic-488 172 7 x[k x[k NOUN hjic-488 172 8 ] ] X hjic-488 172 9 x x SYM hjic-488 172 10 yi yi PROPN hjic-488 173 1 [ [ X hjic-488 173 2 k k X hjic-488 173 3 ] ] X hjic-488 173 4 = = X hjic-488 173 5 ( ( PUNCT hjic-488 173 6 ` ` PUNCT hjic-488 173 7 [ [ X hjic-488 173 8 k k X hjic-488 173 9 ] ] X hjic-488 173 10 r[k r[k PROPN hjic-488 173 11 ] ] PUNCT hjic-488 173 12 ) ) PUNCT hjic-488 173 13 t t PROPN hjic-488 173 14 y[k y[k PROPN hjic-488 173 15 ] ] X hjic-488 173 16 yi yi NOUN hjic-488 174 1 [ [ X hjic-488 174 2 k k X hjic-488 174 3 ] ] X hjic-488 174 4 x̂[k x̂[k PROPN hjic-488 174 5 ] ] PUNCT hjic-488 174 6 ŝ[k ŝ[k PROPN hjic-488 174 7 ] ] X hjic-488 174 8 uikf uikf PROPN hjic-488 174 9 x̂[k x̂[k PROPN hjic-488 174 10 ] ] PUNCT hjic-488 174 11 ˆ̃u[k ˆ̃u[k X hjic-488 174 12 ] ] PUNCT hjic-488 174 13 u[k u[k X hjic-488 174 14 ] ] PUNCT hjic-488 174 15 ckf ckf VERB hjic-488 174 16 x̂[k x̂[k PROPN hjic-488 174 17 ] ] PUNCT hjic-488 174 18 figure figure NOUN hjic-488 174 19 3 3 NUM hjic-488 174 20 : : PUNCT hjic-488 174 21 closed closed ADJ hjic-488 174 22 - - PUNCT hjic-488 174 23 loop loop NOUN hjic-488 174 24 estimation estimation NOUN hjic-488 174 25 setup setup NOUN hjic-488 174 26 used use VERB hjic-488 174 27 in in ADP hjic-488 174 28 the the DET hjic-488 174 29 simulation simulation NOUN hjic-488 174 30 0 0 NUM hjic-488 174 31 1 1 NUM hjic-488 174 32 2 2 NUM hjic-488 174 33 3 3 NUM hjic-488 174 34 4 4 NUM hjic-488 174 35 5 5 NUM hjic-488 174 36 6 6 NUM hjic-488 174 37 7 7 NUM hjic-488 174 38 time time NOUN hjic-488 174 39 [ [ X hjic-488 174 40 s s X hjic-488 174 41 ] ] X hjic-488 174 42 −10 −10 X hjic-488 174 43 0 0 NUM hjic-488 174 44 10 10 NUM hjic-488 174 45 20 20 NUM hjic-488 174 46 30 30 NUM hjic-488 174 47 40 40 NUM hjic-488 174 48 50 50 NUM hjic-488 174 49 60 60 NUM hjic-488 174 50 u u NOUN hjic-488 174 51 f f NOUN hjic-488 174 52 , , PUNCT hjic-488 174 53 ˆ̃ ˆ̃ PROPN hjic-488 174 54 u u NOUN hjic-488 174 55 f f PROPN hjic-488 174 56 , , PUNCT hjic-488 175 1 [ [ X hjic-488 175 2 n n X hjic-488 175 3 ] ] PUNCT hjic-488 175 4 uf uf NOUN hjic-488 176 1 uikf uikf PROPN hjic-488 176 2 ukf ukf NOUN hjic-488 176 3 0 0 NUM hjic-488 176 4 1 1 NUM hjic-488 176 5 2 2 NUM hjic-488 176 6 3 3 NUM hjic-488 176 7 4 4 NUM hjic-488 176 8 5 5 NUM hjic-488 176 9 6 6 NUM hjic-488 176 10 7 7 NUM hjic-488 176 11 time time NOUN hjic-488 176 12 [ [ X hjic-488 176 13 s s X hjic-488 176 14 ] ] X hjic-488 176 15 −1.0 −1.0 PROPN hjic-488 176 16 −0.5 −0.5 PROPN hjic-488 176 17 0.0 0.0 NUM hjic-488 176 18 0.5 0.5 NUM hjic-488 176 19 1.0 1.0 NUM hjic-488 176 20 1.5 1.5 NUM hjic-488 176 21 2.0 2.0 NUM hjic-488 176 22 2.5 2.5 NUM hjic-488 176 23 3.0 3.0 NUM hjic-488 176 24 3.5 3.5 NUM hjic-488 176 25 u u NOUN hjic-488 176 26 c c NOUN hjic-488 176 27 , , PUNCT hjic-488 176 28 ˆ̃ ˆ̃ PROPN hjic-488 176 29 u u NOUN hjic-488 176 30 c c NOUN hjic-488 176 31 , , PUNCT hjic-488 176 32 [ [ X hjic-488 176 33 n n X hjic-488 176 34 m m VERB hjic-488 176 35 ] ] X hjic-488 177 1 uc uc ADP hjic-488 177 2 uikf uikf NOUN hjic-488 177 3 ukf ukf PROPN hjic-488 177 4 figure figure NOUN hjic-488 177 5 4 4 NUM hjic-488 177 6 : : PUNCT hjic-488 177 7 actuating actuate VERB hjic-488 177 8 signals signal NOUN hjic-488 177 9 and and CCONJ hjic-488 177 10 the the DET hjic-488 177 11 estimated estimate VERB hjic-488 177 12 inputs input NOUN hjic-488 177 13 of of ADP hjic-488 177 14 the the DET hjic-488 177 15 system system NOUN hjic-488 177 16 we we PRON hjic-488 177 17 want want VERB hjic-488 177 18 the the DET hjic-488 177 19 state state NOUN hjic-488 177 20 - - PUNCT hjic-488 177 21 feedback feedback NOUN hjic-488 177 22 controller controller NOUN hjic-488 177 23 to to ADP hjic-488 177 24 output output NOUN hjic-488 177 25 u[k u[k PROPN hjic-488 177 26 ] ] X hjic-488 177 27 = = SYM hjic-488 178 1 −k̃x̃[k −k̃x̃[k X hjic-488 178 2 ] ] X hjic-488 178 3 = = SYM hjic-488 178 4 −kx[k −kx[k PROPN hjic-488 178 5 ] ] PUNCT hjic-488 178 6 − − NOUN hjic-488 178 7 kixi kixi NOUN hjic-488 179 1 [ [ X hjic-488 179 2 k k X hjic-488 179 3 ] ] X hjic-488 179 4 . . PUNCT hjic-488 180 1 the the DET hjic-488 180 2 gain gain NOUN hjic-488 180 3 k̃ k̃ PROPN hjic-488 180 4 can can AUX hjic-488 180 5 be be AUX hjic-488 180 6 computed compute VERB hjic-488 180 7 using use VERB hjic-488 180 8 the the DET hjic-488 180 9 eigenvalue eigenvalue ADJ hjic-488 180 10 placement placement NOUN hjic-488 180 11 method method NOUN hjic-488 180 12 implemented implement VERB hjic-488 180 13 in in ADP hjic-488 180 14 matlab matlab PROPN hjic-488 180 15 ’s ’s PART hjic-488 180 16 place place NOUN hjic-488 180 17 algorithm algorithm NOUN hjic-488 180 18 : : PUNCT hjic-488 181 1 k̃ k̃ PROPN hjic-488 181 2 = = SYM hjic-488 181 3 place(φ̃ place(φ̃ PROPN hjic-488 181 4 , , PUNCT hjic-488 181 5 γ̃ γ̃ PROPN hjic-488 181 6 , , PUNCT hjic-488 181 7 λ λ PROPN hjic-488 181 8 ) ) PUNCT hjic-488 181 9 , , PUNCT hjic-488 181 10 where where SCONJ hjic-488 181 11 λ λ PROPN hjic-488 181 12 contains contain VERB hjic-488 181 13 the the DET hjic-488 181 14 chosen choose VERB hjic-488 181 15 eigenvalues eigenvalue NOUN hjic-488 181 16 of of ADP hjic-488 181 17 the the DET hjic-488 181 18 closed closed ADJ hjic-488 181 19 - - PUNCT hjic-488 181 20 loop loop NOUN hjic-488 181 21 system system NOUN hjic-488 181 22 . . PUNCT hjic-488 182 1 in in ADP hjic-488 182 2 continuous continuous ADJ hjic-488 182 3 time time NOUN hjic-488 182 4 they they PRON hjic-488 182 5 are be AUX hjic-488 182 6 −1 −1 NOUN hjic-488 182 7 + + NUM hjic-488 182 8 0.5j 0.5j NOUN hjic-488 182 9 , , PUNCT hjic-488 182 10 −1− −1− NOUN hjic-488 182 11 0.5j 0.5j NOUN hjic-488 182 12 , , PUNCT hjic-488 182 13 −5.1 −5.1 PROPN hjic-488 182 14 , , PUNCT hjic-488 182 15 −5.2 −5.2 PROPN hjic-488 182 16 , , PUNCT hjic-488 182 17 −5.3 −5.3 PROPN hjic-488 182 18 −5.4 −5.4 PROPN hjic-488 182 19 , , PUNCT hjic-488 182 20 −5.5 −5.5 PROPN hjic-488 182 21 , , PUNCT hjic-488 182 22 and and CCONJ hjic-488 182 23 −5.6 −5.6 PROPN hjic-488 182 24 . . PUNCT hjic-488 183 1 the the DET hjic-488 183 2 controller controller NOUN hjic-488 183 3 gains gain NOUN hjic-488 183 4 are be AUX hjic-488 183 5 k k NOUN hjic-488 183 6 = = PRON hjic-488 183 7   VERB hjic-488 184 1 100.594 100.594 NUM hjic-488 184 2 −0.1273 −0.1273 PROPN hjic-488 184 3 0.6011 0.6011 NUM hjic-488 184 4 −1.6765 −1.6765 X hjic-488 184 5 −185.407 −185.407 ADP hjic-488 184 6 0.0458 0.0458 NUM hjic-488 184 7 81.4011 81.4011 NUM hjic-488 184 8 −0.0558 −0.0558 NUM hjic-488 184 9 0.0562 0.0562 NUM hjic-488 184 10 −0.3166 −0.3166 DET hjic-488 184 11 −4.2257 −4.2257 NUM hjic-488 184 12 −0.0195 −0.0195 NUM hjic-488 184 13   PROPN hjic-488 184 14 t t PROPN hjic-488 184 15 , , PUNCT hjic-488 184 16 and and CCONJ hjic-488 184 17 ki ki PROPN hjic-488 184 18 = = PRON hjic-488 184 19 ( ( PUNCT hjic-488 184 20 46.641 46.641 NUM hjic-488 184 21 1.6026 1.6026 NUM hjic-488 184 22 −0.074 −0.074 PROPN hjic-488 184 23 −2.955 −2.955 PROPN hjic-488 184 24 ) ) PUNCT hjic-488 184 25 . . PUNCT hjic-488 185 1 ( ( PUNCT hjic-488 185 2 30 30 NUM hjic-488 185 3 ) ) PUNCT hjic-488 185 4 the