EXAMINATION IN. Hydraulic Servo Systems, TMHP51 / TEN1. Saturday 17 December 2012, at 2 pm - 6 pm

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1 Linköing Teknik Högkol EXMINTION Pge 6 IEI TMHP5/TEN Fluid nd Mecronic Sye 0--7 EXMINTION IN Hydrulic Sero Sye TMHP5 / TEN e: Surdy 7 eceber 0-6 Roo:?? llowed educionl id: Tble: Sndrd Meicl Tble or iilr Hndbook: Tey Forulrie: Forul Book or Hydrulic nd Pneuic LiTH/IEI Meknik Väreeori oc Sröninglär Pocke clculor Nuber o ueion in e exinion: 5 On e ron ge nd on ll ollowing ge e uden u wrie: I-nuber TMHP5/TEN YYMM ge nuber Reonible ecer: rl-erik Rydberg Tel.no. during ex: Will ii : 5:30 nd 7:00 o clock Coure diniror: Ri Enui el.nr ri.enui@liu.e Score: Mxil core on ec ueion i 0. To ge e rk 3 you will need 0 oin To ge e rk 4 you will need 30 oin To ge e rk 5 you will need 40 oin Soluion: You will ind e oluion o i exinion on e noice bord in e building enrnce 7 C-corridor o e rig. Reul: Reul will be nnounced??. OO LUC! 7 eceber 0 rl-erik Rydberg Proeor

2 LINÖPINS TENIS HÖSOL EXMINTION 6 IEI TMHP 5 Fluid nd Mecronic Sye Ciion in oriice Two oriice re conneced in erie own in e igure. Te wo oriice re re nd. Te inle reure o e ir oriice i nd e inl oule reure 5 br. For ec oriice e criicl reure dro or ciion cn be clculed : Δ 0 69 were in i e inle reure. Te oriice low c coeicien i C 067 nd e luid deniy i ρ 890 kg/ 3. in Clcule e reure c wic iniie ciion in oe o e oriice. Clcule e low wen ciion r. 4 b Flow orce on ero le in conn reure ye Te igure ow direc conrolled 4-or ero le ulied by e reure MP. Te le low i. Te ool dilceen x i conrolled by roorionl gne wic cree e orce F. Te le low orce F will c gin e gne orce. Mx gne orce or ool conrol i F x 60 N. Te low orce u lwy be lower n x gne orce o ke e le conrollble. Clcule e xiu le low x gie x low orce F x 08 F x wen co 0358 nd ρ 890 kg/ 3. 3 c Sero le eiciency in conn reure ye Te igure ow le conrolled ero ye were e uly uni i conn reure conrolled rible dilceen u. Te u reure eing i nd e u low i eul o lod low L in ull low rnge. 6 Noinl le low: C w x 70 L N x 0 ρ Clcule nd ow in digr e ero le eiciency η P ou /P in eru e reure in e rnge 4 < < 8 MP conn lod low L LN. 3

3 LINÖPINS TENIS HÖSOL EXMINTION 36 IEI TMHP 5 Fluid nd Mecronic Sye Pilo oered ero le -ge le Te igure ow -ge ero le wi n elecro-ydrulic ilo-ge ulied ro e in P-or cloed X-or in e igure. Exlin uliiely ow e le bndwid b rie ccording o e elecric conrol ignl liude nd uly reure. 3 b Sero le reure gin nd i inluence on oiion ero ine Te igure ow e reure gin L eru i or yeric criicl cenre ero le nd ceic block-digr o cloed loo oiion ero. ecribe wi euion ow e le reure gin nd e edy e ine re eced i e le i exoed o ey wre. c Hydrulic reuency nd ding in ero ye Te igure below ow ceiclly le conrolled ydrulic ero nd i block digr. Wi e cylinder in cenre oiion V V e ydrulic reuency i in 0 rd/ nd e ydrulic ding i in Ue e block-digr o derie n exreion o e ding. Clcule e ydrulic reuency nd e ding e ion oiion were e cylinder olue re V 09 V nd V 0 V ol olue V V V. 4