the DET hjic-488 185 5 closed closed ADJ hjic-488 185 6 - - PUNCT hjic-488 185 7 loop loop NOUN hjic-488 185 8 setup setup NOUN hjic-488 185 9 is be AUX hjic-488 185 10 illustrated illustrate VERB hjic-488 185 11 in in ADP hjic-488 185 12 fig.3 fig.3 PROPN hjic-488 185 13 . . PUNCT hjic-488 186 1 here here ADV hjic-488 186 2 the the DET hjic-488 186 3 integration integration NOUN hjic-488 186 4 is be AUX hjic-488 186 5 done do VERB hjic-488 186 6 using use VERB hjic-488 186 7 the the DET hjic-488 186 8 left left ADJ hjic-488 186 9 rectangle rectangle NOUN hjic-488 186 10 rule rule NOUN hjic-488 186 11 , , PUNCT hjic-488 186 12 and and CCONJ hjic-488 186 13 the the DET hjic-488 186 14 0 0 NUM hjic-488 186 15 1 1 NUM hjic-488 186 16 2 2 NUM hjic-488 186 17 3 3 NUM hjic-488 186 18 4 4 NUM hjic-488 186 19 5 5 NUM hjic-488 186 20 6 6 NUM hjic-488 186 21 7 7 NUM hjic-488 186 22 time time NOUN hjic-488 186 23 [ [ X hjic-488 186 24 s s X hjic-488 186 25 ] ] X hjic-488 186 26 −0.1 −0.1 PROPN hjic-488 186 27 0.0 0.0 NUM hjic-488 186 28 0.1 0.1 NUM hjic-488 186 29 0.2 0.2 NUM hjic-488 186 30 0.3 0.3 NUM hjic-488 186 31 0.4 0.4 NUM hjic-488 186 32 0.5 0.5 NUM hjic-488 186 33 m m PROPN hjic-488 186 34 ea ea PROPN hjic-488 186 35 su su PROPN hjic-488 186 36 re re PROPN hjic-488 186 37 d d PROPN hjic-488 186 38 st st PROPN hjic-488 186 39 a a DET hjic-488 186 40 te te PROPN hjic-488 186 41 s s X hjic-488 187 1 [ [ X hjic-488 187 2 m m X hjic-488 187 3 , , PUNCT hjic-488 187 4 m m VERB hjic-488 187 5 / / SYM hjic-488 187 6 s s PROPN hjic-488 187 7 ] ] X hjic-488 187 8 ` ` PUNCT hjic-488 187 9 r r NOUN hjic-488 187 10 ˙̀ ˙̀ VERB hjic-488 187 11 ṙ ṙ PROPN hjic-488 187 12 0 0 NUM hjic-488 187 13 1 1 NUM hjic-488 187 14 2 2 NUM hjic-488 187 15 3 3 NUM hjic-488 187 16 4 4 NUM hjic-488 187 17 5 5 NUM hjic-488 187 18 6 6 NUM hjic-488 187 19 7 7 NUM hjic-488 187 20 time time NOUN hjic-488 188 1 [ [ X hjic-488 188 2 s s X hjic-488 188 3 ] ] X hjic-488 188 4 −0.4 −0.4 NUM hjic-488 188 5 −0.3 −0.3 PROPN hjic-488 189 1 −0.2 −0.2 PROPN hjic-488 190 1 −0.1 −0.1 PROPN hjic-488 190 2 0.0 0.0 NUM hjic-488 190 3 0.1 0.1 NUM hjic-488 190 4 0.2 0.2 NUM hjic-488 190 5 u u NOUN hjic-488 190 6 n n PRON hjic-488 190 7 m m NOUN hjic-488 190 8 ea ea NOUN hjic-488 190 9 su su PROPN hjic-488 190 10 re re PROPN hjic-488 190 11 d d PROPN hjic-488 190 12 st st PROPN hjic-488 190 13 a a DET hjic-488 190 14 te te PROPN hjic-488 190 15 s s X hjic-488 191 1 [ [ X hjic-488 191 2 r r X hjic-488 191 3 a a PROPN hjic-488 191 4 d d NOUN hjic-488 191 5 , , PUNCT hjic-488 191 6 ra ra PROPN hjic-488 191 7 d d PROPN hjic-488 191 8 / / SYM hjic-488 191 9 s s PROPN hjic-488 191 10 ] ] X hjic-488 191 11 θ θ PROPN hjic-488 191 12 θ̇ θ̇ DET hjic-488 191 13 figure figure NOUN hjic-488 191 14 5 5 NUM hjic-488 191 15 : : PUNCT hjic-488 191 16 state state NOUN hjic-488 191 17 evolution evolution NOUN hjic-488 191 18 of of ADP hjic-488 191 19 the the DET hjic-488 191 20 controlled control VERB hjic-488 191 21 crane crane NOUN hjic-488 191 22 using use VERB hjic-488 191 23 the the DET hjic-488 191 24 true true ADJ hjic-488 191 25 states state NOUN hjic-488 191 26 as as ADP hjic-488 191 27 feedback feedback NOUN hjic-488 191 28 adc adc NOUN hjic-488 191 29 and and CCONJ hjic-488 191 30 dac dac NOUN hjic-488 191 31 blocks block NOUN hjic-488 191 32 are be AUX hjic-488 191 33 analogue analogue NOUN hjic-488 191 34 - - PUNCT hjic-488 191 35 digital digital ADJ hjic-488 191 36 and and CCONJ hjic-488 191 37 digitalanalogue digitalanalogue NOUN hjic-488 191 38 converters converter NOUN hjic-488 191 39 respectively respectively ADV hjic-488 191 40 . . PUNCT hjic-488 192 1 the the DET hjic-488 192 2 dac dac PROPN hjic-488 192 3 uses use VERB hjic-488 192 4 the the DET hjic-488 192 5 zeroorder zeroorder NOUN hjic-488 192 6 hold hold VERB hjic-488 192 7 method method NOUN hjic-488 192 8 for for ADP hjic-488 192 9 signal signal ADJ hjic-488 192 10 reconstruction reconstruction NOUN hjic-488 192 11 . . PUNCT hjic-488 193 1 the the DET hjic-488 193 2 desired desire VERB hjic-488 193 3 state state NOUN hjic-488 193 4 of of ADP hjic-488 193 5 the the DET hjic-488 193 6 system system NOUN hjic-488 193 7 is be AUX hjic-488 193 8 xd xd ADP hjic-488 193 9 = = SYM hjic-488 193 10 ( ( PUNCT hjic-488 193 11 ` ` PUNCT hjic-488 193 12 d d X hjic-488 193 13 r0 r0 NOUN hjic-488 193 14 0 0 NUM hjic-488 193 15 0 0 NUM hjic-488 193 16 0 0 NUM hjic-488 193 17 0 0 NUM hjic-488 193 18 ) ) PUNCT hjic-488 193 19 t t NOUN hjic-488 193 20 , , PUNCT hjic-488 193 21 ` ` PUNCT hjic-488 193 22 d d X hjic-488 193 23 is be AUX hjic-488 193 24 the the DET hjic-488 193 25 desired desire VERB hjic-488 193 26 position position NOUN hjic-488 193 27 of of ADP hjic-488 193 28 the the DET hjic-488 193 29 cart cart NOUN hjic-488 193 30 and and CCONJ hjic-488 193 31 yid yid ADJ hjic-488 193 32 = = PROPN hjic-488 193 33 cixd cixd PROPN hjic-488 193 34 . . PUNCT hjic-488 194 1 since since SCONJ hjic-488 194 2 we we PRON hjic-488 194 3 only only ADV hjic-488 194 4 want want VERB hjic-488 194 5 to to PART hjic-488 194 6 demonstrate demonstrate VERB hjic-488 194 7 the the DET hjic-488 194 8 results result NOUN hjic-488 194 9 of of ADP hjic-488 194 10 the the DET hjic-488 194 11 state state NOUN hjic-488 194 12 estimation estimation NOUN hjic-488 194 13 , , PUNCT hjic-488 194 14 first first ADV hjic-488 194 15 the the DET hjic-488 194 16 real real ADJ hjic-488 194 17 states state NOUN hjic-488 194 18 are be AUX hjic-488 194 19 fed feed VERB hjic-488 194 20 back back ADV hjic-488 194 21 to to ADP hjic-488 194 22 the the DET hjic-488 194 23 controller controller NOUN hjic-488 194 24 . . PUNCT hjic-488 195 1 to to PART hjic-488 195 2 compare compare VERB hjic-488 195 3 the the DET hjic-488 195 4 accuracy accuracy NOUN hjic-488 195 5 of of ADP hjic-488 195 6 our our PRON hjic-488 195 7 methods method NOUN hjic-488 195 8 to to ADP hjic-488 195 9 a a DET hjic-488 195 10 traditional traditional ADJ hjic-488 195 11 solution solution NOUN hjic-488 195 12 , , PUNCT hjic-488 195 13 the the DET hjic-488 195 14 classical classical ADJ hjic-488 195 15 kalman kalman NOUN hjic-488 195 16 filter filter NOUN hjic-488 195 17 ( ( PUNCT hjic-488 195 18 ckf ckf PROPN hjic-488 195 19 ) ) PUNCT hjic-488 196 1 [ [ X hjic-488 196 2 12 12 NUM hjic-488 196 3 ] ] X hjic-488 196 4 is be AUX hjic-488 196 5 also also ADV hjic-488 196 6 implemented implement VERB hjic-488 196 7 . . PUNCT hjic-488 197 1 as as ADP hjic-488 197 2 a a DET hjic-488 197 3 result result NOUN hjic-488 197 4 , , PUNCT hjic-488 197 5 the the DET hjic-488 197 6 kalman kalman NOUN hjic-488 197 7 filters filters AUX hjic-488 197 8 compute compute VERB hjic-488 197 9 the the DET hjic-488 197 10 estimated estimate VERB hjic-488 197 11 state state NOUN hjic-488 197 12 of of ADP hjic-488 197 13 the the DET hjic-488 197 14 system system NOUN hjic-488 197 15 x̂[k x̂[k PROPN hjic-488 197 16 ] ] X hjic-488 197 17 , , PUNCT hjic-488 197 18 and and CCONJ hjic-488 197 19 they they PRON hjic-488 197 20 also also ADV hjic-488 197 21 provide provide VERB hjic-488 