4 LINÖPINS TENIS HÖSOL EXMINTION 46 IEI TMHP 5 Fluid nd Mecronic Sye ngulr oiion nd elociy ero wi le conrolled oor Te igure own n ngulr ero ye e le nd oor ued oiion nd elociy ero reeciely. Te eedbck gin in e oiion ero i nd in e elociy ero. Te conroller re roorionl nd inegring reeciely. Te block digr ow e rner uncion ro le inu curren i c o oor ngle Ө including e non-lineriy ro reold nd urion. Preer: Δi TH 00 i x i x 00 i / /rd 06 V/rd 004 V/rd 78 rd/ in 00 low oor eed. Mx oor eed Clcule e xiu oor eed Ө x cn be reced in e wo ye. b Conroller gin gie e liude rgin 6 db Clcule e conroller gin oiion ero nd elociy ero gie e wo ye e e liude rgin 6 db wen in. ecribe wi euion ow e ydrulic ding in e elociy ero will rie ccording o e oor eed. 4 c Poiion nd eed error eru le Treold e reuency 0 rd/ Clcule e oiion nd eed error ΔӨ ΔӨ cued by le reold Δi TH e reuency 0 rd/ nd e conroller gin ccording o k b. I you no cn ole k b ue e conroller gin reer in your euion. Exlin wy e conrol error in e elociy ero i reuency deenden nd deine e edy e conrol error eoreicl error. 4

5 LINÖPINS TENIS HÖSOL EXMINTION 56 IEI TMHP 5 Fluid nd Mecronic Sye Pu conrolled ngulr elociy ero wi I-conroller Te igure ow e ye nd e block digr or n elecro-ydrulic elociy ero wi u conrolled oor nd n I-conroller I I / were I i in [/V] nd in [/V]. Te u conrol uni i cored o e oor/ lod dynic >. Te ic gin cor in e ydrulic ye e e lue: / 5 rd/ nd 00 V/rd. For e oor/lod dynic e lue re 65 rd/ nd 00 no ding eedbck. Connecion o I-conroller Sow in iliied block-digr ow e I-conroller ll be conneced o e deriie conroller gin c negie ccelerion eedbck wic incree e ydrulic ding. erie n euion or e ydrulic ding wi ccelerion eedbck. 4 b Tuning o I-conroller or e liude rgin 6 db dju e conroller deriie gin o e ydrulic ding rec e lue 040. dju e conroller inegror gin I o e oen loo gin u gie e liude rgin 6 db. 4 c Cloed loo ine erie n exreion o e cloed loo ine reuency rnge <. Δ / Δθ or e low S c T L <

6 LINÖPINS TENIS HÖSOL EXMINTION 66 IEI TMHP 5 Fluid nd Mecronic Sye Liner oiion ero wi le conrolled cylinder nd wo e Te igure below ow le conrolled ydrulic cylinder loded by e e M nd M. Te connecion beween e e include ring nd der ring conn L nd icou ricion coeicien B L. Te ion oiion x i ed bck o roorionl regulor wi e gin reg. Te ero le bndwid i ig. Te block digr ro le inu ignl i o ion elociy X i: were Te lod dynic i decribed by e uncion were <. Te lod rio i M /M nd e reuencie nd ding re: 80 rd/ 38 rd/ 05 nd 087. Lod dynic nd i inluence on ydrulic reuency nd ding Sow in bode-digr e liude o e lod dynic eru reuency or e gien reer. ue e ydrulic ine i lower n e ecnicl ine 05 L. erie ro e gien block-digr exreion or e reuling reuency nd ' ding. ' 6 b Low ecnicl ine L < ue e ecnicl ine i o low < in e ye boe. icu uliiely ow e ydrulic ye dynic will be inluenced by e low ecnicl ine. How will e ydrulic ye dynic be eced by ery low ecnicl ding 0. 4

7 LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 5 IEI TMHP 5 Fluid nd Mecronic Sye 0--7 SOLUTION SUESTIONS FOR EXMINTION TMHP5. Ciion in oriice Te criicl reure dro or ciion: Oriice: nd Δ C 067 ρ 890 kg/ 3 r ciion? C C : 44 c > c ρ c in ρ wic gie wi. Δc 0 69 in gie wic en ciion r ir er oriice. E. gie nd c / br gie: c br. Flow: /. b Flow orce on ero le in conn reure ye : MP F x 60 N F x 08 F x co 0358 nd ρ 890 kg/ 3. 4 Clcule x or F x 08 F x Flow orce nd le low: F C w x Δ co L 0 nd Δ F x 08 F x gie c Sero le eiciency C w x L F ρ co nd x x 6 F ρ x ρ co / 94 l/in L nd C w x 70 L N x 0. ρ Clcule η P ou /P in : η L L. L gie η L /. uing L LN Δ 70 MP η Δ.4 < < 8 MP 3

LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 5 IEI Fluid nd Mecronic Sye TMHP 5 0--7. Pilo oered ero le -ge le -ge ero le wi elecro-ydrulic ilo-ge ulied ro e P-or.