197 22 information information NOUN hjic-488 197 23 about about ADP hjic-488 197 24 the the DET hjic-488 197 25 input input NOUN hjic-488 197 26 . . PUNCT hjic-488 198 1 the the DET hjic-488 198 2 uikf uikf NOUN hjic-488 198 3 estimates estimate VERB hjic-488 198 4 the the DET hjic-488 198 5 friction friction NOUN hjic-488 198 6 loaded load VERB hjic-488 198 7 actuating actuate VERB hjic-488 198 8 signals signal NOUN hjic-488 198 9 directly directly ADV hjic-488 198 10 , , PUNCT hjic-488 198 11 while while SCONJ hjic-488 198 12 the the DET hjic-488 198 13 ukf ukf PROPN hjic-488 198 14 estimates estimate VERB hjic-488 198 15 the the DET hjic-488 198 16 frictional frictional ADJ hjic-488 198 17 forces force NOUN hjic-488 198 18 superposed superpose VERB hjic-488 198 19 to to ADP hjic-488 198 20 the the DET hjic-488 198 21 actuating actuate VERB hjic-488 198 22 signals signal NOUN hjic-488 198 23 . . PUNCT hjic-488 199 1 the the DET hjic-488 199 2 actuating actuate VERB hjic-488 199 3 signals signal NOUN hjic-488 199 4 along along ADP hjic-488 199 5 with with ADP hjic-488 199 6 the the DET hjic-488 199 7 estimates estimate NOUN hjic-488 199 8 of of ADP hjic-488 199 9 the the DET hjic-488 199 10 real real ADJ hjic-488 199 11 inputs input NOUN hjic-488 199 12 provided provide VERB hjic-488 199 13 by by ADP hjic-488 199 14 the the DET hjic-488 199 15 filters filter NOUN hjic-488 199 16 can can AUX hjic-488 199 17 be be AUX hjic-488 199 18 seen see VERB hjic-488 199 19 in in ADP hjic-488 199 20 fig.4 fig.4 PROPN hjic-488 199 21 . . PUNCT hjic-488 200 1 here here ADV hjic-488 200 2 , , PUNCT hjic-488 200 3 the the DET hjic-488 200 4 estimated estimate VERB hjic-488 200 5 input input NOUN hjic-488 200 6 of of ADP hjic-488 200 7 the the DET hjic-488 200 8 ukf ukf NOUN hjic-488 200 9 is be AUX hjic-488 200 10 computed compute VERB hjic-488 200 11 as as ADP hjic-488 200 12 ˆ̃u ˆ̃u PROPN hjic-488 200 13 = = PROPN hjic-488 200 14 u[k]+λŝ[k u[k]+λŝ[k X hjic-488 200 15 ] ] X hjic-488 200 16 . . PUNCT hjic-488 201 1 because because SCONJ hjic-488 201 2 of of ADP hjic-488 201 3 friction friction NOUN hjic-488 201 4 , , PUNCT hjic-488 201 5 the the DET hjic-488 201 6 real real ADJ hjic-488 201 7 inputs input NOUN hjic-488 201 8 are be AUX hjic-488 201 9 estimated estimate VERB hjic-488 201 10 to to PART hjic-488 201 11 be be AUX hjic-488 201 12 76 76 NUM hjic-488 201 13 0 0 NUM hjic-488 201 14 1 1 NUM hjic-488 201 15 2 2 NUM hjic-488 201 16 3 3 NUM hjic-488 201 17 4 4 NUM hjic-488 201 18 5 5 NUM hjic-488 201 19 6 6 NUM hjic-488 201 20 7 7 NUM hjic-488 201 21 time time NOUN hjic-488 201 22 [ [ X hjic-488 201 23 s s X hjic-488 201 24 ] ] X hjic-488 201 25 0.00000 0.00000 NUM hjic-488 201 26 0.00005 0.00005 NUM hjic-488 201 27 0.00010 0.00010 NUM hjic-488 201 28 0.00015 0.00015 NUM hjic-488 201 29 0.00020 0.00020 NUM hjic-488 201 30 0.00025 0.00025 NUM hjic-488 201 31 0.00030 0.00030 NUM hjic-488 201 32 0.00035 0.00035 NUM hjic-488 201 33 ` ` PUNCT hjic-488 201 34 − − PROPN hjic-488 201 35 ˆ̀ ˆ̀ PUNCT hjic-488 202 1 [ [ X hjic-488 202 2 m m X hjic-488 202 3 ] ] X hjic-488 202 4 uikf uikf ADJ hjic-488 202 5 ukf ukf NOUN hjic-488 202 6 0 0 NUM hjic-488 202 7 1 1 NUM hjic-488 202 8 2 2 NUM hjic-488 202 9 3 3 NUM hjic-488 202 10 4 4 NUM hjic-488 202 11 5 5 NUM hjic-488 202 12 6 6 NUM hjic-488 202 13 7 7 NUM hjic-488 202 14 time time NOUN hjic-488 203 1 [ [ X hjic-488 203 2 s s X hjic-488 203 3 ] ] X hjic-488 203 4 −0.001 −0.001 NOUN hjic-488 203 5 0.000 0.000 NUM hjic-488 203 6 0.001 0.001 NUM hjic-488 203 7 0.002 0.002 NUM hjic-488 203 8 0.003 0.003 NUM hjic-488 203 9 0.004 0.004 NUM hjic-488 203 10 0.005 0.005 NUM hjic-488 203 11 ˙̀ ˙̀ VERB hjic-488 203 12 − − PROPN hjic-488 203 13 ˆ̇ ˆ̇ NOUN hjic-488 204 1 ` ` PUNCT hjic-488 204 2 [ [ X hjic-488 204 3 m m X hjic-488 204 4 / / SYM hjic-488 204 5 s s PART hjic-488 204 6 ] ] X hjic-488 204 7 uikf uikf ADJ hjic-488 204 8 ukf ukf NOUN hjic-488 204 9 figure figure NOUN hjic-488 204 10 6 6 NUM hjic-488 204 11 : : PUNCT hjic-488 204 12 error error NOUN hjic-488 204 13 of of ADP hjic-488 204 14 the the DET hjic-488 204 15 position position NOUN hjic-488 204 16 and and CCONJ hjic-488 204 17 velocity velocity NOUN hjic-488 204 18 estimations estimation NOUN hjic-488 204 19 much much ADV hjic-488 204 20 less less ADJ hjic-488 204 21 than than ADP hjic-488 204 22 the the DET hjic-488 204 23 actuating actuate VERB hjic-488 204 24 signals signal NOUN hjic-488 204 25 . . PUNCT hjic-488 205 1 the the DET hjic-488 205 2 large large ADJ hjic-488 205 3 offset offset NOUN hjic-488 205 4 in in ADP hjic-488 205 5 fig.4 fig.4 PROPN hjic-488 205 6 is be AUX hjic-488 205 7 a a DET hjic-488 205 8 consequence consequence NOUN hjic-488 205 9 of of ADP hjic-488 205 10 the the DET hjic-488 205 11 stiction stiction NOUN hjic-488 205 12 , , PUNCT hjic-488 205 13 the the DET hjic-488 205 14 cart cart NOUN hjic-488 205 15 will will AUX hjic-488 205 16 not not PART hjic-488 205 17 move move VERB hjic-488 205 18 until until SCONJ hjic-488 205 19 uf uf PROPN hjic-488 205 20 becomes become VERB hjic-488 205 21 greater great ADJ hjic-488 205 22 than than ADP hjic-488 205 23 a a DET hjic-488 205 24 certain certain ADJ hjic-488 205 25 value value NOUN hjic-488 205 26 ( ( PUNCT hjic-488 205 27 in in ADP hjic-488 205 28 our our PRON hjic-488 205 29 case case NOUN hjic-488 205 30 about about ADV hjic-488 205 31 28 28 NUM hjic-488 205 32 n n CCONJ hjic-488 205 33 ) ) PUNCT hjic-488 205 34 . . PUNCT hjic-488 206 1 when when SCONJ hjic-488 206 2 the the DET hjic-488 206 3 cart cart NOUN hjic-488 206 4 finally finally ADV hjic-488 206 5 stops stop VERB hjic-488 206 6 moving move VERB hjic-488 206 7 , , PUNCT hjic-488 206 8 the the DET hjic-488 206 9 fluctuation fluctuation NOUN hjic-488 206 10 of of ADP hjic-488 206 11 uf uf PROPN hjic-488 206 12 tries try VERB hjic-488 206 13 to to PART hjic-488 206 14 counter counter VERB hjic-488 206 15 the the DET hjic-488 206 16 load load NOUN hjic-488 206 17 sway sway NOUN hjic-488 206 18 , , PUNCT hjic-488 206 19 during during ADP hjic-488 206 20 which which PRON hjic-488 206 21 the the DET hjic-488 206 22 measured measured ADJ hjic-488 206 23 states state NOUN hjic-488 206 24 do do AUX hjic-488 206 25 not not PART hjic-488 206 26 change change VERB hjic-488 206 27 . . PUNCT hjic-488 207 1 this this PRON hjic-488 207 2 is be AUX hjic-488 207 3 the the DET hjic-488 207 4 reason reason NOUN hjic-488 207 5 why why SCONJ hjic-488 207 6 the the DET hjic-488 207 7 estimators estimator NOUN hjic-488 207 8 find find VERB hjic-488 207 9 the the DET hjic-488 207 10 input input NOUN hjic-488 207 11 to to PART hjic-488 207 12 be be AUX hjic-488 207 13 zero zero NUM hjic-488 207 14 . . PUNCT hjic-488 208 1 fig.5 fig.5 NOUN hjic-488 208 2 shows show VERB hjic-488 208 3 the the DET hjic-488 208 4 transient transient NOUN hjic-488 208 5 of of ADP hjic-488 208 6 the the DET hjic-488 208 7 states state NOUN hjic-488 208 8 in in ADP hjic-488 208 9 a a DET hjic-488 208 10 closedloop closedloop NOUN hjic-488 208 11 . . PUNCT hjic-488 209 1 results result NOUN hjic-488 209 2 show show VERB hjic-488 209 3 that that SCONJ hjic-488 209 4 the the DET hjic-488 209 5 controller controller NOUN hjic-488 209 6 can can AUX hjic-488 209 7 bring bring VERB hjic-488 209 8 the the DET hjic-488 209 9 system system NOUN hjic-488 209 10 into into ADP hjic-488 209 11 the the DET hjic-488 209 12 desired desire VERB hjic-488 209 13 state state NOUN hjic-488 209 14 , , PUNCT hjic-488 209 15 but but CCONJ hjic-488 209 16 friction friction NOUN hjic-488 209 17 prevents prevent VERB hjic-488 209 18 it it PRON hjic-488 209 19 from from ADP hjic-488 209 20 stopping stop VERB hjic-488 209 21 the the DET hjic-488 209 22 low low ADJ hjic-488 209 23 amplitude amplitude NOUN hjic-488 209 24 swinging swinging NOUN hjic-488 209 25 of of ADP hjic-488 209 26 the the DET hjic-488 209 27 load load NOUN hjic-488 209 28 , , PUNCT hjic-488 209 29 because because SCONJ hjic-488 209 30 it it PRON hjic-488 209 31 makes make VERB hjic-488 209 32 quick quick ADJ hjic-488 209 33 , , PUNCT hjic-488 209 34 short short ADJ hjic-488 209 35 motions motion NOUN hjic-488 209 36 impossible impossible ADJ hjic-488 209 37 . . PUNCT hjic-488 210 1 error error NOUN hjic-488 210 2 estimates estimate NOUN hjic-488 210 3 are be AUX hjic-488 210 4 illustrated illustrate VERB hjic-488 210 5 by by ADP hjic-488 210 6 figs fig NOUN hjic-488 210 7 . . PUNCT hjic-488 211 1 6 6 NUM hjic-488 211 2 and and CCONJ hjic-488 211 3 7 7 NUM hjic-488 211 4 . . NOUN hjic-488 212 1 in in ADP hjic-488 212 2 all all DET hjic-488 212 3 cases case NOUN hjic-488 212 4 , , PUNCT hjic-488 212 5 the the DET hjic-488 212 6 error error NOUN hjic-488 212 7 becomes become VERB hjic-488 212 8 zero zero NUM hjic-488 212 9 when when SCONJ hjic-488 212 10 the the DET hjic-488 212 11 crane crane NOUN hjic-488 212 12 reaches reach VERB hjic-488 212 13 the the DET hjic-488 212 14 desired desire VERB hjic-488 212 15 state state NOUN hjic-488 212 16 . . PUNCT hjic-488 213 1 this this PRON hjic-488 213 2 is be AUX hjic-488 213 3 not not PART hjic-488 213 4 true true ADJ hjic-488 213 5 for for ADP hjic-488 213 6 the the DET hjic-488 213 7 angle angle NOUN hjic-488 213 8 and and CCONJ hjic-488 213 9 its its PRON hjic-488 213 10 derivative derivative NOUN hjic-488 213 11 in in ADP hjic-488 213 12 fig.8 fig.8 PROPN hjic-488 213 13 . . PUNCT hjic-488 214 1 the the DET hjic-488 214 2 error error NOUN hjic-488 214 3 decreases decrease VERB hjic-488 214 4 at at ADP hjic-488 214 5 the the DET hjic-488 214 6 end end NOUN hjic-488 214 7 of of ADP hjic-488 214 8 the the DET hjic-488 214 9 state state NOUN hjic-488 214 10 transient transient NOUN hjic-488 214 11 , , PUNCT hjic-488 214 12 but but CCONJ hjic-488 214 13 does do AUX hjic-488 214 14 not not PART hjic-488 214 15 become become VERB hjic-488 214 16 zero zero NUM hjic-488 214 17 . . PUNCT hjic-488 215 1 when when SCONJ hjic-488 215 2 the the DET hjic-488 215 3 cart cart NOUN hjic-488 215 4 stops stop VERB hjic-488 215 5 and and CCONJ hjic-488 215 6 the the DET hjic-488 215 7 load load NOUN hjic-488 215 8 swings swing NOUN hjic-488 215 9 , , PUNCT hjic-488 215 10 the the DET hjic-488 215 11 measurements measurement NOUN hjic-488 215 12 are be AUX hjic-488 215 13 all all ADV hjic-488 215 14 constant constant ADJ hjic-488 215 15 thus thus ADV hjic-488 215 16 they they PRON hjic-488 215 17 carry carry VERB hjic-488 215 18 no no DET hjic-488 215 19 information information NOUN hjic-488 215 20 regarding regard VERB hjic-488 215 21 θ θ PROPN hjic-488 215 22 and and CCONJ hjic-488 215 23 θ̇. θ̇. NUM hjic-488 215 24 in in ADP hjic-488 215 25 these these DET hjic-488 215 26 situations situation NOUN hjic-488 215 27 the the DET hjic-488 215 28 cart cart NOUN hjic-488 215 29 and and CCONJ hjic-488 215 30 winch winch NOUN hjic-488 215 31 are be AUX hjic-488 215 32 usually usually ADV hjic-488 215 33 also also ADV hjic-488 215 34 motionless motionless ADJ hjic-488 215 35 due due ADP hjic-488 215 36 to to ADP hjic-488 215 37 friction friction NOUN hjic-488 215 38 . . PUNCT hjic-488 216 1 consequently consequently ADV hjic-488 216 2 , , PUNCT hjic-488 216 3 the the DET hjic-488 216 4 estimation estimation NOUN hjic-488 216 5 error error NOUN hjic-488 216 6 of of ADP hjic-488 216 7 these these DET hjic-488 216 8 quantities quantity NOUN hjic-488 216 9 never never ADV hjic-488 216 10 becomes become VERB hjic-488 216 11 zero zero NUM hjic-488 216 12 . . PUNCT hjic-488 217 1 it it PRON hjic-488 217 2 is be AUX hjic-488 217 3 possible possible ADJ hjic-488 217 4 to to PART hjic-488 217 5 decrease decrease VERB hjic-488 217 6 the the DET hjic-488 217 7 estimation estimation NOUN hjic-488 217 8 error error NOUN hjic-488 217 9 using use VERB hjic-488 217 10 two two NUM hjic-488 217 11 laser laser NOUN hjic-488 217 12 slot slot NOUN hjic-488 217 13 sensors sensor NOUN hjic-488 217 14 . . PUNCT hjic-488 218 1 with with ADP hjic-488 218 2 the the DET hjic-488 218 3 help help NOUN hjic-488 218 4 of of ADP hjic-488 218 5 such such ADJ hjic-488 218 6 devices device NOUN hjic-488 218 7 , , PUNCT hjic-488 218 8 θ θ PROPN hjic-488 218 9 can can AUX hjic-488 218 10 be be AUX hjic-488 218 11 measured measure VERB hjic-488 218 12 accurately accurately ADV hjic-488 218 13 in in ADP hjic-488 218 14 two two NUM hjic-488 218 15 positions position NOUN hjic-488 218 16 and and CCONJ hjic-488 218 17 through through ADP hjic-488 218 18 the the DET hjic-488 218 19 application application NOUN hjic-488 218 20 of of ADP hjic-488 218 21 proper proper ADJ hjic-488 218 22 sensor sensor NOUN hjic-488 218 23 fusion fusion NOUN hjic-488 218 24 techniques technique VERB hjic-488 218 25 the the DET hjic-488 218 26 estimation estimation NOUN hjic-488 218 27 of of ADP hjic-488 218 28 the the DET hjic-488 218 29 angle angle NOUN hjic-488 218 30 can can AUX hjic-488 218 31 become become VERB hjic-488 218 32 more more ADV hjic-488 218 33 precise precise ADJ hjic-488 218 34 in in ADP hjic-488 218 35 between between ADP hjic-488 218 36 the the DET hjic-488 218 37 chosen choose VERB hjic-488 218 38 positions position NOUN hjic-488 218 39 as as ADV hjic-488 218 40 well well ADV hjic-488 218 41 . . PUNCT hjic-488 219 1 in in ADP hjic-488 219 2 fig.9 fig.9 ADP hjic-488 219 3 the the DET hjic-488 219 4 estimation estimation NOUN hjic-488 219 5 error error NOUN hjic-488 219 6 of of ADP hjic-488 219 7 θ θ PROPN hjic-488 219 8 and and CCONJ hjic-488 219 9 θ̇ θ̇ NOUN hjic-488 219 10 is be AUX hjic-488 219 11 illustrated illustrate VERB hjic-488 219 12 using use VERB hjic-488 219 13 ckf ckf NOUN hjic-488 219 14 . . PUNCT hjic-488 220 1 the the DET hjic-488 220 2 filter filter NOUN hjic-488 220 3 was be AUX hjic-488 220 4 designed design VERB hjic-488 220 5 for for ADP hjic-488 220 6 the the DET hjic-488 220 7 dynamics dynamic NOUN hjic-488 220 8 given give VERB hjic-488 220 9 by by ADP hjic-488 220 10 eq.(7 eq.