8 LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 5 IEI Fluid nd Mecronic Sye TMHP Pilo oered ero le -ge le -ge ero le wi elecro-ydrulic ilo-ge ulied ro e P-or. Bndwid eru conrol ignl liude: Flow urion in e ilo ge gie x elociy or e in ool conrol. Tereore e le bndwid b will be reduced or ig ignl liude. Bndwid eru uly reure: Since e ilo ge i ued ero or oiion conrol o e in ool i conrol loo gin i roorion o wic gie b b Sero le reure gin nd i inluence on oiion ero ine 3 Vle reure gin nd i inluence on edy e ine: Te Block-digr nd Forul Book gie S c ΔFL ΔX 0 i ce i were i i e reure gin. Hey le wre en reduced i nd ereby reduced ine. 3 c Hydrulic reuency nd ding in ero ye : in 0 rd/ nd in 05. V 09 V nd V 0 V V V V Exreion o.: Te - eedbck loo in e block-digr gie e unc. V VM V β cem e V βe cem were nd V VM V 4 V or V 09 V nd V 0 V V V ; V 09 V V 0 V V V V V V V wic gie: in 00 rd/ nd in in 4

9 LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 35 IEI Fluid nd Mecronic Sye TMHP ngulr oiion nd elociy ero wi le conrolled oor Preer: Δi TH 00 i x i x 00 i / /rd 06 V/rd 004 V/rd 78 rd/ in 00 low oor eed. Mx oor eed Mx oor eed Ө x : Block-digr gie θ θ x i i θ i x x 58 rd/. Te e x eed or e wo ye. i0 b Conroller gin gie e liude rgin 6 db Se u or e wo ye gie or 6 db 56 /. in Poiion ero: nd i0 i /V. Velociy ero: nd i0 i /V. Hydrulic ding in elociy ero: θ i x c θ 4 c Poiion nd eed error eru le Treold e reuency 0 rd/ Se le in e wo ye gie e reold: Δi TH 00 i x 000. Poiion error eru Treold: Velociy error eru Treold: Conrol error E in e elociy ero: Δi TH Δθ. Δi TH Δ θ. Δθ rd Δθ 034 rd/ Δ i Δi U c U E E. Freuency-deenden E en 0 E 0 edy e conrol error. 4

10 LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 45 IEI TMHP 5 Fluid nd Mecronic Sye Pu conrolled ngulr elociy ero / 5 rd/ 00 V/rd 65 rd/ nd 00 6 db. I-conroller I I / were I i in [/V] nd in [/V] Connecion o I-conroller Block-digr o e I-conroller connecion o c ccelerion eedbck:. Togeer wi gien block-digr wi e ye dynic becoe wic gie e ydrulic ding : 4 b Tuning o I-conroller or e liude rgin 6 db By reducion o e conroller -cion ino e ye dynic ju ec ding e oen loo gin bece u were I. Tuning o or 040: /V. Tuning o I or 6 db: I I Nuericl: I 0 /V. 4 c Cloed loo ine Sedy e ine: Te block-digr gie: L c C T S Δ Δ < θ

LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 55 IEI TMHP 5 Fluid nd Mecronic Sye 0--7 5. Liner oiion ero wi le conrolled cylinder loded by wo e were : M /M 80 rd/ 38 rd/ 05 nd 087.

11 LINÖPINS UNIVERSITET SOLUTIONS FOR EXMINTION 55 IEI TMHP 5 Fluid nd Mecronic Sye Liner oiion ero wi le conrolled cylinder loded by wo e were : M /M 80 rd/ 38 rd/ 05 nd 087. Lod dynic nd i inluence on ydrulic reuency nd ding Bode-digr or : Te block-digr gie e rner uncion X /i : / i X i were e ce e V M M V M M 4 β β ince i uc lower n nd.0 ccording o e bode-digr. 6 b Low ecnicl ine L < Low ecnicl ine giing < en > 0. By wriing e rner uncion in ndrd or : / i i cn be een e ydrulic reuency nd ding will be inluenced. > 0 will incree e reuency nd reduce e ding. Very low ecnicl ding 0 will gie ey ocillion in e ye. 4

Section P.1 Notes Page 1 Section P.1 Precalculus and Trigonometry Review

Section P.1 Notes Page 1 Section P.1 Precalculus and Trigonometry Review Secion P Noe Pge Secion P Preclculu nd Trigonomer Review ALGEBRA AND PRECALCULUS Eponen Lw: Emple: 8 Emple: Emple: Emple: b b Emple: 9 EXAMPLE: Simplif: nd wrie wi poiive eponen Fir I will flip e frcion