(7 NOUN hjic-488 220 11 ) ) PUNCT hjic-488 220 12 except except SCONJ hjic-488 220 13 that that SCONJ hjic-488 220 14 it it PRON hjic-488 220 15 does do AUX hjic-488 220 16 not not PART hjic-488 220 17 consider consider VERB hjic-488 220 18 the the DET hjic-488 220 19 inputs input NOUN hjic-488 220 20 unknown unknown ADJ hjic-488 220 21 . . PUNCT hjic-488 221 1 the the DET hjic-488 221 2 results result NOUN hjic-488 221 3 show show VERB hjic-488 221 4 that that SCONJ hjic-488 221 5 the the DET hjic-488 221 6 error error NOUN hjic-488 221 7 is be AUX hjic-488 221 8 substantially substantially ADV hjic-488 221 9 higher high ADJ hjic-488 221 10 than than ADP hjic-488 221 11 in in ADP hjic-488 221 12 the the DET hjic-488 221 13 case case NOUN hjic-488 221 14 of of ADP hjic-488 221 15 the the DET hjic-488 221 16 uikf uikf NOUN hjic-488 221 17 or or CCONJ hjic-488 221 18 ukf ukf NOUN hjic-488 221 19 . . PUNCT hjic-488 221 20 0 0 NUM hjic-488 221 21 1 1 NUM hjic-488 221 22 2 2 NUM hjic-488 221 23 3 3 NUM hjic-488 221 24 4 4 NUM hjic-488 221 25 5 5 NUM hjic-488 221 26 6 6 NUM hjic-488 221 27 7 7 NUM hjic-488 221 28 time time NOUN hjic-488 221 29 [ [ X hjic-488 221 30 s s X hjic-488 221 31 ] ] X hjic-488 221 32 −0.00005 −0.00005 X hjic-488 221 33 0.00000 0.00000 NUM hjic-488 221 34 0.00005 0.00005 NUM hjic-488 221 35 0.00010 0.00010 NUM hjic-488 221 36 0.00015 0.00015 NUM hjic-488 221 37 r r NOUN hjic-488 221 38 − − NOUN hjic-488 221 39 r̂ r̂ NOUN hjic-488 222 1 [ [ X hjic-488 222 2 m m X hjic-488 222 3 ] ] X hjic-488 222 4 uikf uikf ADJ hjic-488 222 5 ukf ukf NOUN hjic-488 222 6 0 0 NUM hjic-488 222 7 1 1 NUM hjic-488 222 8 2 2 NUM hjic-488 222 9 3 3 NUM hjic-488 222 10 4 4 NUM hjic-488 222 11 5 5 NUM hjic-488 222 12 6 6 NUM hjic-488 222 13 7 7 NUM hjic-488 222 14 time time NOUN hjic-488 222 15 [ [ X hjic-488 222 16 s s X hjic-488 222 17 ] ] X hjic-488 222 18 −0.0010 −0.0010 NOUN hjic-488 222 19 −0.0005 −0.0005 NOUN hjic-488 222 20 0.0000 0.0000 NUM hjic-488 222 21 0.0005 0.0005 NUM hjic-488 222 22 0.0010 0.0010 NUM hjic-488 222 23 0.0015 0.0015 NUM hjic-488 222 24 0.0020 0.0020 NUM hjic-488 222 25 0.0025 0.0025 NUM hjic-488 222 26 0.0030 0.0030 NUM hjic-488 222 27 0.0035 0.0035 NUM hjic-488 222 28 ṙ ṙ NOUN hjic-488 222 29 − − PROPN hjic-488 222 30 ˆ̇ ˆ̇ NOUN hjic-488 222 31 r r NOUN hjic-488 223 1 [ [ X hjic-488 223 2 m m NOUN hjic-488 223 3 / / SYM hjic-488 223 4 s s PART hjic-488 223 5 ] ] X hjic-488 223 6 uikf uikf ADJ hjic-488 223 7 ukf ukf NOUN hjic-488 223 8 figure figure NOUN hjic-488 223 9 7 7 NUM hjic-488 223 10 : : PUNCT hjic-488 223 11 error error NOUN hjic-488 223 12 of of ADP hjic-488 223 13 the the DET hjic-488 223 14 rope rope NOUN hjic-488 223 15 length length NOUN hjic-488 223 16 and and CCONJ hjic-488 223 17 hoisting hoist VERB hjic-488 223 18 velocity velocity NOUN hjic-488 223 19 estimations estimation NOUN hjic-488 223 20 0 0 NUM hjic-488 223 21 1 1 NUM hjic-488 223 22 2 2 NUM hjic-488 223 23 3 3 NUM hjic-488 223 24 4 4 NUM hjic-488 223 25 5 5 NUM hjic-488 223 26 6 6 NUM hjic-488 223 27 7 7 NUM hjic-488 223 28 time time NOUN hjic-488 224 1 [ [ X hjic-488 224 2 s s X hjic-488 224 3 ] ] X hjic-488 224 4 −0.003 −0.003 ADJ hjic-488 224 5 −0.002 −0.002 NOUN hjic-488 224 6 −0.001 −0.001 NOUN hjic-488 224 7 0.000 0.000 NUM hjic-488 224 8 0.001 0.001 NUM hjic-488 224 9 0.002 0.002 NUM hjic-488 224 10 0.003 0.003 NUM hjic-488 224 11 0.004 0.004 NUM hjic-488 224 12 0.005 0.005 NUM hjic-488 224 13 θ θ NOUN hjic-488 224 14 − − NOUN hjic-488 224 15 θ̂ θ̂ PUNCT hjic-488 225 1 [ [ X hjic-488 225 2 r r X hjic-488 225 3 a a PROPN hjic-488 225 4 d d X hjic-488 225 5 ] ] PUNCT hjic-488 225 6 uikf uikf PROPN hjic-488 225 7 ukf ukf NOUN hjic-488 225 8 0 0 NUM hjic-488 225 9 1 1 NUM hjic-488 225 10 2 2 NUM hjic-488 225 11 3 3 NUM hjic-488 225 12 4 4 NUM hjic-488 225 13 5 5 NUM hjic-488 225 14 6 6 NUM hjic-488 225 15 7 7 NUM hjic-488 225 16 time time NOUN hjic-488 225 17 [ [ X hjic-488 225 18 s s X hjic-488 225 19 ] ] X hjic-488 225 20 −0.020 −0.020 X hjic-488 225 21 −0.015 −0.015 X hjic-488 225 22 −0.010 −0.010 NOUN hjic-488 225 23 −0.005 −0.005 PROPN hjic-488 225 24 0.000 0.000 NUM hjic-488 225 25 0.005 0.005 NUM hjic-488 225 26 0.010 0.010 NUM hjic-488 225 27 0.015 0.015 NUM hjic-488 225 28 0.020 0.020 NUM hjic-488 225 29 0.025 0.025 NUM hjic-488 225 30 θ̇ θ̇ PRON hjic-488 225 31 − − NOUN hjic-488 225 32 ˆ̇ ˆ̇ ADJ hjic-488 225 33 θ θ PROPN hjic-488 226 1 [ [ X hjic-488 226 2 r r X hjic-488 226 3 a a PROPN hjic-488 226 4 d d PROPN hjic-488 226 5 / / SYM hjic-488 226 6 s s PROPN hjic-488 226 7 ] ] X hjic-488 226 8 uikf uikf ADJ hjic-488 226 9 ukf ukf NOUN hjic-488 226 10 figure figure NOUN hjic-488 226 11 8 8 NUM hjic-488 226 12 : : PUNCT hjic-488 226 13 error error NOUN hjic-488 226 14 of of ADP hjic-488 226 15 the the DET hjic-488 226 16 angle angle NOUN hjic-488 226 17 and and CCONJ hjic-488 226 18 angular angular ADJ hjic-488 226 19 velocity velocity NOUN hjic-488 226 20 estimations estimation NOUN hjic-488 226 21 fig.8 fig.8 PROPN hjic-488 226 22 shows show VERB hjic-488 226 23 the the DET hjic-488 226 24 estimation estimation NOUN hjic-488 226 25 error error NOUN hjic-488 226 26 of of ADP hjic-488 226 27 the the DET hjic-488 226 28 ukf ukf NOUN hjic-488 226 29 to to PART hjic-488 226 30 be be AUX hjic-488 226 31 less less ADJ hjic-488 226 32 . . PUNCT hjic-488 227 1 we we PRON hjic-488 227 2 applied apply VERB hjic-488 227 3 this this DET hjic-488 227 4 estimator estimator NOUN hjic-488 227 5 in in ADP hjic-488 227 6 a a DET hjic-488 227 7 closed closed ADJ hjic-488 227 8 - - PUNCT hjic-488 227 9 loop loop NOUN hjic-488 227 10 scenario scenario NOUN hjic-488 227 11 identical identical ADJ hjic-488 227 12 to to ADP hjic-488 227 13 the the DET hjic-488 227 14 one one NOUN hjic-488 227 15 presented present VERB hjic-488 227 16 in in ADP hjic-488 227 17 fig.3 fig.3 PROPN hjic-488 227 18 , , PUNCT hjic-488 227 19 but but CCONJ hjic-488 227 20 instead instead ADV hjic-488 227 21 of of ADP hjic-488 227 22 x[k x[k NOUN hjic-488 227 23 ] ] X hjic-488 227 24 the the DET hjic-488 227 25 x̂[k x̂[k PROPN hjic-488 227 26 ] ] PUNCT hjic-488 227 27 of of ADP hjic-488 227 28 the the DET hjic-488 227 29 ukf ukf NOUN hjic-488 227 30 was be AUX hjic-488 227 31 used use VERB hjic-488 227 32 in in ADP hjic-488 227 33 the the DET hjic-488 227 34 feedback feedback NOUN hjic-488 227 35 loop loop NOUN hjic-488 227 36 . . PUNCT hjic-488 228 1 the the DET hjic-488 228 2 state state NOUN hjic-488 228 3 evolution evolution NOUN hjic-488 228 4 of of ADP hjic-488 228 5 the the DET hjic-488 228 6 crane crane NOUN hjic-488 228 7 in in ADP hjic-488 228 8 this this DET hjic-488 228 9 simulation simulation NOUN hjic-488 228 10 is be AUX hjic-488 228 11 illustrated illustrate VERB hjic-488 228 12 in in ADP hjic-488 228 13 fig.10 fig.10 PROPN hjic-488 228 14 . . PUNCT hjic-488 229 1 the the DET hjic-488 229 2 system system NOUN hjic-488 229 3 ’s ’s PART hjic-488 229 4 behaviour behaviour NOUN hjic-488 229 5 is be AUX hjic-488 229 6 only only ADV hjic-488 229 7 slightly slightly ADV hjic-488 229 8 different different ADJ hjic-488 229 9 from from ADP hjic-488 229 10 the the DET hjic-488 229 11 case case NOUN hjic-488 229 12 when when SCONJ hjic-488 229 13 the the DET hjic-488 229 14 actual actual ADJ hjic-488 229 15 states state NOUN hjic-488 229 16 were be AUX hjic-488 229 17 used use VERB hjic-488 229 18 in in ADP hjic-488 229 19 the the DET hjic-488 229 20 feedback feedback NOUN hjic-488 229 21 control control NOUN hjic-488 229 22 in in ADP hjic-488 229 23 fig.5 fig.5 PROPN hjic-488 229 24 . . PUNCT hjic-488 230 1 77 77 NUM hjic-488 230 2 0 0 NUM hjic-488 230 3 1 1 NUM hjic-488 230 4 2 2 NUM hjic-488 230 5 3 3 NUM hjic-488 230 6 4 4 NUM hjic-488 230 7 5 5 NUM hjic-488 230 8 6 6 NUM hjic-488 230 9 7 7 NUM hjic-488 230 10 time time NOUN hjic-488 231 1 [ [ X hjic-488 231 2 s s X hjic-488 231 3 ] ] X hjic-488 231 4 −0.2 −0.2 PROPN hjic-488 231 5 0.0 0.0 NUM hjic-488 231 6 0.2 0.2 NUM hjic-488 231 7 0.4 0.4 NUM hjic-488 231 8 0.6 0.6 NUM hjic-488 231 9 0.8 0.8 NUM hjic-488 231 10 1.0 1.0 NUM hjic-488 231 11 1.2 1.2 NUM hjic-488 231 12 1.4 1.4 NUM hjic-488 231 13 θ θ NOUN hjic-488 231 14 − − NOUN hjic-488 231 15 θ̂ θ̂ PUNCT hjic-488 232 1 [ [ X hjic-488 232 2 r r X hjic-488 232 3 a a X hjic-488 232 4 d d X hjic-488 232 5 ] ] PUNCT hjic-488 232 6 0 0 NUM hjic-488 232 7 1 1 NUM hjic-488 232 8 2 2 NUM hjic-488 232 9 3 3 NUM hjic-488 232 10 4 4 NUM hjic-488 232 11 5 5 NUM hjic-488 232 12 6 6 NUM hjic-488 232 13 7 7 NUM hjic-488 232 14 time time NOUN hjic-488 233 1 [ [ X hjic-488 233 2 s s X hjic-488 233 3 ] ] X hjic-488 233 4 −5 −5 NOUN hjic-488 233 5 −4 −4 X hjic-488 233 6 −3 −3 X hjic-488 233 7 −2 −2 PROPN hjic-488 233 8 −1 −1 NOUN hjic-488 233 9 0 0 NUM hjic-488 233 10 1 1 NUM hjic-488 233 11 2 2 NUM hjic-488 233 12 3 3 NUM hjic-488 233 13 θ̇ θ̇ NOUN hjic-488 233 14 − − NOUN hjic-488 233 15 ˆ̇ ˆ̇ NOUN hjic-488 233 16 θ θ PROPN hjic-488 234 1 [ [ X hjic-488 234 2 r r X hjic-488 234 3 a a PROPN hjic-488 234 4 d d PROPN hjic-488 234 5 / / SYM hjic-488 234 6 s s PROPN hjic-488 234 7 ] ] X hjic-488 234 8 figure figure NOUN hjic-488 234 9 9 9 NUM hjic-488 234 10 : : PUNCT hjic-488 234 11 error error NOUN hjic-488 234 12 of of ADP hjic-488 234 13 the the DET hjic-488 234 14 angle angle NOUN hjic-488 234 15 and and CCONJ hjic-488 234 16 angular angular ADJ hjic-488 234 17 velocity velocity NOUN hjic-488 234 18 estimations estimation NOUN hjic-488 234 19 using use VERB hjic-488 234 20 ckf ckf NOUN hjic-488 234 21 conclusion conclusion NOUN hjic-488 234 22 it it PRON hjic-488 234 23 was be AUX hjic-488 234 24 shown show VERB hjic-488 234 25 that that SCONJ hjic-488 234 26 in in ADP hjic-488 234 27 most most ADJ hjic-488 234 28 mechanical mechanical ADJ hjic-488 234 29 systems system NOUN hjic-488 234 30 the the DET hjic-488 234 31 disturbing disturbing ADJ hjic-488 234 32 effect effect NOUN hjic-488 234 33 of of ADP hjic-488 234 34 friction friction NOUN hjic-488 234 35 can can AUX hjic-488 234 36 be be AUX hjic-488 234 37 reduced reduce VERB hjic-488 234 38 to to ADP hjic-488 234 39 the the DET hjic-488 234 40 actuating actuate VERB hjic-488 234 41 signals signal NOUN hjic-488 234 42 . . PUNCT hjic-488 235 1 based base VERB hjic-488 235 2 on on ADP hjic-488 235 3 this this DET hjic-488 235 4 statement statement NOUN hjic-488 235 5 , , PUNCT hjic-488 235 6 two two NUM hjic-488 235 7 estimation estimation NOUN hjic-488 235 8 methods method NOUN hjic-488 235 9 were be AUX hjic-488 235 10 provided provide VERB hjic-488 235 11 for for ADP hjic-488 235 12 the the DET hjic-488 235 13 computation computation NOUN hjic-488 235 14 of of ADP hjic-488 235 15 the the DET hjic-488 235 16 unmeasured unmeasured ADJ hjic-488 235 17 states state NOUN hjic-488 235 18 . . PUNCT hjic-488 236 1 one one NUM hjic-488 236 2 of of ADP hjic-488 236 3 these these DET hjic-488 236 4 techniques technique NOUN hjic-488 236 5 considers consider VERB hjic-488 236 6 the the DET hjic-488 236 7 inputs input NOUN hjic-488 236 8 completely completely ADV hjic-488 236 9 unknown unknown ADJ hjic-488 236 10 and and CCONJ hjic-488 236 11 uses use VERB hjic-488 236 12 uikf uikf NOUN hjic-488 236 13 for for ADP hjic-488 236 14 the the DET hjic-488 236 15 estimation estimation NOUN hjic-488 236 16 . . PUNCT hjic-488 237 1 the the DET hjic-488 237 2 other other ADJ hjic-488 237 3 algorithm algorithm NOUN hjic-488 237 4 treats treat VERB hjic-488 237 5 the the DET hjic-488 237 6 inputs input NOUN hjic-488 237 7 as as SCONJ hjic-488 237 8 distorted distort VERB hjic-488 237 9 by by ADP hjic-488 237 10 an an DET hjic-488 237 11 additive additive ADJ hjic-488 237 12 disturbance disturbance NOUN hjic-488 237 13 , , PUNCT hjic-488 237 14 and and CCONJ hjic-488 237 15 applies apply VERB hjic-488 237 16 ukf ukf NOUN hjic-488 237 17 with with ADP hjic-488 237 18 a a DET hjic-488 237 19 load load NOUN hjic-488 237 20 predictor predictor NOUN hjic-488 237 21 extension extension NOUN hjic-488 237 22 . . PUNCT hjic-488 238 1 simulation simulation NOUN hjic-488 238 2 results result VERB hjic-488 238 3 in in ADP hjic-488 238 4 a a DET hjic-488 238 5 closed closed ADJ hjic-488 238 6 - - PUNCT hjic-488 238 7 loop loop NOUN hjic-488 238 8 controlled control VERB hjic-488 238 9 scenario scenario NOUN hjic-488 238 10 were be AUX hjic-488 238 11 provided provide VERB hjic-488 238 12 to to PART hjic-488 238 13 prove prove VERB hjic-488 238 14 the the DET hjic-488 238 15 applicability applicability NOUN hjic-488 238 16 of of ADP hjic-488 238 17 the the DET hjic-488 238 18 concepts concept NOUN hjic-488 238 19 . . PUNCT hjic-488 239 1 it it PRON hjic-488 239 2 was be AUX hjic-488 239 3 also also ADV hjic-488 239 4 pointed point VERB hjic-488 239 5 out out ADP hjic-488 239 6 , , PUNCT hjic-488 239 7 that that SCONJ hjic-488 239 8 the the DET hjic-488 239 9 precision precision NOUN hjic-488 239 10 of of ADP hjic-488 239 11 the the DET hjic-488 239 12 estimators estimator NOUN hjic-488 239 13 could could AUX hjic-488 239 14 be be AUX hjic-488 239 15 improved improve VERB hjic-488 239 16 using use VERB hjic-488 239 17 laser laser NOUN hjic-488 239 18 slot slot NOUN hjic-488 239 19 sensors sensor NOUN hjic-488 239 20 . . PUNCT hjic-488 240 1 this this PRON hjic-488 240 2 will will AUX hjic-488 240 3 be be AUX hjic-488 240 4 the the DET hjic-488 240 5 subject subject NOUN hjic-488 240 6 of of ADP hjic-488 240 7 a a DET hjic-488 240 8 forthcoming forthcoming ADJ hjic-488 240 9 paper paper NOUN hjic-488 240 10 . . PUNCT hjic-488 241 1 references reference NOUN hjic-488 241 2 [ [ X hjic-488 241 3 1 1 NUM hjic-488 241 4 ] ] PUNCT hjic-488 241 5 hyla hyla ADJ hjic-488 241 6 p. p. NOUN hjic-488 241 7 : : PUNCT hjic-488 242 1 the the DET hjic-488 242 2 crane crane NOUN hjic-488 242 3 control control NOUN hjic-488 242 4 systems system NOUN hjic-488 242 5 : : PUNCT hjic-488 242 6 a a DET hjic-488 242 7 survey survey NOUN hjic-488 242 8 , , PUNCT hjic-488 242 9 proc proc NOUN hjic-488 242 10 . . PUNCT hjic-488 242 11 17th 17th ADJ hjic-488 242 12 int int PROPN hjic-488 242 13 . . PUNCT hjic-488 243 1 conf conf NOUN hjic-488 243 2 . . PUNCT hjic-488 244 1 methods method NOUN hjic-488 244 2 and and CCONJ hjic-488 244 3 models model NOUN hjic-488 244 4 in in ADP hjic-488 244 5 automation automation NOUN hjic-488 244 6 and and CCONJ hjic-488 244 7 robotics robotic NOUN hjic-488 244 8 ( ( PUNCT hjic-488 244 9 mmar mmar NOUN hjic-488 244 10 ) ) PUNCT hjic-488 244 11 , , PUNCT hjic-488 244 12 2012 2012 NUM hjic-488 244 13 , , PUNCT hjic-488 244 14 505–509 505–509 NUM hjic-488 244 15 [ [ X hjic-488 244 16 2 2 NUM hjic-488 244 17 ] ] PUNCT hjic-488 244 18 schindele schindele PROPN hjic-488 244 19 d. d. PROPN hjic-488 244 20 , , PUNCT hjic-488 244 21 menn menn PROPN hjic-488 244 22 i. i. PROPN hjic-488 244 23 , , PUNCT hjic-488 244 24 aschemann aschemann PROPN hjic-488 244 25 h. h. PROPN hjic-488 244 26 : : PUNCT hjic-488 244 27 nonlinear nonlinear ADJ hjic-488 244 28 optimal optimal ADJ hjic-488 244 29 control control NOUN hjic-488 244 30 of of ADP hjic-488 244 31 an an DET hjic-488 244 32 overhead overhead ADJ hjic-488 244 33 travelling travel VERB hjic-488 244 34 crane crane NOUN hjic-488 244 35 , , PUNCT hjic-488 244 36 proc proc NOUN hjic-488 244 37 . . PUNCT hjic-488 245 1 18th 18th ADJ hjic-488 245 2 ieee ieee PROPN hjic-488 245 3 int int NOUN hjic-488 245 4 . . PUNCT hjic-488 246 1 conf conf PROPN hjic-488 246 2 . . PUNCT hjic-488 247 1 control control NOUN hjic-488 247 2 applications application NOUN hjic-488 247 3 , , PUNCT hjic-488 247 4 2009 2009 NUM hjic-488 247 5 , , PUNCT hjic-488 247 6 1045–1050 1045–1050 NUM hjic-488 248 1 [ [ X hjic-488 248 2 3 3 X hjic-488 248 3 ] ] PUNCT hjic-488 248 4 boustany boustany PROPN hjic-488 248 5 f. f. PROPN hjic-488 248 6 , , PUNCT hjic-488 248 7 d’andrea d’andrea PROPN hjic-488 248 8 novel novel PROPN hjic-488 248 9 b. b. PROPN hjic-488 248 10 : : PUNCT hjic-488 248 11 adaptive adaptive ADJ hjic-488 248 12 control control NOUN hjic-488 248 13 of of ADP hjic-488 248 14 an an DET hjic-488 248 15 overhead overhead ADJ hjic-488 248 16 crane crane NOUN hjic-488 248 17 using use VERB hjic-488 248 18 dynamic dynamic ADJ hjic-488 248 19 feedback feedback NOUN hjic-488 248 20 linearization linearization NOUN hjic-488 248 21 and and CCONJ hjic-488 248 22 estimation estimation NOUN hjic-488 248 23 design design NOUN hjic-488 248 24 , , PUNCT hjic-488 248 25 proc proc NOUN hjic-488 248 26 . . PUNCT hjic-488 249 1 ieee ieee PROPN hjic-488 249 2 int int PROPN hjic-488 249 3 . . PUNCT hjic-488 250 1 con con PROPN hjic-488 250 2 . . PUNCT hjic-488 250 3 robotics robotic NOUN hjic-488 250 4 and and CCONJ hjic-488 250 5 automation automation NOUN hjic-488 250 6 , , PUNCT hjic-488 250 7 1992 1992 NUM hjic-488 250 8 , , PUNCT hjic-488 250 9 1963–1968 1963–1968 NUM hjic-488 250 10 0 0 NUM hjic-488 250 11 1 1 NUM hjic-488 250 12 2 2 NUM hjic-488 250 13 3 3 NUM hjic-488 250 14 4 4 NUM hjic-488 250 15 5 5 NUM hjic-488 250 16 6 6 NUM hjic-488 250 17 7 7 NUM hjic-488 250 18 time time NOUN hjic-488 251 1 [ [ X hjic-488 251 2 s s X hjic-488 251 3 ] ] X hjic-488 251 4 −0.1 −0.1 PROPN hjic-488 251 5 0.0 0.0 NUM hjic-488 251 6 0.1 0.1 NUM hjic-488 251 7 0.2 0.2 NUM hjic-488 251 8 0.3 0.3 NUM hjic-488 251 9 0.4 0.4 NUM hjic-488 251 10 0.5 0.5 NUM hjic-488 251 11 m m PROPN hjic-488 251 12 ea ea PROPN hjic-488 251 13 su su PROPN hjic-488 251 14 re re PROPN hjic-488 251 15 d d PROPN hjic-488 251 16 st st PROPN hjic-488 251 17 a a DET hjic-488 251 18 te te PROPN hjic-488 251 19 s s X hjic-488 252 1 [ [ X hjic-488 252 2 m m X hjic-488 252 3 , , PUNCT hjic-488 252 4 m m VERB hjic-488 252 5 / / SYM hjic-488 252 6 s s PROPN hjic-488 252 7 ] ] X hjic-488 252 8 ` ` PUNCT hjic-488 252 9 r r NOUN hjic-488 252 10 ˙̀ ˙̀ VERB hjic-488 252 11 ṙ ṙ PROPN hjic-488 252 12 0 0 NUM hjic-488 252 13 1 1 NUM hjic-488 252 14 2 2 NUM hjic-488 252 15 3 3 NUM hjic-488 252 16 4 4 NUM hjic-488 252 17 5 5 NUM hjic-488 252 18 6 6 NUM hjic-488 252 19 7 7 NUM hjic-488 252 20 time time NOUN hjic-488 253 1 [ [ X hjic-488 253 2 s s X hjic-488 253 3 ] ] X hjic-488 253 4 −0.4 −0.4 NUM hjic-488 253 5 −0.3 −0.3 PROPN hjic-488 254 1 −0.2 −0.2 PROPN hjic-488 255 1 −0.1 −0.1 PROPN hjic-488 255 2 0.0 0.0 NUM hjic-488 255 3 0.1 0.1 NUM hjic-488 255 4 0.2 0.2 NUM hjic-488 255 5 u u NOUN hjic-488 255 6 n n PRON hjic-488 255 7 m m NOUN hjic-488 255 8 ea ea NOUN hjic-488 255 9 su su PROPN hjic-488 255 10 re re PROPN hjic-488 255 11 d d PROPN hjic-488 255 12 st st PROPN hjic-488 255 13 a a DET hjic-488 255 14 te te PROPN hjic-488 255 15 s s X hjic-488 256 1 [ [ X hjic-488 256 2 r r X hjic-488 256 3 a a PROPN hjic-488 256 4 d d NOUN hjic-488 256 5 , , PUNCT hjic-488 256 6 ra ra PROPN hjic-488 256 7 d d PROPN hjic-488 256 8 / / SYM hjic-488 256 9 s s PROPN hjic-488 256 10 ] ] X hjic-488 256 11 θ θ PROPN hjic-488 256 12 θ̇ θ̇ DET hjic-488 256 13 figure figure NOUN hjic-488 256 14 10 10 NUM hjic-488 256 15 : : PUNCT hjic-488 256 16 state state NOUN hjic-488 256 17 evolution evolution NOUN hjic-488 256 18 of of ADP hjic-488 256 19 the the DET hjic-488 256 20 controlled control VERB hjic-488 256 21 crane crane NOUN hjic-488 256 22 using use VERB hjic-488 256 23 the the DET hjic-488 256 24 ukf ukf NOUN hjic-488 256 25 ’s ’s PART hjic-488 256 26 estimated estimate VERB hjic-488 256 27 states state NOUN hjic-488 256 28 as as ADP hjic-488 256 29 feedback feedback NOUN hjic-488 256 30 [ [ X hjic-488 256 31 4 4 NUM hjic-488 256 32 ] ] X hjic-488 256 33 neupert neupert PROPN hjic-488 256 34 j. j. PROPN hjic-488 256 35 , , PUNCT hjic-488 256 36 hildebrandt hildebrandt PROPN hjic-488 256 37 a. a. PROPN hjic-488 256 38 , , PUNCT hjic-488 256 39 sawodny sawodny VERB hjic-488 256 40 o. o. PROPN hjic-488 256 41 , , PUNCT hjic-488 256 42 schneider schneider PROPN hjic-488 256 43 k. k. PROPN hjic-488 256 44 : : PUNCT hjic-488 256 45 trajectory trajectory NOUN hjic-488 256 46 tracking tracking NOUN hjic-488 256 47 for for ADP hjic-488 256 48 boom boom NOUN hjic-488 256 49 cranes crane NOUN hjic-488 256 50 using use VERB hjic-488 256 51 a a DET hjic-488 256 52 flatness flatness NOUN hjic-488 256 53 based base VERB hjic-488 256 54 approach approach NOUN hjic-488 256 55 , , PUNCT hjic-488 256 56 proc proc NOUN hjic-488 256 57 . . PUNCT hjic-488 257 1 int int NOUN hjic-488 257 2 . . PUNCT hjic-488 258 1 joint joint ADJ hjic-488 258 2 conf conf NOUN hjic-488 258 3 . . PUNCT hjic-488 259 1 sice sice ADJ hjic-488 259 2 - - PUNCT hjic-488 259 3 icase icase NOUN hjic-488 259 4 , , PUNCT hjic-488 259 5 2006 2006 NUM hjic-488 259 6 , , PUNCT hjic-488 259 7 1812–1816 1812–1816 NUM hjic-488 259 8 [ [ X hjic-488 259 9 5 5 NUM hjic-488 259 10 ] ] PUNCT hjic-488 259 11 rózsa rózsa PROPN hjic-488 259 12 t. t. PROPN hjic-488 259 13 , , PUNCT hjic-488 259 14 kiss kiss PROPN hjic-488 259 15 b. b. PROPN hjic-488 259 16 : : PUNCT hjic-488 259 17 tracking track VERB hjic-488 259 18 control control NOUN hjic-488 259 19 for for ADP hjic-488 259 20 towdimensional towdimensional ADJ hjic-488 259 21 overhead overhead ADJ hjic-488 259 22 crane crane NOUN hjic-488 259 23 , , PUNCT hjic-488 259 24 proc proc NOUN hjic-488 259 25 . . PUNCT hjic-488 260 1 8th 8th ADJ hjic-488 260 2 int int NOUN hjic-488 260 3 . . PUNCT hjic-488 260 4 conf conf NOUN hjic-488 260 5 . . PUNCT hjic-488 261 1 informatics informatic NOUN hjic-488 261 2 in in ADP hjic-488 261 3 control control NOUN hjic-488 261 4 , , PUNCT hjic-488 261 5 automation automation NOUN hjic-488 261 6 , , PUNCT hjic-488 261 7 and and CCONJ hjic-488 261 8 robotics robotic NOUN hjic-488 261 9 , , PUNCT hjic-488 261 10 icinco icinco NOUN hjic-488 261 11 , , PUNCT hjic-488 261 12 2011 2011 NUM hjic-488 261 13 , , PUNCT hjic-488 261 14 1 1 NUM hjic-488 261 15 , , PUNCT hjic-488 261 16 427–432 427–432 NUM hjic-488 261 17 [ [ X hjic-488 261 18 6 6 NUM hjic-488 261 19 ] ] PUNCT hjic-488 261 20 kiss kiss PROPN hjic-488 261 21 b. b. PROPN hjic-488 261 22 , , PUNCT hjic-488 261 23 levine levine PROPN hjic-488 261 24 j. j. PROPN hjic-488 261 25 , , PUNCT hjic-488 261 26 mullhaupt mullhaupt PROPN hjic-488 261 27 p. p. NOUN hjic-488 261 28 : : PUNCT hjic-488 261 29 a a DET hjic-488 261 30 simple simple ADJ hjic-488 261 31 output output NOUN hjic-488 261 32 feedback feedback NOUN hjic-488 261 33 pd pd PROPN hjic-488 261 34 controller controller NOUN hjic-488 261 35 for for ADP hjic-488 261 36 nonlinear nonlinear ADJ hjic-488 261 37 cranes crane NOUN hjic-488 261 38 , , PUNCT hjic-488 261 39 proc proc NOUN hjic-488 261 40 . . PUNCT hjic-488 261 41 39th 39th ADJ hjic-488 261 42 ieee ieee NOUN hjic-488 261 43 conference conference NOUN hjic-488 261 44 on on ADP hjic-488 261 45 decision decision NOUN hjic-488 261 46 and and CCONJ hjic-488 261 47 control control NOUN hjic-488 261 48 , , PUNCT hjic-488 261 49 2000 2000 NUM hjic-488 261 50 , , PUNCT hjic-488 261 51 5 5 NUM hjic-488 261 52 , , PUNCT hjic-488 261 53 5097–5101 5097–5101 NUM hjic-488 261 54 [ [ X hjic-488 261 55 7 7 NUM hjic-488 261 56 ] ] X hjic-488 261 57 kiss kiss PROPN hjic-488 261 58 b. b. PROPN hjic-488 261 59 , , PUNCT hjic-488 261 60 lévine lévine PROPN hjic-488 261 61 j. j. PROPN hjic-488 261 62 , , PUNCT hjic-488 261 63 müllhaupt müllhaupt PROPN hjic-488 261 64 p. p. NOUN hjic-488 261 65 : : PUNCT hjic-488 262 1 modelling modelling NOUN hjic-488 262 2 , , PUNCT hjic-488 262 3 flatness flatness NOUN hjic-488 262 4 and and CCONJ hjic-488 262 5 simulation simulation NOUN hjic-488 262 6 of of ADP hjic-488 262 7 a a DET hjic-488 262 8 class class NOUN hjic-488 262 9 of of ADP hjic-488 262 10 cranes crane NOUN hjic-488 262 11 , , PUNCT hjic-488 262 12 electrical electrical ADJ hjic-488 262 13 engineering engineering NOUN hjic-488 262 14 , , PUNCT hjic-488 262 15 1999 1999 NUM hjic-488 262 16 , , PUNCT hjic-488 262 17 43 43 NUM hjic-488 262 18 , , PUNCT hjic-488 262 19 215–225 215–225 NUM hjic-488 262 20 [ [ X hjic-488 262 21 8 8 NUM hjic-488 262 22 ] ] X hjic-488 262 23 lantos lantos PROPN hjic-488 262 24 b. b. PROPN hjic-488 262 25 : : PUNCT hjic-488 262 26 theory theory NOUN hjic-488 262 27 and and CCONJ hjic-488 262 28 design design NOUN hjic-488 262 29 of of ADP hjic-488 262 30 control control PROPN hjic-488 262 31 systems systems PROPN hjic-488 262 32 i. i. PROPN hjic-488 262 33 , , PUNCT hjic-488 262 34 akadémia akadémia ADV hjic-488 262 35 kiadó kiadó NOUN hjic-488 262 36 , , PUNCT hjic-488 262 37 2001 2001 NUM hjic-488 262 38 ( ( PUNCT hjic-488 262 39 in in ADP hjic-488 262 40 hungarian hungarian NOUN hjic-488 262 41 ) ) PUNCT hjic-488 263 1 [ [ X hjic-488 263 2 9 9 NUM hjic-488 263 3 ] ] PUNCT hjic-488 263 4 darouach darouach NOUN hjic-488 263 5 m. m. NOUN hjic-488 263 6 , , PUNCT hjic-488 263 7 zasadzinski zasadzinski PROPN hjic-488 263 8 m. m. NOUN hjic-488 263 9 , , PUNCT hjic-488 263 10 onana onana PROPN hjic-488 263 11 a.b a.b PROPN hjic-488 263 12 . . PROPN hjic-488 263 13 , , PUNCT hjic-488 263 14 nowakowski nowakowski PROPN hjic-488 263 15 s. s. PROPN hjic-488 263 16 : : PUNCT hjic-488 263 17 kalman kalman PROPN hjic-488 263 18 filtering filter VERB hjic-488 263 19 with with ADP hjic-488 263 20 unknown unknown ADJ hjic-488 263 21 inputs input NOUN hjic-488 263 22 via via ADP hjic-488 263 23 optimal optimal ADJ hjic-488 263 24 state state NOUN hjic-488 263 25 estimation estimation NOUN hjic-488 263 26 of of ADP hjic-488 263 27 singular singular PROPN hjic-488 263 28 systems system NOUN hjic-488 263 29 , , PUNCT hjic-488 263 30 int int NOUN hjic-488 263 31 . . PUNCT hjic-488 264 1 j. j. PROPN hjic-488 264 2 sys sys PROPN hjic-488 264 3 . . PUNCT hjic-488 265 1 sci sci PROPN hjic-488 265 2 . . PROPN hjic-488 265 3 , , PUNCT hjic-488 265 4 1995 1995 NUM hjic-488 265 5 , , PUNCT hjic-488 265 6 26(10 26(10 NUM hjic-488 265 7 ) ) PUNCT hjic-488 265 8 , , PUNCT hjic-488 265 9 2015–2028 2015–2028 NUM hjic-488 265 10 [ [ X hjic-488 265 11 10 10 NUM hjic-488 265 12 ] ] X hjic-488 265 13 haykin haykin PROPN hjic-488 265 14 s.s s.s PROPN hjic-488 265 15 . . PROPN hjic-488 265 16 : : PUNCT hjic-488 266 1 kalman kalman PROPN hjic-488 266 2 filtering filtering NOUN hjic-488 266 3 and and CCONJ hjic-488 266 4 neural neural ADJ hjic-488 266 5 networks network NOUN hjic-488 266 6 , , PUNCT hjic-488 266 7 john john PROPN hjic-488 266 8 wiley wiley PROPN hjic-488 266 9 & & CCONJ hjic-488 266 10 sons sons PROPN hjic-488 266 11 , , PUNCT hjic-488 266 12 inc inc PROPN hjic-488 266 13 . . PROPN hjic-488 266 14 , , PUNCT hjic-488 266 15 2001 2001 NUM hjic-488 266 16 [ [ X hjic-488 266 17 11 11 NUM hjic-488 266 18 ] ] X hjic-488 266 19 armstrong armstrong PROPN hjic-488 266 20 - - PUNCT hjic-488 266 21 hélouvry hélouvry PROPN hjic-488 266 22 b. b. PROPN hjic-488 266 23 , , PUNCT hjic-488 266 24 dupont dupont PROPN hjic-488 266 25 p. p. PROPN hjic-488 266 26 , , PUNCT hjic-488 266 27 de de PROPN hjic-488 266 28 wit wit ADJ hjic-488 266 29 c.c c.c PROPN hjic-488 266 30 . . PROPN hjic-488 266 31 : : PUNCT hjic-488 266 32 a a DET hjic-488 266 33 survey survey NOUN hjic-488 266 34 of of ADP hjic-488 266 35 models model NOUN hjic-488 266 36 , , PUNCT hjic-488 266 37 analysis analysis NOUN hjic-488 266 38 tools tool NOUN hjic-488 266 39 and and CCONJ hjic-488 266 40 compensation compensation NOUN hjic-488 266 41 methods method NOUN hjic-488 266 42 for for ADP hjic-488 266 43 the the DET hjic-488 266 44 control control NOUN hjic-488 266 45 of of ADP hjic-488 266 46 machines machine NOUN hjic-488 266 47 with with ADP hjic-488 266 48 friction friction NOUN hjic-488 266 49 , , PUNCT hjic-488 266 50 automatica automatica PROPN hjic-488 266 51 , , PUNCT hjic-488 266 52 1994 1994 NUM hjic-488 266 53 , , PUNCT hjic-488 266 54 30 30 NUM hjic-488 266 55 , , PUNCT hjic-488 266 56 1083–1138 1083–1138 NUM hjic-488 266 57 [ [ X hjic-488 266 58 12 12 NUM hjic-488 266 59 ] ] X hjic-488 266 60 kalman kalman PROPN hjic-488 266 61 r.e r.e PROPN hjic-488 266 62 . . PROPN hjic-488 266 63 : : PUNCT hjic-488 266 64 a a DET hjic-488 266 65 new new ADJ hjic-488 266 66 approach approach NOUN hjic-488 266 67 to to ADP hjic-488 266 68 linear linear ADJ hjic-488 266 69 filtering filtering NOUN hjic-488 266 70 and and CCONJ hjic-488 266 71 prediction prediction NOUN hjic-488 266 72 problems problem NOUN hjic-488 266 73 , , PUNCT hjic-488 266 74 journal journal NOUN hjic-488 266 75 of of ADP hjic-488 266 76 basic basic ADJ hjic-488 266 77 engineering engineering NOUN hjic-488 266 78 , , PUNCT hjic-488 266 79 1960 1960 NUM hjic-488 266 80 , , PUNCT hjic-488 266 81 82 82 NUM hjic-488 266 82 , , PUNCT hjic-488 266 83 35–45 35–45 NUM